the network's overall sensitivity, enabling a larger detection volume and improved precision in measurement. As the number of detections grows, the uncertainty in key cosmological parameters like $H_0$ will decrease. Specifically, for neutron star-neutron star (NS-NS) mergers, the uncertainty in $H_0$ estimates is expected to improve by approximately $15\%/\sqrt{N}$, where N is the number of detections. This progress underscores the pivotal role of the LIGO-Virgo-KAGRA network in refining our understanding of the Universe.

* **Laser Interferometer Space Antenna (LISA):** LISA [597] will be the first space-based GW detector, consisting of three spacecraft in a triangular configuration, separated by millions of kilometers, and following a heliocentric orbit. Scheduled for launch in the mid-2030s, LISA will primarily focus on astrophysical phenomena, including high-redshift mergers, extreme mass ratio inspirals, galactic binaries, and planetary objects. However, its contributions to cosmology will be equally groundbreaking. One of LISA's key cosmological objectives is to dramatically expand the catalog of dark sirens. These GW events, devoid of electromagnetic counterparts, serve as alternative standard candles, independent of the traditional cosmological distance ladder. By leveraging statistical methods with galaxy catalogs or identifying electromagnetic counterparts where possible, LISA will test the distance-redshift relation on cosmological scales, providing new constraints on DE models. With sensitivity extending to redshifts as high as $z \sim 10$, LISA will open a window to the Universe's distant past, offering unprecedented opportunities to explore the nature of DE at scales inaccessible to current methods. Furthermore, LISA's observations will enable precise and independent measurements of $H_0$, contributing to resolving the persistent cosmological tensions.

* **Einstein Telescope (ET):** ET [4253-4255] is a proposed next-generation GW observatory designed to achieve unprecedented sensitivity through advancements in quantum noise suppression, cryogenics, and interferometry. With a triangular configuration and a planned underground location to minimize seismic noise, the ET represents a significant leap forward from current ground-based detectors. A pathfinder prototype [4256], established at Maastricht University in 2021, has already demonstrated promising results in key enabling technologies, paving the way for the full-scale project. Like LISA, the ET will test the distance-redshift relation on cosmological scales and provide independent measurements of $H_0$, free from the assumptions of the traditional distance ladder [654]. This will primarily be achieved through the detection of binary compact object coalesces, which serve as robust standard sirens. Beyond $H_0$, the ET will be uniquely equipped to detect SGWBs of cosmological origin, offering a direct window into the early Universe. These observations could shed light on fundamental processes such as inflation, the formation of primordial black holes, phase transitions in the early Universe, and potential topological defects. The ET's ability to probe these phenomena would significantly deepen our understanding of the Universe's origins and evolution, making it a cornerstone of future GW astronomy and cosmology.

* **Cosmic Explorer (CE):** The proposed CE observatory [594,595] will build on the design principles of LIGO, but with significantly enhanced capabilities. Its arms, each spanning 40 km, will dramatically improve sensitivity, particularly in the low-frequency range. This enhanced sensitivity will enable the detection of black hole-black hole mergers at unprecedented distances and increase the detection rate to as many as $10^5$ events per year. With its ability to observe GWs in the 5-4000 Hz frequency band, CE will produce an unparalleled map of the GW sky, reaching back to high redshifts of $z \sim 20$ [4257,4258]. By probing this deep into the Universe's

history, CE will offer complementary insights into binary mergers, tracing their origins to the first stars and providing critical information on the star formation rate and galaxy evolution over cosmic time. In addition to astrophysical discoveries, CE will play a pivotal role in cosmology. By observing a vast catalog of dark sirens, CE will enable precise inferences of $H_0$ and provide a valuable independent check on the expansion history of the Universe. This makes CE an essential component of next-generation GW astronomy and its intersection with cosmology.

* **TianQin:** TianQin [4259,4260] is a proposed Chinese space-based GW observatory designed to detect GWs in the millihertz frequency range. It will consist of three spacecraft in a geocentric orbit, forming an equilateral triangle with arm lengths of approximately $10^5$ km. TianQin's primary scientific objectives include the detection of signals from supermassive black hole mergers, extreme mass ratio inspirals (EMRIs), and SGWBs. One of TianQin's unique features is its orbit near the Earth, which facilitates precise laser interferometry while minimizing challenges associated with deep-space communication. Similar to LISA, TianQin will employ advanced laser metrology and drag-free control to achieve exceptional sensitivity to low-frequency GWs. In the context of cosmology, TianQin will contribute significantly to resolving cosmological tensions. By expanding the catalog of both bright and dark sirens, TianQin will enable independent measurements of $H_0$ and test the distance-redshift relation on cosmological scales. Additionally, its observations will probe the early Universe, offering insights into the SGWB and potential new physics beyond the standard model. TianQin is expected to launch in the 2030s, complementing other space-based observatories and advancing the era of precision GW cosmology.

* **Taiji:** Taiji [4261] is a proposed Chinese space-based GW observatory designed to detect GWs in the millihertz frequency band. Unlike TianQin, which operates in a geocentric orbit, Taiji will be positioned at the Sun-Earth Lagrange point $L_2$, providing a quieter observational environment and allowing for longer baselines. Its design includes three spacecraft forming an equilateral triangle with arm lengths of $3 \times 10^6$ km, optimized for detecting low-frequency GWs. Taiji's scientific goals include probing the evolution of the Universe at redshifts as high as $z \sim 20$ and detecting GWs from sources such as massive black hole binaries, intermediate-mass black hole mergers, and the SGWB. Its high sensitivity will also enable the study of rare cosmic phenomena inaccessible to other observatories, offering an unparalleled view of early-Universe processes. In cosmology, Taiji will contribute to addressing key tensions, including the $H_0$ discrepancy, by expanding the catalog of dark sirens and providing precise measurements of the distance-redshift relation. Additionally, Taiji will enhance our understanding of DE and inflation by exploring signals from primordial GWs, phase transitions, and primordial black holes. Scheduled for launch in the 2030s, Taiji complements the capabilities of both TianQin and LISA, focusing on high-redshift phenomena and deepening our understanding of the early Universe while advancing China's leadership in GW astronomy.

* **DECi-hertz Interferometer Gravitational Wave Observatory (DECIGO):** DECIGO [4262] is a proposed Japanese space-based GW observatory designed to fill the frequency gap between ground-based detectors like LIGO and Virgo and low-frequency observatories like LISA. With a target frequency range centered around decihertz (0.1-10 Hz), DECIGO will enable the study of intermediate-mass black hole binaries, early Universe GW backgrounds, and other phenomena inaccessible to existing detectors. The DECIGO mission will consist of three spacecraft forming a triangular configuration with arm lengths of 1,000 km, operating in a heliocentric orbit. The observatory will use highly sensitive laser interferometry and drag-free control technologies to
achieve unprecedented precision in GW detection. A prototype mission, B-DECIGO, is planned to demonstrate key technologies in Earth orbit before the full-scale DECIGO mission launches. In cosmology, DECIGO will provide unique insights by detecting GWs from primordial sources such as phase transitions, cosmic strings, and inflation. Its sensitivity to the SGWB will allow for constraints on the physics of the early Universe, offering a direct window into energy scales far beyond those probed by CMB. DECIGO will also expand the catalog of standard sirens, enabling precise measurements of $H_0$ and the distance-redshift relation, which are crucial for resolving cosmological tensions. DECIGO's ability to study GWs from $z \sim 1000$ to the present will bridge the gap between early-Universe physics and late-time structure formation, providing complementary data to missions like LISA, Taiji, and TianQin. Expected to launch in the mid-2030s, DECIGO represents a major advancement in GW astronomy, with profound implications for cosmology and fundamental physics.

* **Pulsar Timing Arrays (PTAs):** Pulsar Timing Arrays are an innovative approach to detecting low-frequency GWs in the nanohertz frequency band. Unlike ground- or space-based interferometers, PTAs utilize the precise timing of millisecond pulsars as natural clocks to measure distortions in spacetime caused by passing GWs. International collaborations, such as the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) [4263], the European Pulsar Timing Array (EPTA), the Parkes Pulsar Timing Array (PPTA) [4264], and the International Pulsar Timing Array (IPTA) [4265], form a global network to maximize sensitivity and coverage. PTAs are particularly sensitive to GWs produced by supermassive black hole binaries (SMBHBs), which emit at nanohertz frequencies during their inspiral phase. Additionally, PTAs can probe the SGWB arising from the superposition of signals from numerous SMBHBs or from cosmological sources, such as cosmic strings, phase transitions, or inflation. In cosmology, PTAs provide unique insights by constraining the evolution of structure and the formation of massive galaxies. These measurements complement other GW observatories by covering a distinct frequency range, extending the spectrum of observable GWs. PTAs can also indirectly contribute to addressing the $H_0$ tension by improving our understanding of galaxy mergers and structure growth. Recent breakthroughs, such as the NANOGrav 15-year data release, have hinted at the first detection of a SGWB. These results, if confirmed, would open a new window into the Universe's evolution and provide evidence for processes occurring at very high energy scales, far beyond the reach of current particle accelerators. PTAs represent an essential component of the global GW detection strategy, providing a unique and complementary perspective to ground- and space-based observatories. With the advent of next-generation radio telescopes like SKAO, the sensitivity of PTAs is expected to dramatically improve, enabling more precise measurements and extending the range of detectable sources.

### 5.1.5. 21 Cm cosmology

The 21 cm line, arising from the hyperfine transition of neutral hydrogen (HI), provides a powerful and versatile tool for probing the Universe's structure and evolution across a wide range of redshifts. This signal serves as a unique tracer of the IGM and large-scale structure, enabling the study of key epochs such as the cosmic dawn, the EoR, and the post-reionization era. Unlike traditional probes, 21 cm cosmology captures three-dimensional information, offering tomographic insights into the distribution of matter and its interaction with radiation fields over cosmic time. The potential of the 21 cm line extends beyond mapping large-scale structure. It offers a novel avenue to address key cosmological tensions, including constraints on $H_0$ and the amplitude of matter fluctuations $S_8$. Moreover, the sensitivity of 21 cm surveys

to high-redshift phenomena makes them an invaluable complement to other cosmological probes such as CMB, BAO, and WL.

In this part, we outline the current and future 21 cm experiments, their capabilities, and their expected contributions to cosmology. Special emphasis is placed on their role in addressing fundamental questions about the early Universe, the formation of cosmic structures, and the underlying physics driving cosmic tensions:

* **Low-Frequency Array (LOFAR):** LOFAR [2351] is a cutting-edge radio interferometer designed to observe the Universe at low radio frequencies, operating primarily in the range of 10 MHz to 240 MHz. With its core located in the Netherlands and stations distributed across Europe, LOFAR provides high-resolution imaging and wide-field observations. A key focus of LOFAR is probing the 21 cm hydrogen signal from the EoR, offering insights into the period when the first stars and galaxies ionized the IGM. By mapping the structure of neutral hydrogen during this era, LOFAR aims to uncover the processes governing cosmic reionization and the emergence of the first luminous sources. Additionally, LOFAR's sensitivity to low-frequency signals makes it a valuable tool for studying other phenomena, including cosmic magnetism, DM, and the large-scale structure of the Universe. The array's modular and scalable design allows it to complement ongoing and future surveys.

* **Murchison Widefield Array (MWA):** MWA [4266] is a cutting-edge low-frequency radio interferometer located in Western Australia, designed to observe the Universe at frequencies between 80 MHz and 300 MHz. With its compact configuration of 4,096 dipole antennas spread across 1.5 kilometers, the MWA excels at capturing wide-field, low-frequency observations. A primary objective of the MWA is to detect the 21 cm hydrogen signal from the EoR, enabling a detailed study of the processes that ionized the early Universe and the formation of the first stars and galaxies. Additionally, the MWA probes large-scale cosmic structures, providing insights into the distribution of matter and the role of DE in cosmic evolution. The array is a precursor instrument to the SKAO and serves as a testbed for developing advanced techniques in calibration, foreground removal, and signal extraction. Its location at the radio-quiet Murchison Radioastronomy Observatory ensures minimal interference, enhancing its sensitivity to faint cosmological signals. Beyond cosmology, the MWA is also used to study solar physics, ionospheric science, and transient phenomena, making it a versatile instrument for advancing astrophysical research.

* **Hydrogen Epoch of Reionization Array (HERA):** HERA [2352] is a dedicated radio interferometer designed specifically to study the 21 cm hydrogen signal from the EoR. Located in the radio-quiet Karoo region of South Africa, HERA consists of 350 closely packed parabolic dishes, each 14 m in diameter, optimized for high sensitivity to faint cosmological signals at redshifts corresponding to the EoR ($6 < z < 12$). HERA's primary goal is to provide a detailed characterization of the IGM during the EoR, tracing the formation and evolution of the first luminous sources — stars, galaxies, and black holes — and their impact on the ionization state of the Universe. By mapping fluctuations in the 21 cm emission, HERA will constrain the timing and progression of reionization, offering insights into the astrophysical processes driving it. The array's design prioritizes simplicity and precision calibration, which are critical for mitigating systematics and isolating the faint EoR signal from overwhelming foreground contamination. As a successor to PAPER, HERA incorporates lessons learned from earlier experiments, significantly improving sensitivity and resolution. HERA is expected to complement other 21 cm experiments like LOFAR, MWA, and SKAO by focusing specifically on the EoR. Its measurements will also provide valuable data for testing models of cosmic structure formation, the
properties of the first galaxies, and potential new physics beyond
the standard cosmological model.

* **The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH):** REACH [4267] is an innovative experiment designed to detect the globally averaged 21 cm signal from neutral hydrogen, targeting the cosmic dawn and the EoR. What sets REACH apart is its novel calibration techniques and an advanced antenna design aimed at mitigating the impact of instrumental systematics and foreground contamination, long-standing challenges in 21 cm cosmology. By achieving unprecedented precision in isolating the faint cosmological signal, REACH opens a new window into the thermal and ionization history of the early Universe. Beyond its methodological advancements, REACH has the potential to address broader cosmological tensions. Its ability to constrain the timing and physics of reionization provides indirect insights into the nature of DM and DE. Additionally, deviations in the 21 cm signal from standard theoretical predictions could indicate new physics, such as interactions between baryons and DM or non-standard early heating mechanisms. These contributions place REACH at the forefront of innovative probes for resolving foundational challenges in cosmology.

* **Canadian Hydrogen Intensity Mapping Experiment (CHIME):** Located at the Dominion Radio Astrophysical Observatory in Canada, CHIME [4239] operates in the 400-800 MHz band, corresponding to a redshift range of 0.8 to 2.5. Its primary goal is to map neutral hydrogen intensity across this range to measure the expansion history of the Universe. By producing the largest three-dimensional map of hydrogen intensity in this critical epoch, CHIME provides unprecedented insights into the large-scale structure of the Universe and probes cosmic evolution during the dark ages through the 21 cm transition line. In addition to tracing the evolution of structure, CHIME offers statistical constraints on BAO using the Hydrogen Intensity Mapping technique. These measurements enable synergistic analyses with other cosmological surveys, enhancing the precision of constraints on fundamental parameters like $H_0$ and the amplitude of matter fluctuations $S_8$. Since beginning operations in 2018, CHIME has already yielded significant data, with planned upgrades set to further improve the precision and resolution of intensity maps.

* **Giant Metrewave Radio Telescope (GMRT):** Located near Pune, India, the GMRT [4268] is an array of 30 fully steerable parabolic dishes, each 45 m in diameter, operating in the frequency range of 50 MHz to 1.5 GHz. It is one of the most sensitive radio telescopes for low-frequency observations and plays a significant role in 21 cm cosmology. GMRT has been used extensively to study the 21 cm hydrogen signal from the Cosmic Dawn and the EoR. Its ability to probe neutral hydrogen at different redshifts provides critical insights into the thermal and ionization history of the IGM and the formation of the first luminous sources. In addition to EoR studies, GMRT contributes to understanding large-scale structures, galaxy formation, and the properties of DE and DM. As an established facility, GMRT continues to produce high-impact results and serves as a vital complement to ongoing and upcoming experiments such as LOFAR, HERA, and SKAO.

* **Five-hundred-meter Aperture Spherical Telescope (FAST):** FAST [4269], located in Guizhou, China, is the world's largest single-dish radio telescope, with an aperture of 500 m. Operating in the frequency range of 70 MHz to 3 GHz, FAST is a highly versatile instrument capable of a broad range of astrophysical studies, including 21 cm observations. Its massive collecting area provides unparalleled sensitivity, making it an invaluable tool for studying neutral hydrogen in the Universe. FAST contributes to 21 cm cosmology by probing the large-scale distribution of hydrogen gas, investigating the EoR, and tracing the evolution of cosmic structures during the Cosmic Dawn. Its ability to perform

both single-dish and interferometric measurements allows it to
complement other instruments in the global effort to constrain
models of cosmic evolution. Beyond 21 cm studies, FAST is used
for pulsar searches, extragalactic surveys, and studies of ISM
dynamics. With its extraordinary sensitivity and high precision,
FAST is poised to make new contributions to our understanding
of the early Universe and fundamental physics.

* **Hydrogen Intensity and Real-time Analysis eXperiment (HIRAX):** Building on the technology of CHIME, HIRAX [1846] is located near the SKAO site in South Africa and is designed to achieve similar scientific objectives in the southern sky. Operating in the 400-800 MHz frequency band, HIRAX aims to map neutral hydrogen intensity over the redshift range of 0.8 to 2.5, providing critical insights into the evolution of the Universe during this epoch. The array consists of 1,000 closely packed 6 m radio dishes, which will create a high-resolution hydrogen intensity map of the southern sky using the 21 cm emission line. Initially conceived as a demonstration of SKAO technology, HIRAX has evolved into an ambitious project, poised to deliver a detailed three-dimensional map of large-scale structure in this redshift range. A primary science goal of HIRAX is to measure BAO signature in the matter distribution, enabling precise constraints on the expansion history of the Universe. HIRAX's southern sky coverage complements CHIME's northern sky observations, offering an opportunity for joint analyses to refine measurements of cosmological parameters, including $H_0$ and $S_8$.

* **Square Kilometre Array Observatory (SKAO):** The SKAO [4245] is expected to begin operations for Phase 1 in the late 2020s, with sites located in Australia (covering low-frequency observations) and South Africa (mid-frequency observations). Together, these will form the world's largest radio telescope system, with a total collecting area of approximately 1 km², enabling unprecedented sensitivity and resolution. Operating across a frequency range of 50 MHz to 14 GHz, the SKAO will span a physical radius of roughly 3,000 km, hosting hundreds of radio dishes and over 100,000 antennas. By producing the most comprehensive 21 cm hydrogen intensity maps to date, the SKAO will probe the large-scale structure of the Universe, reaching back to the first galaxies and stars. This ambitious project will provide new insights into the EoR, the emergence of the first luminous sources, and the role of DE in shaping cosmic evolution. Additionally, it will complement other observational probes, offering synergies with WL, BAO, and CMB experiments to refine our understanding of cosmological tensions.

5.1.6. *Type Ia supernovae and distance ladder*

SNIa play a pivotal role in modern cosmology as highly reliable
standard candles for measuring cosmic distances. By leveraging the uni-
form intrinsic luminosity of these SNIa, calibrated through the cosmic
distance ladder, precise determinations of $H_0$ are possible. The cosmic
distance ladder comprises several hierarchical steps: (1) geometric
distance measurements using Cepheid variables, TRGB stars, masers,
etc.; (2) calibration of SNIa luminosities based on these measure-
ments; and (3) application of SNIa to measure $H_0$ in the Hubble flow,
where cosmic expansion dominates. Recent advancements in distance
ladder measurements have refined the determination of $H_0$, notably
through Cepheid-calibrated SNIa in the SHOES project, which reports a
value significantly higher than early Universe estimates from the CMB.
This discrepancy, known as the Hubble tension, remains one of the
most pressing challenges in cosmology. Complementary approaches,
including TRGB, Mira variables, and SBF methods, offer alternative
calibrations and independent cross-checks, helping to ensure robustness
and reduce systematic biases. However, all these methods consistently
yield higher $H_0$ values than those derived from early Universe probes,
highlighting the tension.
Future surveys and advanced instrumentation promise to transform SNIa measurements and distance ladder studies. JWST's unprecedented resolution has already begun improving Cepheid observations in crowded fields, while upcoming missions aim to reduce systematic uncertainties further. New facilities will also increase the number and diversity of SNIa observations, extending measurements to higher redshifts and improving statistical power. Below, we highlight ongoing and planned SN and distance ladder experiments and their contributions to addressing cosmological tensions.

*   **Dark Energy Survey (DES):** DES [4251], conducted from 2013 to 2019, used the 4-meter Blanco Telescope at Cerro Tololo Inter-American Observatory (CTIO) to observe approximately 5000 deg² of the southern sky. DES contributed significantly to supernova cosmology by discovering and monitoring thousands of SNIa across a broad redshift range ($z \sim 0.01$ to 1.2). Its high-quality photometry enabled precise constraints on $H_0$ and DE properties. DES complements other distance ladder experiments by providing a statistically robust dataset of SNIa at intermediate redshifts, improving constraints on the cosmic expansion history and addressing potential systematics in supernova cosmology.

*   **The Gaia mission:** Gaia [143], operating since 2013, has revolutionized the cosmic distance ladder by providing precise parallaxes for millions of stars, including Cepheid variables and TRGB stars. These highly accurate measurements are critical for calibrating the absolute luminosities of SNIa and improving the determination of the Hubble constant. Gaia's unparalleled astrometric precision significantly reduces uncertainties in the local distance scale and mitigates systematic biases in SNIa calibrations. By anchoring the first rung of the distance ladder, Gaia plays a key role in addressing the Hubble tension and refining our understanding of cosmic expansion.

*   **Zwicky Transient Facility (ZTF):** The ZTF [4270], operating since 2018 at the Palomar Observatory, utilizes a 48-inch Schmidt Telescope with a wide field of view (47 deg²) for high-cadence transient surveys. ZTF has been instrumental in discovering and monitoring nearby SNIa, providing critical data for calibrating the distance ladder. By targeting local SNIa, ZTF supports precise measurements of $H_0$ and cross-validates calibrations derived from other standard candles, such as Cepheids and TRGB stars. Its extensive dataset complements space-based missions like Gaia and JWST by increasing the sample size of well-observed SNIa.

*   **Nearby Supernova Factory (SNfactory):** The SNfactory [4271], an international collaboration, focuses on obtaining detailed spectrophotometry of low-redshift SNIa. Using the SuperNova Integral Field Spectrograph (SNIFS) on the University of Hawaii's 2.2-meter telescope, SNfactory has been essential in characterizing the diversity of SNIa and improving standardization techniques. SNfactory's precise spectrophotometric data reduce systematic uncertainties in SNIa luminosities, refining the calibration of the distance ladder and improving constraints on $H_0$.

*   **Asteroid Terrestrial-impact Last Alert System (ATLAS):** Although primarily designed for asteroid detection, ATLAS [4272], operating on multiple telescopes in Hawaii, South Africa, and Chile, has made substantial contributions to supernova cosmology. Its wide field of view and high-cadence observations are well-suited for identifying and monitoring nearby SNIa. ATLAS's discoveries provide valuable data for calibrating the distance ladder, especially at low redshifts, complementing ground-based and space-based missions in improving the accuracy of $H_0$ measurements and addressing cosmological tensions.

*   **James Webb Space Telescope (JWST):** JWST [291], launched in 2021, provides unparalleled near-infrared imaging and spectroscopy, enabling precise observations of Cepheid variables and TRGB stars in crowded fields. These measurements significantly enhance the calibration of SNIa and improve the accuracy of $H_0$. JWST's ability to observe faint objects at high resolution allows it to extend the cosmic distance ladder to greater distances and reduce systematic uncertainties. By complementing ground- and space-based surveys, JWST plays a crucial role in addressing the Hubble tension and probing potential new physics beyond ΛCDM.

*   **Rubin Observatory's Legacy Survey of Space and Time (LSST):** The Rubin Observatory [4244], currently under construction in Chile, will conduct the LSST, a ten-year survey covering approximately 18,000 deg² of the southern sky. With its 8.4-meter aperture and a 9.6-square-degree field of view, Rubin's LSST will discover and monitor hundreds of thousands of SNIa across a broad redshift range ($z \sim 0.01$ to 1.2). Rubin's LSST will revolutionize supernova cosmology by significantly increasing the sample size and improving statistical precision in measuring $H_0$. Its high-cadence, multi-band photometry will mitigate systematics such as dust extinction and host-galaxy effects, and its synergy with spectroscopic follow-up surveys will ensure robust classifications and redshift measurements.

*   **Roman Space Telescope (formerly WFIRST):** The Roman Space Telescope [896], scheduled for launch in the late 2020s, will perform a High Latitude Survey to observe thousands of SNIa across a broad redshift range ($z \sim 0.1$ to 2.0). With its wide field of view and high-resolution imaging in the near-infrared, Roman will extend the cosmic distance ladder, improving the precision and accuracy of the Hubble constant. Roman's deep multi-band photometry will reduce systematics like dust extinction and enhance the calibrations of standard candles. By complementing ground-based surveys such as Rubin's LSST and incorporating follow-up spectroscopy, Roman will play a critical role in resolving the Hubble tension.

*   **Extremely Large Telescope (ELT):** The ELT [4273], currently under construction in Chile, will leverage its 39-meter aperture and advanced adaptive optics to achieve unprecedented precision in SNIa observations. By providing high-resolution imaging and spectroscopy, the ELT will play a vital role in calibrating the distance ladder through Cepheids, TRGB stars, and direct measurements of SNIa in the local Universe. The ELT's ability to observe SNIa at higher redshifts will complement space-based surveys like Rubin's LSST and Roman, reducing systematic uncertainties and improving the determination of the Hubble constant.

*   **Future Extremely Large Telescopes (GMT and TMT):** Beyond the ELT, upcoming ground-based observatories such as the Giant Magellan Telescope (GMT) [4274] and the Thirty Meter Telescope (TMT) [4275] will significantly enhance SNIa and distance ladder measurements. With their large apertures of 24.5 meters (GMT) and 30 meters (TMT), these telescopes will provide unparalleled resolution and sensitivity, enabling precise observations of Cepheids, TRGB stars, and SNIa in both the local and high-redshift Universe. These telescopes will extend the reach of the distance ladder by detecting fainter Cepheids and SNIa at greater distances, improving calibration precision and reducing systematic uncertainties. Their advanced instrumentation will complement space-based missions like JWST and Roman by providing high-resolution follow-up spectroscopy and imaging, further refining $H_0$ and contributing to resolving the Hubble tension.

### 5.1.7. Time delay cosmography

The strong lensing of QSOs and SN offers a unique opportunity to measure the expansion rate of the Universe across different redshifts. This approach leverages the variable nature of these objects, enabling the use of the time-delay method — an independent high-redshift cosmological probe that does not rely on the distance ladder. The technique involves observing multiple images of a strongly lensed source, such as a QSO or SN, produced by an intermediary lensing
galaxy. The mass profile of this galaxy, combined with the respective distances between the observer, lens, and source, determines the offsets of the lensed images and is crucial for obtaining precise estimates of cosmological parameters.

This method relies on the time delays between light rays traveling along different paths, caused by both geometric differences in the light geodesics and the distribution of matter within the lensing galaxy. By accurately measuring these delays, the time-delay method provides an estimate of the Hubble constant, independent of large-scale structure parameters.

Strong lensing is inherently challenging due to the specific alignment required between the observer, lens, and source. Moreover, the rarity of suitable QSOs or SN reduces the probability of detection. Despite these challenges, over 300 strongly lensed QSOs have been identified to date, typically in the redshift range ~ 1–3, with lensing galaxies found at redshifts ~ 0.2–0.8. The lensed images are usually separated by a few arcseconds, well within the resolution capabilities of modern ground-based telescopes. Time delays ranging from a few days to a year are sufficient for accurate measurements, making the time-delay method a powerful tool for cosmology.

Below, we highlight ongoing and planned experiments leveraging the time-delay method and their contributions to measuring $H_0$ and addressing cosmological tensions.

* **Very Large Telescope Interferometer (VLTI):** The VLTI [4276], operated by the European Southern Observatory (ESO), provides ultra-high angular resolution imaging through its interferometric array of telescopes. With its ability to resolve fine details in strongly lensed QSOs, VLTI plays a critical role in time-delay cosmography by enabling precise measurements of the lensing geometry and time delays. Its high spatial resolution is particularly useful for modeling lensing galaxies and reducing systematic uncertainties in the determination of $H_0$.

* **Atacama Large Millimeter/submillimeter Array (ALMA):** ALMA [4277], located in Chile, offers unparalleled sensitivity and resolution for observing lensed submillimeter galaxies and QSOs. By measuring time delays in radio and submillimeter wavelengths, ALMA provides a complementary approach to optical time-delay cosmography, reducing systematic biases and refining constraints on the Hubble constant.

* **Keck Observatory:** The Keck Observatory [4278], located on Maunakea, Hawaii, features two 10-meter telescopes equipped with advanced adaptive optics systems. These capabilities allow Keck to obtain high-resolution imaging and spectroscopy of strongly lensed QSOs and SN, essential for precise time-delay measurements. Keck's sensitivity and angular resolution enable detailed modeling of lensing galaxies and accurate determination of light path geometries, contributing to independent constraints on $H_0$. Its role as a follow-up instrument for time-delay cosmography complements surveys like Rubin's LSST and Euclid, providing critical data for refining cosmological models.

* **Subaru Telescope:** The Subaru Telescope [4242], a 8.2-meter optical-infrared telescope located on Maunakea, Hawaii, plays a key role in observing strong lensing systems for time-delay cosmography. Equipped with instruments such as the HSC, Subaru excels at wide-field imaging and detailed follow-up of lensed systems. Subaru's capabilities allow it to identify and resolve lensed QSO systems and SN, particularly in crowded fields, enabling precise time-delay measurements. Its contributions to modeling lensing mass distributions and improving light path geometries are vital for reducing systematic uncertainties in the determination of $H_0$. Subaru serves as a valuable complement to space-based missions like Roman and ground-based facilities like Keck.

* **Euclid:** The Euclid mission [4241], covering a 14,000 deg² area of the sky, is expected to observe approximately 170,000 strong lensing events during its lifetime. These events will provide valuable insights into the properties of DM halos in dwarf galaxies, the mass distribution within galaxies, and galaxy cluster structures in the redshift range 0 < z < 2. Strong lensing events are inherently rare and require robust detection methods. To address this challenge, Euclid employs CNNs, which are trained on extensive simulated datasets to extract image features and identify strong lensing properties. These advanced pipelines allow for precise identification of lensing phenomena, including sharp Einstein rings, which are expected to be detectable down to an angular resolution of 0.5 arcseconds. Additionally, Euclid is anticipated to detect up to ~ 2300 strongly lensed QSO sources, enabling precise measurements of time delays. The time-delay cosmography enabled by Euclid's high-resolution imaging will place stringent constraints on $H_0$, making it one of the most powerful tools for addressing cosmological tensions.

* **Rubin Observatory's Legacy Survey of Space and Time (LSST):** The Rubin Observatory's [4244] unparalleled depth and sky coverage will enable the discovery of up to ten million QSOs over its operational lifetime, spanning a redshift range of z ~ 0–7. This extensive dataset will have profound implications for QSO-related physics, including strong lensing and time-delay cosmography. Rubin's LSST is expected to detect approximately ~ 2600 time-delayed lensing systems, assuming optimistic projections. These systems will play a pivotal role in refining measurements of $H_0$ and probing the dynamical properties of DE at high redshifts. With its deep and wide survey capabilities, Rubin's LSST will significantly enhance the statistical precision of time-delay cosmography, providing critical insights into the expansion history of the Universe.

* **Roman Space Telescope (formerly WFIRST):** The Roman Space Telescope [896], set to launch in the late 2020s, will make significant contributions to time-delay cosmography through its deep, high-resolution near-infrared imaging and wide field of view. Roman is expected to detect thousands of strongly lensed QSOs and SN, enabling precise measurements of time delays across a broad redshift range. With its exceptional sensitivity, Roman will identify and characterize lensing systems with high precision, including detailed modeling of lensing galaxies. These observations will reduce uncertainties in the Hubble constant $H_0$ and provide crucial constraints on the properties of DE. Roman's synergy with other surveys, such as Rubin's LSST, will further enhance the statistical power and accuracy of time-delay cosmography.

* **Square Kilometre Array Observatory (SKAO):** The SKAO [4245], with its radio arrays in South Africa and Australia, will enable high-resolution observations of strongly lensed radio sources. By detecting and monitoring time-delayed radio-lensed systems, SKAO will provide independent measurements of $H_0$. Its sensitivity to faint radio signals and ability to resolve sub-arcsecond structures make it a powerful tool for time-delay cosmography.

* **Extremely Large Telescope (ELT):** The ELT [4273], currently under construction in Chile, will leverage its 39-meter aperture to achieve unparalleled angular resolution and sensitivity. This will allow for detailed imaging and spectroscopy of strongly lensed QSOs and supernovae, facilitating precise time-delay measurements. The ELT's advanced instrumentation will help model lensing galaxies with greater accuracy, reducing uncertainties in the determination of the Hubble constant.

* **Thirty Meter Telescope (TMT):** The TMT [4275], planned for construction in Hawaii or the Canary Islands, will provide high-resolution imaging and spectroscopic capabilities, enabling detailed observations of strongly lensed systems. By resolving lensed images with extreme precision, the TMT will contribute to time-lensing events during its lifetime. These events will provide valuable insights into the properties of DM halos in dwarf galaxies, the mass distribution within galaxies, and galaxy cluster structures in the redshift range 0 < z < 2. Strong lensing events are inherently rare and require robust detection methods. To address this challenge, Euclid employs CNNs, which are trained on extensive simulated datasets to extract image features and identify strong lensing properties. These advanced pipelines allow for precise identification of lensing phenomena, including sharp Einstein rings, which are expected to be detectable down to an angular resolution of 0.5 arcseconds. Additionally, Euclid is anticipated to detect up to ~ 2300 strongly lensed QSO sources, enabling precise measurements of time delays. The time-delay cosmography enabled by Euclid's high-resolution imaging will place stringent constraints on $H_0$, making it one of the most powerful tools for addressing cosmological tensions.
delay cosmography by improving measurements of $H_0$ and prob-
ing the dynamics of DE.

*   **Giant Magellan Telescope (GMT):** The GMT [4274], under construction in Chile, will utilize its segmented 24.5-meter primary mirror to achieve exceptional imaging and spectroscopic capabilities. Its high resolution and sensitivity will support time-delay cosmography by enabling precise modeling of lensed systems and accurate measurements of $H_0$, particularly at intermediate redshifts.

5.1.8. Fast radio bursts (FRBs)

FRBs are extremely bright, short-duration radio transients lasting only a few milliseconds, with the potential to serve as powerful tools for probing cosmology. Their extragalactic origin is supported by their large dispersion measures, which are observed to evolve with redshift. A significant number of FRBs have been localized to host galaxies, allowing their redshifts to be determined and their origins, such as possible magnetar emissions, to be studied.

Localized FRBs provide valuable insights into several cosmological phenomena, including the baryon fraction in the IGM, strong lensing events, the equivalence principle, the expansion history of the Universe, and the cosmic reionization history. The interaction of FRBs with the IGM makes them excellent probes of baryonic matter in these regions, as the interaction of radio signals with gas distributions offers a new perspective on the “missing baryon problem”. Regarding the Hubble constant $H_0$, FRBs alone face degeneracies that limit their ability to directly constrain $H_0$. However, combining FRB data with complementary datasets such as CMB, BBN, or GW measurements breaks these degeneracies and enables precise cosmological constraints.

Below, we highlight the list of ongoing and planned experiments leveraging FRBs to address cosmological tensions and improve our understanding of the Universe's evolution.

*   **Canadian Hydrogen Intensity Mapping Experiment (CHIME):** CHIME [4239], situated in British Columbia, Canada, is a pioneering radio telescope designed to monitor transient radio signals, including FRBs. Its fixed-cylinder design and wide field of view allow CHIME to observe the sky continuously, detecting thousands of FRBs annually across a range of redshifts. This high detection rate enables the identification of rare FRBs suitable for cosmological studies, such as those with high dispersion measures or unique signatures that indicate strong lensing events. CHIME's advanced time-domain sensitivity is optimized for detecting short-duration radio transients, making it a valuable tool for measuring the arrival times of FRBs with high precision. These capabilities allow CHIME to constrain propagation effects, such as delays caused by intervening structures, which can be cross-referenced with GW studies to extract cosmological information. Its unparalleled FRB detection volume provides a complementary dataset for investigating the evolution of the cosmic expansion when paired with optical and GW experiments.

*   **Australian Square Kilometer Array Pathfinder (ASKAP):** ASKAP [4279], located in Western Australia, is a cutting-edge radio telescope optimized for detecting and localizing FRBs. Its unique combination of wide field-of-view and interferometric imaging capabilities allows ASKAP to efficiently detect and pinpoint FRBs to sub-arcsecond accuracy. This precise localization is critical for identifying host galaxies and determining redshifts of FRB sources. ASKAP's advanced beamforming technology enables the detection of high-redshift FRBs, providing insights into the IGM and the evolution of the cosmic expansion. Its ability to associate FRBs with host galaxies allows for independent constraints on $H_0$ when combined with other cosmological probes.

*   **Upgrade of the Molonglo Observatory Synthesis Telescope (UTMOST):** UTMOST [4280], located in Australia, is a recon-

figured radio telescope optimized for detecting FRBs. Its high-
cadence observing strategy makes it ideal for the real-time dis-
covery and timing of FRBs, particularly at low redshifts. Although
less sensitive than newer facilities, UTMOST's rapid response
capability enables timely follow-up studies and statistical surveys
of FRBs. By characterizing nearby FRBs, UTMOST complements
high-sensitivity instruments such as ASKAP and FAST, contribut-
ing to our understanding of the local FRB population and its
cosmological implications.

*   **MeerKAT:** MeerKAT [4281], situated in South Africa, is a highly sensitive radio telescope designed for high-resolution imaging and precision timing, making it an invaluable tool for studying FRBs. Its wide frequency coverage and long baselines enable MeerKAT to detect faint and distant FRBs, particularly those at high redshifts, offering insights into the early Universe. MeerKAT excels in pinpointing FRB host galaxies and measuring dispersion measures with high precision. This allows for a detailed study of the large-scale structure of the Universe and the evolution of baryonic matter over cosmic time. MeerKAT also plays a complementary role to SKAO by serving as a pathfinder and refining techniques for future large-scale FRB surveys. Its contributions to the Hubble constant determination and reionization studies position MeerKAT as a crucial instrument for resolving cosmological tensions.

*   **Five-hundred-meter Aperture Spherical Telescope (FAST):** FAST [4269], located in Guizhou, China, is the world's largest single-dish radio telescope, offering unparalleled sensitivity for detecting faint and distant FRBs. Its ability to detect FRBs with extremely high signal-to-noise ratios enables precise measurements of dispersion measures and localization for follow-up studies. FAST contributes significantly to cosmology by detecting high-redshift FRBs and analyzing their interaction with the IGM. Its sensitivity allows it to probe the cosmic expansion and test reionization models, complementing large-scale surveys such as SKAO and CHIME. FAST's unique capabilities make it a critical instrument for advancing FRB-based cosmological studies.

*   **Deep Synoptic Array (DSA-110):** The DSA-110 [4282], located in California, is a dedicated radio array designed exclusively for detecting and localizing FRBs. With 110 antennas operating in the 1.28 GHz band, the array achieves sub-arcsecond localization accuracy, enabling precise identification of FRB host galaxies. DSA-110's focus on real-time detection and localization provides critical insights into the redshift distribution of FRBs and their cosmological applications. By linking FRBs to their host environments, DSA-110 contributes to breaking degeneracies in cosmological parameter estimation, particularly when combined with other datasets such as GW observations and optical surveys.

*   **Giant Metrewave Radio Telescope (GMRT):** The GMRT [4268], located in Pune, India, has been instrumental in studying FRBs at low radio frequencies. Its unique sensitivity and wide frequency coverage make it a valuable tool for characterizing the spectral properties of FRBs and their interaction with the IGM. GMRT has been used for follow-up observations of FRBs detected by other instruments, particularly at frequencies below 800 MHz. These observations complement higher-frequency detections by telescopes like CHIME and ASKAP, providing new insights into FRB emission mechanisms and their propagation through cosmic structures. While not a dedicated FRB facility, GMRT's versatility and precision continue to support advancements in FRB cosmology.

*   **Very Large Array Low-band Ionosphere and Transient Experiment (VLITE):** VLITE [4283], operating on the Very Large Array (VLA), focuses on low-frequency transient detection, including FRBs. Its ability to monitor the sky continuously allows it to
identify faint FRBs and investigate their spectral properties at lower frequencies.

* **Square Kilometre Array Observatory (SKAO):** The SKAO [4245], under construction in South Africa and Australia, is poised to become the largest and most sensitive radio telescope array in the world. Its exceptional capabilities will enable precise localization of FRBs at sub-arcsecond resolution and direct measurement of their redshifts, significantly advancing FRB cosmology. By detecting and studying FRBs across a broad redshift range, SKAO will provide insights into the evolution of the IGM, reionization history, and cosmic expansion. Its ability to map dispersion measures over cosmic time will complement other datasets, such as GW observations and optical surveys, to break degeneracies in cosmological parameters, including $H_0$. While its primary focus is on large-scale structure studies through 21 cm intensity mapping, SKAO's FRB-specific contributions, including redshift localization and host galaxy characterization, make it a new instrument for addressing cosmological tensions.

* **Next Generation Deep Synoptic Array (DSA-2000):** DSA-2000 [4284], a planned expansion of the DSA-110, will feature 2000 antennas, dramatically increasing sensitivity and detection rates for FRBs. This next-generation array will provide precise localization for tens of thousands of FRBs across a wide redshift range. With its enhanced capabilities, DSA-2000 will enable detailed studies of the cosmic expansion, baryon distribution, and reionization history.

* **Low-Frequency Array (LOFAR2.0):** LOFAR2.0 [1148], an upgraded version of the Low-Frequency Array, will provide enhanced sensitivity and temporal resolution for detecting FRBs at low frequencies. Its broad frequency coverage and improved capabilities will allow it to probe previously inaccessible redshift ranges for FRBs, making it a unique tool for studying the early Universe. LOFAR2.0's ability to detect low-frequency FRBs will contribute to understanding their emission mechanisms and their interaction with the IGM.

* **APERTURE Tile In Focus (Apertif):** Apertif [4285], an upgrade to the Westerbork Synthesis Radio Telescope (WSRT) in the Netherlands, provides wide-field imaging for detecting FRBs. Its combination of sensitivity and survey speed enables it to identify transient events, contributing to population studies of FRBs and complementing other instruments in the field.

* **Burst Transient Telescope (BURSTT):** BURSTT is a planned experiment designed to search for FRBs with enhanced detection rates and localization capabilities. Its wide field of view will make it particularly effective in identifying high-redshift FRBs and improving constraints on their cosmological applications.

* **Canadian Hydrogen Observatory and Radio-transient Detector (CHORD):** CHORD [4286], a planned successor to CHIME, will combine higher sensitivity with improved localization capabilities for FRBs. CHORD is expected to detect tens of thousands of FRBs across a broad redshift range, providing critical insights into the evolution of cosmic structures and addressing cosmological tensions.

* **Pathfinder for Real-time Extragalactic Cosmic Intensity Survey Experiment (PRECISE):** PRECISE is a dedicated pathfinder for FRB studies, focusing on real-time detection and precise localization of FRBs. It will enhance the study of their host galaxies and the IGM, making it a valuable addition to the next generation of FRB experiments.

### 5.1.9. Line-intensity mapping

The large-scale structure of the Universe can be surveyed through the radiation intensity emitted by gas clouds, in a manner similar to galaxy surveys, but without resolving individual sources. This approach significantly accelerates the survey process. While many surveys focus

exclusively on the 21 cm line associated with the hyperfine transition of neutral hydrogen, line-intensity mapping (LIM) extends this technique to include additional spectral lines, such as carbon monoxide (CO) and ionized carbon (CII), which provide complementary tracers of large-scale structure and galaxy evolution. The intensity distribution maps derived from LIM can be translated into matter fluctuation power spectra and enable studies across a broader range of cosmic epochs.

Unlike traditional 21 cm experiments, which focus specifically on the neutral hydrogen distribution, LIM captures the integrated emission of multiple spectral lines, making it a more versatile approach. This broader capability allows LIM to probe different phases of the ISM and the EoR, as well as to reduce parameter degeneracies by spanning a wider range of redshifts and tracers.

This innovative technique employs angular resolution observations to trace the spatial distribution of matter, even at high redshifts where traditional galaxy surveys face challenges. If foreground contamination can be effectively mitigated, line-intensity mapping has the potential to (1) provide wide redshift coverage, averaging out cosmological parameter degeneracies across different redshifts, (2) yield large-scale information that could reveal signatures of inflation and gravitational effects, and (3) access matter density modes that are less affected by non-linear physics. By complementing 21 cm experiments, LIM plays a critical role in addressing cosmological tensions, such as the $H_0$ and $S_8$ discrepancies. Its ability to combine data from multiple spectral lines and explore different epochs of cosmic evolution allows it to test new models of DE, modifications to gravity, and other potential extensions to the standard cosmological model.

The further development of this technique will require advancements in millimeter-wave detectors and the refinement of data analysis methods to mitigate astrophysical and modeling systematics. Below, we identify the key ongoing and planned experiments leveraging line-intensity mapping to study cosmic large-scale structures and the EoR using this method.

* **The Hobby-Eberly Telescope Dark Energy Experiment (HETDEX):** HETDEX [4287] is a groundbreaking survey leveraging line-intensity mapping of Lyman-$\alpha$ emitters to study the large-scale structure of the Universe. By mapping the intensity distribution of Lyman-$\alpha$ emission over the redshift range $1.9 < z < 3.5$, HETDEX provides insights into the matter power spectrum and the evolution of cosmic structures during a pivotal epoch in the Universe's history. HETDEX's line-intensity mapping measurements play a crucial role in addressing cosmological tensions by offering independent constraints on large-scale structure and its growth, as well as the expansion history of the Universe. Additionally, HETDEX's use of intensity mapping reduces reliance on resolving individual sources, enabling efficient surveys of faint, distant cosmic structures.

* **CO Mapping Array Project (COMAP):** COMAP [4249] is a pioneering experiment designed to map the large-scale structure of the Universe through intensity mapping of the CO rotational transition lines. By targeting the $z \sim 2.4 - 3.4$ redshift range, COMAP traces the distribution of molecular gas in galaxies during the peak of star formation activity, offering insights into galaxy evolution and the assembly of cosmic structures. COMAP plays a crucial role in addressing cosmological tensions by providing independent constraints on the large-scale matter distribution and the expansion history.

* **CarbON CII line in post-rEionization and ReionizaTiOn epoch (CONCERTO):** CONCERTO [4288] is a state-of-the-art experiment designed to study the large-scale structure of the Universe using line-intensity mapping of the [CII] emission line. Operating in the redshift range $4.5 < z < 8.5$, CONCERTO aims to trace the distribution of ionized carbon during the EoR and the early stages of galaxy formation. By capturing the integrated [CII] signal from unresolved sources, it provides a unique probe of the
ISM and star formation in high-redshift galaxies. CONCERTO's sensitivity to high-redshift structures complements other intensity mapping experiments and traditional surveys, enabling a more detailed understanding of reionization-era physics and its connection to late-time cosmological parameters. Furthermore, by probing large-scale modes, CONCERTO helps refine models of DE, inflation, and modifications to gravity, providing new insights into the underlying causes of cosmological tensions.

* **Spectro-Photometer for the History of the Universe, Epoch of Reionization, and Ices Explorer (SPHEREx):** This proposed all-sky survey aims to provide spatial distribution data using various tracers to explore different cosmic eras [4248]. The survey will utilize the $H\alpha$, $H\beta$, and [OIII] lines to probe $0.1 < z < 5$, $0.5 < z < 2$, and $0.5 < z < 3$, respectively, mapping low-redshift gas clouds. The higher redshift range, spanning $5.2 < z < 8$, will be investigated using the Lyman-$\alpha$ line, providing a direct probe of the EoR. By spanning a wide range of redshifts and utilizing multiple spectral lines, SPHEREx can help address cosmological tensions, such as the $H_0$ and $S_8$ discrepancies, by providing independent measurements of large-scale structure growth and the expansion history of the Universe.

* **Tomographic Ionized-Carbon Mapping Experiment (TIME):** TIME [4289] is designed to probe the EoR by mapping the redshifted $157.7 \ \mu\text{m}$ emission line of singly ionized carbon ([CII]) over the redshift range $5 \le z \le 9$. In addition, it observes carbon monoxide (CO) rotational transitions from galaxies at intermediate redshifts $0.5 \le z \le 2$. These measurements aim to trace the early stages of galaxy formation and star formation history, providing a complementary view of large-scale structure during key epochs in cosmic evolution.

* **The Cosmic Dawn Intensity Mapper (CDIM):** CDIM [4290] is a proposed space-based mission designed to explore the large-scale structure of the Universe through line-intensity mapping of multiple spectral lines. By targeting key tracers such as hydrogen Lyman-$\alpha$, $H\alpha$, $H\beta$, and [OIII], CDIM will probe a wide redshift range, spanning from the EoR ($6 < z < 10$) to the era of peak star formation ($z \sim 2$). These measurements will provide a comprehensive view of the distribution of ionized and molecular gas, as well as star formation processes. CDIM's ability to map the matter distribution across a wide range of redshifts and tracers reduces parameter degeneracies and systematic uncertainties. By bridging the gap between early- and late-time probes, CDIM provides complementary data to galaxy surveys and CMB experiments. Additionally, its sensitivity to faint, diffuse emission makes it a powerful tool for studying large-scale modes that are less accessible with traditional surveys.

* **Fred Young Submillimeter Telescope (CCAT-prime):** CCAT-prime [4291], equipped with the advanced Prime-Cam instrument, is designed to perform line-intensity mapping of emission lines such as [CII] at redshifts relevant to the EoR and cosmic dawn. By tracing the [CII] line, along with other potential tracers, CCAT-prime aims to explore the star formation history, the ISM, and the role of galaxies in reionizing the early Universe. Its high-altitude site and state-of-the-art instrumentation provide exceptional sensitivity for mapping large-scale structure during key phases of cosmic evolution.

### 5.1.10. Potential new probes

As our understanding of the Universe deepens, new observational techniques and theoretical frameworks are being developed to challenge existing paradigms and explore unresolved tensions in cosmology. These potential new probes leverage advanced technologies and novel methodologies to address persistent discrepancies in key cosmological parameters, such as the Hubble constant $H_0$, the amplitude of matter

fluctuations $S_8$, etc. By pushing the boundaries of precision measurements and theoretical modeling, these probes aim to uncover new physics or systematic effects that may underlie these tensions.

This section explores these innovative probes, highlighting their potential contributions to resolving the current challenges in cosmology and paving the way for new discoveries about the Universe.

* **Visible and Infrared Survey Telescope for Astronomy (VISTA):** VISTA [4292] is a ground-based facility dedicated to wide-field surveys in the visible and near-infrared wavelengths. Equipped with an advanced infrared camera, VISTA is uniquely suited to mapping the large-scale structure of the Universe by detecting galaxies and QSOs at high redshifts. Its unprecedented sensitivity and wide-field capabilities allow it to probe the cosmic web, trace the distribution of matter, and explore the evolution of structures over cosmic time. By providing precise measurements of galaxy clustering and WL signals, VISTA contributes to addressing key cosmological tensions, such as those related to the amplitude of matter fluctuations $S_8$ and the Hubble constant $H_0$. Furthermore, its ability to survey large areas of the sky with high resolution offers unique opportunities to identify deviations from standard cosmological models, potentially unveiling signatures of new physics.

* **Transient High-Energy Sky and Early Universe Surveyor (THESEUS):** THESEUS [655] is a proposed space-based mission designed to explore the high-energy transient sky and study the early Universe. By detecting GRBs from the first generation of stars (Pop III stars) and other energetic phenomena, THESEUS provides a unique probe into the era of cosmic reionization and early star formation. THESEUS combines wide-field monitoring and precise localization of GRBs with follow-up spectroscopy, enabling measurements of the cosmic star formation rate and the chemical enrichment history of the Universe. Its ability to observe the high-energy sky at unprecedented sensitivity offers a complementary approach to resolving cosmological tensions, such as refining constraints on the matter density parameter ($\Omega_{m,0}$) and testing models of DE. By bridging the gap between high-energy astrophysics and cosmology, THESEUS represents a transformative tool for uncovering new physics and deepening our understanding of the early Universe.

* **Quasars as Geometric Rulers:** QSOs, the luminous cores of AGN, offer a novel approach to cosmological measurements by serving as geometric rulers. Their variability over time, combined with precise measurements of time delays in gravitationally lensed QSOs, enables the determination of absolute distances in the Universe. This method bypasses many of the traditional assumptions in standard candles or rulers, providing an independent means of measuring $H_0$ and testing the expansion history of the Universe. In addition to their role in time-delay cosmography, QSOs also probe the large-scale structure of the Universe through clustering and absorption-line studies. This dual utility allows QSOs to contribute to resolving tensions in cosmological parameters, such as $H_0$ and $S_8$. Their utility as geometric rulers and tracers of structure represents a powerful avenue for exploring deviations from the standard cosmological model.

* **Redshift Drift with ANDES (ArmazoNes High Dispersion Echelle Spectrograph):** ANDES, a planned instrument for the ELT, offers a unique opportunity to measure the redshift drift — a direct, model-independent observation of the Universe's expansion history. By observing spectral lines of distant QSOs and tracking their subtle changes over decades, ANDES aims to detect the tiny redshift drift predicted by the standard cosmological model. This groundbreaking method provides a direct probe of the dynamics of the Universe, bypassing the need for distance ladder calibrations or assumptions about standard candles or rulers. By directly measuring the acceleration or deceleration
of cosmic expansion, ANDES will place new constraints on DE, modifications to gravity, and the fundamental properties of the Universe. Its unparalleled precision makes it a new tool for addressing unresolved tensions in cosmological parameters.

*   **CMB Spectral Distortions:** Deviations from a perfect blackbody spectrum of the CMB encode information about energy injections in the early Universe. These distortions arise due to processes such as Silk damping of primordial perturbations, decaying or annihilating particles, and early structure formation. The two primary types of distortions, μ-distortions (sensitive to energy injections at $z \gtrsim 10^5$) and γ-distortions (from later energy injections), provide a complementary approach to testing the standard ΛCDM model. Measurements of spectral distortions could reveal signatures of new physics, including primordial non-Gaussianity, modifications to the recombination history, or interactions between DM and radiation. Future space missions such as PIXIE and PRISM aim to achieve the required sensitivity to detect these distortions, opening new avenues for cosmological exploration.

*   **Lunar Astronomy:** Lunar astronomy [4293], leveraging the unique environment of the Moon, presents a groundbreaking opportunity to probe the cosmos in ways that are challenging or impossible from Earth. The Moon's lack of atmosphere eliminates atmospheric distortions, enabling precise observations across a wide range of wavelengths, including radio, infrared, and X-rays. Furthermore, the Moon's far side provides an unparalleled radio-quiet environment, ideal for low-frequency observations of the early Universe, including the cosmic dawn and the EoR. Lunar observatories have the potential to address cosmological tensions by providing high-precision measurements of large-scale structure, the CMB, and the 21 cm signal from neutral hydrogen. Additionally, their stable environment offers the possibility of ultra-long-term observations, enabling direct measurements of cosmological parameters such as the Hubble constant and constraints on the nature of DE. By extending observational capabilities beyond Earth-based and space-based platforms, lunar astronomy could transform our understanding of the Universe.

## 5.2. Recommendations

The open question of cosmic tensions presents a unique opportunity to reassess how observational measurements in cosmology are reconciled with physical models through diverse data analysis approaches. This may signal a turning point in our understanding of how to interpret measurements, particularly in the presence of potential systematics at a fundamental level. Such a systematic effect would need to manifest across all phenomena in local distance ladder measurements or be ubiquitous in early-time measurements. Another possibility is the emergence of new, independent measurements that do not rely on either the distance ladder or early Universe constraints. In particular, advances in GW astronomy, where standard sirens provide a novel approach to constructing distance scales, hold great promise. While this method remains in its early stages and has yet to reach the precision required to compete with traditional approaches, its continued development — particularly with upcoming detectors such as LISA and third-generation ground-based observatories — could play a crucial role in resolving cosmic tensions in the future.

A key tool in analyzing observational data and potential systematics, alongside the exploration of fundamental physics theories, is the application of data analysis methods. Traditionally, data analysis has relied on Bayesian statistical techniques, both for interpreting observational data and for comparing physical models. However, there is growing interest in developing frequentist approaches more broadly, given their reduced dependence on prior information. At the same time, there is strong motivation to advance statistical methods that leverage the broad range of ML techniques. These include supervised learning approaches such as GP, as well as unsupervised methods

like neural networks. The development of toolkits based on these statistical frameworks holds significant potential, both in enhancing the extraction of information from observational data and in refining model-building strategies. In particular, such tools could provide valuable insights into fundamental physics by systematically addressing the open issues surrounding cosmic tensions. It will be essential to integrate these methodologies into standard analysis pipelines for upcoming large-scale surveys.

A plethora of physically motivated fundamental physics theories have been studied in recent years, with particular attention given to their connection to resolving the open problem of cosmic tensions and associated questions within the standard model of cosmology. These efforts have focused on further developing geometric gravity, exploring potential physics beyond the standard model of particle physics, and investigating emergent phenomenology and possible quantum gravity effects. On the other hand, many practical theories in these approaches were originally motivated by theoretical or semi-physical considerations. The further integration of the growing body of observational evidence into the development of new classes of physical theories will drive the next generation of cosmological models, aligning them with the most pressing questions from observational surveys. Additionally, the use and advancement of model-building toolkits will contribute to the creation of physically motivated theoretical models that address cosmic tensions while preserving the successes of the current standard model of cosmology.

The breadth of observational surveys has been reviewed in Section 2, where their potential systematics are discussed in detail. In Section 3, recent developments in traditional data analysis approaches are examined alongside discussions of emerging statistical tools that are expected to become competitive in the coming years, including those based on ML methods. The development of new physically motivated fundamental theories is explored in Section 4, with a focus on their potential to resolve cosmological tensions while preserving the successful elements of the current standard model of cosmology. The future of the field will depend not only on the advancement of each of these areas individually but also on the ability of the community to integrate these diverse approaches into a coherent framework to address the growing challenges posed by cosmic tensions. This effort will require close collaboration between observational cosmologists, data analysts, and fundamental physicists. In the coming decade, it will be essential to:

*   Leverage next-generation observational surveys to improve the precision of key cosmological parameters and systematically test for hidden systematics.

*   Incorporate advanced statistical techniques, including ML-based inference methods and profile likelihood approaches, into standard cosmological pipelines.

*   Continue developing theoretical models that remain consistent with observational constraints while addressing the root causes of cosmological tensions.

*   Encourage interdisciplinary collaboration between observational, computational, and theoretical communities to ensure that different approaches are synthesized into a cohesive framework.

Resolving the cosmic tensions represents a defining challenge for the cosmology community. Success in this endeavor will require a concerted effort across multiple fronts, balancing innovative new techniques with a rigorous assessment of existing methodologies. By systematically integrating new data, analysis techniques, and theoretical advancements, the next decade of cosmological research has the potential to transform our understanding of the Universe's fundamental properties.
## Challenges in observational cosmology:

* **Cepheid variables** — The next generation of ground- and space-based optical surveys will provide deep time-series observations of distant galaxies, expanding the volume over which the universality of the period–luminosity relation can be tested. These observations will also improve our understanding of the impact of metallicity in different environments. As new Cepheids are discovered and observational precision increases, reducing uncertainties in Cepheid measurements will require better constraints on dust reddening, zero-point corrections in Cepheid parallaxes, and new geometric anchors in the distance ladder.

* **Masers** — Systematics in megamaser-hosting galaxies, such as non-circular orbits and non-gravitational forces, do not significantly impact constraints on cosmological parameters. However, the primary challenge for maser-based techniques lies in discovering new high-quality megamaser-hosting galaxies suitable for precise distance measurements.

* **Tip of the Red Giant Branch (TRGB)** — This method relies on a statistical approach to standardizing TRGB stars, making the calibration process a critical aspect of the analysis. The main challenges in applying the TRGB method include (1) potential imbalances between TRGB and calibrating galaxy brightness intensities, (2) the need for accurate calibration of the target field, and (3) effective outlier detection methods for poorly sampled LFs.

* **Mira variables** — Oxygen-rich Mira stars can serve as anchors in the first rung of the distance ladder for calibrating absolute magnitudes. However, their luminosity, color, large angular size, and surface variations introduce significant uncertainties in parallax measurements. On the second rung, the number of known Mira stars remains low, presenting an opportunity for future observations to expand their use in distance calibration.

* **Type Ia supernovae** — SNIa primarily appear in the second and third rungs of the three-rung distance ladder. Their systematics are among the most extensively studied and best mitigated. However, the effects of (1) calibration systematics, (2) redshift-dependent biases in the third rung, and (3) stellar physics and sample selection may each contribute to potential changes in the estimates of certain cosmological parameters. Another challenge in this sector is the potential expansion of the distance ladder framework to include higher or lower rungs.

* **J-regions of the asymptotic giant branch (JAGB)** — This is a relatively new but promising method for extending the distance ladder. The primary challenges for establishing this approach as a robust distance indicator include a better understanding of the effects of metallicity, atmospheric influences on photometry, and variations in pulsation across different stellar populations.

* **Type II supernovae** — SNII offer an independent path to circumvent SNIa systematics while introducing different systematic considerations. This method has the potential to achieve greater precision with the addition of further calibrators and a better understanding of how spectroscopic data can be leveraged to improve the standardization procedure.

* **Surface brightness fluctuations (SBF) methods** — SBF-based methods have shown promise in constraining distances to very distant galaxies, relying primarily on imaging data. The next generation of optical telescopes will provide opportunities to refine these techniques further. Given the statistical nature of the approach, a deeper understanding of stellar population studies and peculiar evolutionary stages will help reduce systematic uncertainties. Addressing these factors will enable SBF to continue improving as a robust method for constraining cosmological parameters.

* **Cosmic chronometers** — This method has the advantage of being theoretically economical in terms of its underlying assumptions while providing a direct numerical measurement of the Hubble parameter in redshift space. Beyond the need to increase the number of measurements using this approach, some systematic challenges include (1) uncertainties in stellar metallicity estimates, (2) errors in star formation history modeling and underlying assumptions, and (3) contamination by young or star-forming outliers.

* **HII galaxies** — These galaxies are characterized by bursts of massive star formation, and their strong emission in specific spectral lines makes them valuable probes for high-redshift cosmology. However, for this method to become more robust, several systematics need to be addressed, including (1) improved physical modeling of emission line width profiles, (2) better understanding of stellar age effects, (3) corrections for extinction-induced deformations in emission lines, and (4) refined metallicity distribution calibrations.

* **Baryonic Tully–Fisher relation methods** — The Tully–Fisher and BTFR can be applied to cosmology to constrain the Hubble constant, given an underlying cosmological model. While this method offers good control over systematics, the relatively small number of observed galactic objects currently limits its competitiveness compared to other techniques. This limitation will be addressed with upcoming large-scale surveys. On the modeling side, further development may help reduce model dependence, for instance, by incorporating ML techniques into the analysis.

* **Strong lensing and time-delay cosmography** — Strong lensing provides a distance-ladder-independent method for measuring $H_0$ through time-delay cosmography. However, several systematics currently limit its precision, including uncertainties in lens mass modeling, the impact of line-of-sight structures, and degeneracies in the inferred time delays. Additionally, assumptions about mass profile parametrizations can introduce biases in cosmological constraints. Improving this technique will require higher-resolution imaging, better characterizations of lens environments, and larger statistical samples of well-measured lensing systems to reduce both statistical and systematic uncertainties.

* **Gravitational wave astronomy** — Free from electromagnetic radiation, GW cosmology provides uniquely independent methods to constrain cosmological parameters, separate from all other approaches. Standard sirens offer the additional advantage of serving as absolute distance indicators, making them independent of a cosmological model in determining the Hubble constant. However, an electromagnetic counterpart is required to identify the host galaxy, which is then used to infer certain galactic properties; alternatively, statistical methods utilizing galaxy catalogs can be employed. On the other hand, dark sirens suffer from potential systematics related to assumptions about galactic properties.

* **Cosmic microwave background (CMB) radiation** — Like other observatories, CMB experiments are subject to instrumentation systematics and internal tensions, which can be more pronounced given the precision of the measurements and the vast volume of data collected. Ensuring consistency between high- and low-multipole analyses in cosmological parameter estimation remains a critical challenge for future CMB surveys. The next generation of CMB experiments will aim to minimize instrumental and astrophysical systematics, improving constraints on fundamental physics. By reducing these contamination effects, it may even become possible to robustly measure B-mode polarization, which remains a crucial target for detecting primordial GWs and probing inflationary physics.

* **Baryon acoustic oscillations (BAO)** — This method enables robust cosmological analyses based on millions of extragalactic
objects. However, its statistical nature introduces a number of systematics that must be carefully accounted for. One key challenge is that the source density field is displaced due to peculiar motions, particularly in low-redshift regions, which is corrected using density field reconstruction techniques. As more galaxies are observed with higher precision, these reconstruction methods must continue to improve. Another important aspect of BAO surveys is the reliance on an underlying fiducial cosmology to transform between coordinate systems. While the influence of this model is relatively small, developing techniques to further reduce this dependence remains a priority. Additionally, BAO measurements are taken relative to the sound horizon, introducing another model-dependent feature that should be further refined to minimize its impact.

* **Galaxy clustering** — The growth of large-scale structures can be inferred from the statistical clustering of galaxies in redshift space, which depends on estimates of correlation functions and power spectra. The statistical nature of these measurements introduces several systematics, including those originating from measurement techniques (such as atmospheric and extragalactic extinction corrections), galaxy survey systematics (such as calibration errors and foreground contamination), and uncertainties in nonlinear modeling for redshift-space galaxy clustering.

* **Large-scale structure and higher-order statistics** — Beyond two-point statistics such as the galaxy correlation function and power spectrum, higher-order statistics and cosmic web topology provide additional tools to probe cosmology. Measurements of cosmic voids, filament structures, and the bispectrum offer sensitivity to non-Gaussianities and potential modifications to gravity. The main challenges in this sector include modeling nonlinear structure formation, correcting for observational systematics, and integrating these statistics into existing cosmological frameworks.

* **Weak lensing** — Weak gravitational lensing surveys rely on statistically significant samples of galaxies, introducing several challenges that must be addressed. These include uncertainties in individual galaxy redshift estimates due to the inherent limitations of photometric redshift determinations, systematic biases in shear and shape ellipticity measurements, and difficulties in accurately modeling nonlinearities in the matter power spectrum. Improving these aspects will be essential for maximizing the precision of WL constraints on cosmological parameters.

* **Galaxy cluster counts** — Galaxy clusters are the largest gravitationally bound structures in the Universe and are highly sensitive to cosmic evolution and the underlying cosmological parameters. Aside from the challenge of distinguishing how different cosmological models affect cluster evolution, a major issue in this method is the mass calibration problem. This refers to the relationship between the total halo mass and observable cluster properties, which is crucial for using cluster counts as a cosmological probe. The primary method for determining halo masses is WL, which itself introduces additional systematic uncertainties. As survey data become more precise, the mass calibration problem will increasingly become a limiting factor in the effectiveness of this approach.

* **Quasar and GRB distance ladder** — Both QSOs and GRBs have shown strong potential as probes of the high-redshift Universe, providing constraints across multiple cosmological parameters. However, their precision remains limited compared to other methods, partly due to systematics related to the physical nature of the sources, which remain an active area of discussion in the literature. Resolving these open questions would significantly enhance the statistical power of cosmological parameter constraints when these data are used in combination with other survey observations.

* **Fast radio bursts (FRBs)** — The relatively recent discovery of FRBs provides a powerful new probe of cosmological models. These events have shown promising potential to independently constrain the Hubble constant, as well as other cosmological parameters, particularly offering insights into the matter density parameter within $\Lambda$CDM. However, systematics related to the modeling of DM contributions and the IGM remain crucial open questions for this technique. Refinements in these areas will be necessary to improve its precision.

* **Radio background excess** — The discrepancy between the expected emission from known astrophysical and cosmological sources and the observed brightness in the electromagnetic spectrum presents an anomaly in the radio segment of the spectrum. Resolving this requires a careful balance in accounting for infrared radiation production in early galaxies, X-ray contributions affecting inverse Compton scattering of CMB photons, the depth of the 21 cm signal, and constraints from the cross-correlated angular power spectrum with optical sources. The next generation of observatories has the potential to refine and test possible explanations for this excess signal.

* **Bulk flow measurements** — The average peculiar velocity of a statistically significant sample of galaxies should diminish at sufficiently high redshifts. However, measurements of bulk flows face several challenges, including large uncertainties in peculiar velocity estimates and biases in the spatial distribution of observed galaxies. Recent studies have suggested that bulk flow magnitudes increase with distance, a result that appears counterintuitive. Addressing this challenge will require the continued development of bulk flow measurement techniques, as well as improved observational data quality at higher redshifts.

* **Cosmic dipole and anisotropies** — The observed CMB dipole is expected to be consistent with the dipole measured in other astrophysical tracers. However, discrepancies in dipole measurements using different observational datasets suggest the possibility of systematic effects or new physics. Additionally, potential anisotropies in cosmological parameters such as $H_0$ and $S_8$ challenge the assumption of statistical isotropy. Addressing these issues requires improved methodologies and cross-correlations between independent datasets to test for underlying systematics or signatures of new physics.

* **Cross-correlations between cosmological probes** — Combining different observational techniques provides a means to reduce systematics and improve cosmological parameter constraints. Key cross-correlations include (1) WL and galaxy clustering to calibrate galaxy bias and structure formation models, (2) CMB lensing and large-scale structure to refine DM distribution models, and (3) standard sirens and BAO measurements to independently test the cosmic expansion history. As observational precision improves, cross-correlations will become increasingly important in resolving cosmological tensions.

* **21 cm intensity mapping** — The neutral hydrogen 21 cm signal provides a powerful method to trace the large-scale structure of the Universe across a wide range of redshifts. This technique has the potential to probe the cosmic dawn, reionization, and the post-reionization epochs, offering insights into the distribution of matter over cosmic time. However, several challenges must be addressed, including foreground contamination from astrophysical sources, calibration uncertainties, and the need for precise theoretical modeling of the signal's evolution.

* **Line-intensity mapping (LIM)** — LIM provides a promising method to trace large-scale structure by measuring integrated emission from spectral lines such as CO and Lyman-$\alpha$ rather than relying on resolved galaxy surveys. This method has the potential to map cosmic structure at high redshifts, but faces
challenges such as foreground contamination and the need for precise theoretical modeling.

* **Sunyaev-Zel'dovich (SZ) and X-ray surveys** — Measurements of galaxy clusters using the SZ effect and X-ray emission offer valuable constraints on cosmic structure formation and expansion. However, systematic uncertainties related to gas physics, temperature profiles, and mass calibration remain key challenges.

* **Multi-messenger cosmology** — Observations across multiple cosmic messengers, including electromagnetic signals, GWs, and high-energy particles, provide new opportunities for constraining cosmological parameters and testing fundamental physics. By combining information from different observational channels, multi-messenger approaches can help break degeneracies inherent in individual methods. However, challenges remain, including the low detection rates of some sources, difficulties in precise localization, and uncertainties in the modeling of extreme astrophysical environments.

* **Neutrino Cosmology** — Neutrinos remain among the least understood fundamental particles, and their extremely weak interactions make direct measurements of their properties exceptionally difficult. A key open question is whether these particles have a nonzero mass. Moreover, terrestrial neutrino oscillation experiments provide constraints that appear to contrast with indirect cosmological measurements, potentially hinting at physics beyond the Standard Model in the neutrino sector. Reconciling these discrepancies will require further advancements in both laboratory-based and cosmological neutrino studies.

## Challenges in the development of numerical and data analysis tools:

* **Model constraints in conjunction with Bayesian statistics** — Bayesian statistical methods have been widely used to constrain cosmological model parameters against observational data, and they now feature a broad suite of tools designed to meet these challenges. However, as survey data volumes increase and cosmological models become more complex, the computational demands of traditional Bayesian approaches are becoming increasingly problematic. This motivates the development of more efficient algorithms and novel implementations of Bayesian inference techniques to maintain accuracy while improving computational feasibility.

* **Frequentist approaches** — Profile likelihoods provide a standard statistical method for analyzing cosmological models with high-dimensional parameter spaces, particularly when the likelihood surfaces exhibit non-Gaussian features. This approach involves running multiple traditional MCMC analyses for fixed parameters to construct a profile likelihood. Several community tools already implement this method, some incorporating ML techniques to enhance performance. However, due to the computationally intensive nature of this approach, further work on accelerating the sampling process will be crucial for making it more practical for a wider range of applications.

* **Hybrid Bayesian-Frequentist approaches** — While Bayesian inference dominates cosmological data analysis, frequentist methods such as profile likelihoods and bootstrapping offer complementary insights, particularly in scenarios where priors strongly influence results. Hybrid approaches that combine these frameworks can provide more robust parameter constraints, reduce sensitivity to prior assumptions, and improve statistical interpretability in high-dimensional cosmological models.

* **Fast approximate inference techniques** — Traditional Bayesian inference methods such as MCMC can be computationally prohibitive, especially for high-dimensional cosmological models.

Alternative approaches such as Hamiltonian Monte Carlo, Variational Inference, and Neural Density Estimation offer promising routes to accelerate parameter estimation while maintaining accuracy. Developing and benchmarking these techniques for cosmological applications is an open challenge.

* **Cosmology simulator inference techniques** — The vast amount of information contained in the large-scale structure of the Universe presents a significant challenge for traditional simulation and analysis methods. Extracting cosmological parameters from these simulations is particularly difficult, as non-Gaussian and higher-order effects may become increasingly relevant for improving accuracy. Recent advances, including neural network architectures and decision tree learning approaches, have shown promise in addressing these challenges. However, the availability of community tools and a robust comparison of different inference techniques remain open issues that need further exploration.

* **Computational challenges in large-scale simulations** — Cosmological simulations are essential for understanding structure formation and model testing. However, the increasing size of observational datasets and complexity of simulations present major computational challenges. Key issues include (1) optimizing numerical algorithms for high-performance computing architectures, (2) improving resolution and scalability in N-body and hydrodynamical simulations, and (3) reducing computational costs while maintaining accuracy in statistical inference from simulations.

* **Reconstruction techniques** — The use of observational survey data to reconstruct physical models is still in its early stages; however, powerful techniques have already been developed and made publicly available. The development of more mature and statistically robust reconstruction methods, including those leveraging ML approaches, will be an important aspect of progress in this direction. A major challenge for these techniques lies in effectively utilizing the wide variety of available datasets, which may include background, perturbative, and other physical aspects of cosmological models.

* **Genetic algorithm model selection** — GAs provide a mechanism to explore an otherwise infinite model space within a finite time by applying selection criteria. These methods primarily rely on Bayesian constraint analyses, but practical toolkits for their implementation are not yet publicly available in the literature. The development of such toolkits is essential for advancing this technique into a more comprehensive classification framework. Additionally, combining GAs with other, faster constraint methods may enhance their suitability for practical model selection analyses.

* **Machine learning for theoretical model selection** — The increasing complexity of cosmological models necessitates efficient methods for exploring large parameter spaces. ML techniques, such as deep learning classifiers and GP regression, are being developed to identify viable theoretical models by learning patterns in high-dimensional likelihood landscapes. However, challenges remain in ensuring interpretability, robustness, and generalization across different datasets.

* **Calibration and validation of machine learning in cosmology** — ML algorithms are increasingly used for inference, parameter estimation, and anomaly detection in cosmological datasets. However, ensuring that these models generalize well across different observational conditions, remain unbiased, and do not overfit to specific datasets is a key challenge. Benchmarking ML models against traditional methods and developing interpretable AI approaches will be crucial for their broader adoption in cosmology.

* **Dark siren cosmology** — The number of standard sirens without an associated electromagnetic counterpart continues to grow.
These sources can also be used to constrain cosmological parameters, albeit through a statistical reconstruction of their population properties using galaxy catalogs. However, the simultaneous modeling of cosmology and mass distributions introduces computational challenges that must be addressed to extract robust constraints.

* **Spectroscopical sirens** — The use of spectroscopic data from host galaxies associated with GW events offers a promising avenue for improving the precision of standard siren measurements. By obtaining redshift information through spectroscopic observations, it is possible to reduce uncertainties in distance measurements and break degeneracies in cosmological parameter estimation. However, challenges remain in accurately identifying the host galaxy among multiple candidates, mitigating observational systematics in spectroscopic measurements, and optimizing survey strategies to maximize the detection of viable spectroscopical sirens.

* **Systematics mitigation in statistical inference** — The increasing precision of cosmological surveys requires robust methods to identify and mitigate systematics in data analysis. Key challenges include (1) the impact of prior choices on Bayesian inference, (2) biases introduced by incomplete or inhomogeneous datasets, and (3) uncertainties in the modeling of astrophysical and instrumental effects. The development of statistical techniques that can cross-validate results across different datasets while minimizing these biases remains an important open problem.

* **Big Bang Nucleosynthesis numerical estimates** — The precision of BBN predictions for primordial element abundances has significantly improved in recent years. Advanced numerical codes have revealed tensions in some species ratios that were not apparent in previous lower-order calculations. Future numerical developments incorporating these higher-order effects will be crucial for reassessing these tensions and refining BBN constraints on early Universe physics.

* **Cross-correlations and multi-probe statistical methods** — Combining multiple cosmological probes is essential for breaking degeneracies and improving parameter constraints. However, this requires sophisticated statistical frameworks to account for systematics, survey-specific biases, and correlated uncertainties across datasets. Developing robust cross-correlation pipelines that integrate WL, large-scale structure, and CMB measurements is a key challenge for upcoming surveys.

* **Data-driven approaches for systematics mitigation** — Systematic uncertainties remain a major challenge in cosmology, particularly in photometric redshift estimation, instrumental biases, and survey calibration. ML, GP, and hybrid statistical methods can provide real-time corrections for systematics, but require careful validation to ensure robustness across different datasets.

* **High-volume and high-dimensional data processing** — The increasing size of cosmological datasets from next-generation surveys requires the development of scalable numerical methods and high-performance computing techniques. Challenges include managing high-dimensional parameter spaces, optimizing data compression without loss of information, and implementing real-time data processing pipelines for massive observational datasets.

## Challenges in fundamental physics:

* **Early-time physics** — The early Universe provides a compelling regime for introducing exotic physics that remains shielded by recombination. Mechanisms such as early scalar fields, additional neutrino species, or modified expansion histories primarily affect the sound horizon at recombination, which in turn impacts inferences of the Hubble constant. These early modifications

also present opportunities for testing inflationary scenarios. However, a significant challenge remains in explaining the evolution of large-scale structure, ensuring that any proposed early-time physics can simultaneously produce the correct growth rate to remain consistent with all cosmological observations.

* **Inflation** — Phenomenological models successfully provide a spectrum of scenarios that can alleviate some tensions even under the assumption of Gaussian fields. However, it remains crucial to construct physically realistic explicit models that respect fundamental physical principles such as locality, causality, and unitarity, while also approximating key features of these phenomenological models. As future galaxy surveys improve precision on possible non-Gaussian features associated with primordial conditions, it will become increasingly important to develop accurate numerical simulations and theoretical descriptions of the nonlinear aspects of the evolution of these fields.

* **Big Bang Nucleosynthesis (BBN) tensions** — BBN predictions generally exhibit strong agreement with $\Lambda$CDM in the production rates of primordial species. However, discrepancies remain, particularly for lithium isotopes, and increasingly for helium and deuterium, when compared with their relative abundances inferred from observations of the oldest stars. These discrepancies may stem from stellar astrophysics rather than cosmological considerations, but they could also signal challenges for early Universe dynamics in non-standard cosmological models. Resolving these tensions requires improved modeling of stellar evolution, nuclear reaction rates, and alternative BBN scenarios.

* **Primordial magnetic fields** — The possible existence of non-negligible PMFs could have influenced CMB anisotropies and small-scale inhomogeneities in the large-scale structure of the Universe. Various realizations of these fields have shown promise in addressing aspects of cosmic tensions, particularly in modifying early-Universe physics. However, more precise small-scale measurements of CMB anisotropies are needed to robustly test these scenarios and establish whether PMFs play a significant cosmological role.

* **Quantum decoherence in the early Universe** — The classical nature of primordial perturbations is assumed in standard cosmology, yet their quantum mechanical origin requires a consistent explanation of decoherence processes. Understanding how quantum fluctuations transitioned to classical density perturbations and testing for potential residual quantum signatures remains an unresolved issue in fundamental physics.

* **Parity violations in cosmology** — Parity-violating interactions, such as those arising in extensions to general relativity or axion-like particles coupled to gravity, could leave unique imprints on the CMB polarization or large-scale structure. The detection of a nonzero cosmic birefringence signal, or deviations in E/B-mode power spectra, could offer evidence for such interactions. However, current observational constraints remain inconclusive, and refining the observational tests for parity violation remains an open challenge.

* **Nonflat spatial curvature** — The cosmological curvature parameter is a fundamental aspect of the FLRW geometric background and is predicted to be zero in most inflationary models. However, any possible nonzero value remains highly degenerate with other cosmological parameters in standard analyses. Methods to break this degeneracy, such as BAO measurements or other observational techniques, could provide important insights into potential departures from the standard model and their role in addressing cosmological tensions.

* **Testing the Cosmological Principle** — The standard model of cosmology assumes large-scale homogeneity and isotropy. However, several observations, including cosmic dipoles, bulk flows, and peculiar velocity anomalies, suggest that these assumptions
may need to be tested more rigorously. Developing more precise observational tests and statistical methodologies to assess the validity of the cosmological principle remains an important challenge in the field.

*   **Nonvanishing cosmic dipoles** — The cosmic dipole represents the largest expected deviation from isotropy if the cosmological principle is broken at any level. Potential dipole signals have been investigated in various datasets, including the CMB, QSO distributions, fine-structure constant measurements, SNIa, radio galaxies, GRBs, and bulk flow studies. Recent observations have hinted at slight nonvanishing dipoles in some of these probes. To assess the validity and implications of such findings, it is necessary to develop more robust cosmological backgrounds that can accommodate or rule out these potential departures from isotropy.

*   **CMB anisotropy anomalies** — Several features in the CMB anisotropic power spectrum exhibit mild tensions with the predictions of the $Λ$CDM model. Early Universe modifications that explain or incorporate these features more naturally may offer new insights into fundamental physics beyond standard cosmology. These anomalies include: (1) a stronger-than-expected ISW effect in certain analyses, (2) non-Gaussian features in the CMB, such as the Cold Spot, (3) a slight hemispherical asymmetry in the CMB power spectrum, (4) an unexpected lack of large-scale CMB temperature correlations, (5) a higher-than-predicted lensing parameter, and (6) a moderate inconsistency between parameter values derived from high- and low-multipole regions of the CMB power spectrum. Understanding whether these features stem from new physics or residual systematics remains an important challenge for upcoming surveys.

*   **Anomalous Integrated Sachs-Wolfe (ISW) effect** — The ISW effect arises from the interaction of CMB photons with evolving gravitational potentials associated with large-scale structure. Observations suggest a discrepancy between the predicted ISW signal in $Λ$CDM and its measured imprint in cosmic superstructures and supervoids, both in amplitude and sign. This may indicate a more complex growth history than expected in the concordance model. Understanding whether this excess signal can be reconciled within $Λ$CDM, or if it points to new physics, remains an open question.

*   **The nature of dark matter** — The connection between the fundamental properties of DM and cosmic evolution has significant implications both for the early Universe, through thermal and non-thermal relic physics, and for the late Universe, influencing the formation of large-scale structure. Modeling how the thermal history and other fundamental characteristics of DM may lead to deviations from standard cosmology via solutions of the Boltzmann equation will be crucial in assessing whether DM plays a role in alleviating cosmological tensions.

*   **Axion-like particles and ultralight fields** — The existence of ultralight scalar fields, such as axion-like particles, could impact the evolution of the Universe through novel interactions with DM, DE, or radiation. These fields have been proposed to address cosmic tensions by altering the expansion rate or structure growth. Developing observational tests for their presence and impact remains a crucial task.

*   **Complex dark sector interactions** — Many extensions to $Λ$CDM propose that DM and DE may not be independent, but instead part of a larger dark sector with self-interactions or couplings to other fields. These models introduce new forces in the dark sector that could impact structure formation, cosmic expansion, and small-scale clustering. However, constraining these interactions remains difficult, as current probes (e.g., CMB, BAO, WL) primarily test gravitational effects rather than direct couplings.

*   **Modified gravity** — Extensions beyond $Λ$CDM may involve modifications to gravity, ranging from mild to radical departures from General Relativity. The literature is rich with competing formulations of MG theories, but many are disfavored at smaller scales and exhibit strong degeneracies both among themselves and with scalar-tensor theories. Additionally, MG theories often introduce challenges such as unwanted fifth-force effects. On the other hand, these theories provide an avenue for constructing alternative cosmological models independent of $Λ$CDM, which could yield departures from concordance cosmology in both early- and late-time evolution.

*   **Late-time physics** — Measurements in the local Universe place strict constraints on the cosmic expansion profile, leaving little room for significant deviations from $Λ$CDM. However, recent results from large-scale surveys suggest possible hints of dynamical properties in DE at late-times. While numerous competing theories focus on late-time modifications, many of their observational properties remain highly degenerate. To address this issue, the development of more distinct and testable theoretical models, as well as more precise predictions from specific scenarios, would be beneficial.

*   **Exotic dark energy models** — The majority of DE models assume a scalar-field-driven component, but alternative formulations involving vector or tensor fields have been proposed. These include vector–tensor theories, emergent gravity models, and Lorentz-violating DE frameworks. Understanding the observational signatures and constraints on these exotic models is an open challenge.

*   **Variation of fundamental constants** — The possible variation of fundamental constants could arise from various exotic physics scenarios, including non-Standard Model particle interactions, MG, or coupled scalar fields, among others. Temporal or spatial variations in fundamental constants would have profound consequences for fundamental physics, potentially impacting atomic structure, nuclear reactions, and cosmological evolution. Observational efforts have primarily focused on detecting variations in the fine-structure constant and the electron mass, as these have shown promise in providing an alternative explanation for the Hubble tension. However, current CMB observations lack the precision to distinguish between models that allow for varying fundamental constants. Addressing this challenge will require next-generation observatories with significantly improved sensitivity to such effects.

*   **Higher-dimensional cosmological models** — Theories incorporating extra spatial dimensions, such as brane-world scenarios and string-inspired cosmologies, propose modifications to gravity that could influence cosmic expansion, the dark sector, or structure formation. Developing testable predictions for these theories and determining their viability in explaining cosmic tensions remains a key theoretical challenge.

*   **Cosmological quantum gravity** — It is expected that classical gravity breaks down at high energy scales, but the impact of UV-complete quantum gravity theories on cosmological observables remains unclear. In particular, it is uncertain whether such effects could resolve the Hubble tension or other cosmic anomalies. Possible quantum gravitational effects, such as the GUP, Lorentz invariance violations, or nonlinear modifications, could provide a new perspective on cosmic tensions as manifestations of non-classical physics. However, fully developed quantum gravity models that remain consistent with small-scale physics while simultaneously addressing these challenges are still in early stages of development.

*   **Testing the equivalence principle on cosmological scales** — The equivalence principle, a cornerstone of general relativity, has been tested at small scales with high precision. However,
cosmological tests remain limited. Anomalies in the behavior of standard sirens, WL, or cosmic dipoles could indicate potential violations. Future large-scale surveys will play a crucial role in refining these tests.

* **Relic neutrinos and direct detection** — The cosmic neutrino background (CvB) is a fundamental prediction of Big Bang cosmology, yet it has never been directly detected. Cosmological observations place strong constraints on its properties, but upcoming laboratory experiments and indirect probes may provide the first evidence for relic neutrinos. If detected, these neutrinos could offer crucial insights into early-Universe physics, including possible deviations from the Standard Model.

By confronting these challenges, the cosmology community will be poised to revolutionize our understanding of the Universe, ensuring that future cosmological models remain consistent with increasingly precise observations while harnessing the full power of advanced statistical and computational methodologies.

### 5.3. Conclusions

The issue of cosmic tensions has emerged over the past decade as a significant challenge to the ΛCDM concordance model, which also faces underlying consistency issues and additional anomalies. While this is not unexpected for a phenomenological framework, the mounting observational discrepancies suggest that a new concordance model may ultimately be required to resolve these tensions. Despite the long-standing success of ΛCDM, the breadth and persistence of cosmic tensions represent the most serious and potentially insurmountable test for the standard cosmological paradigm.

Among these challenges, the continued statistical significance of the Hubble constant tension has solidified its status as a defining question in cosmology. This tension not only tests the robustness of the concordance model but also probes the ability of the cosmology community to reconcile local (late-time) measurements with global (early-time) constraints. The latter, being model-dependent, introduces additional complexities, while the former is subject to astrophysical systematics that may exert only a limited influence on the magnitude of the discrepancy. However, the widespread and consistent detection of the Hubble tension across independent measurement techniques casts doubt on the plausibility of a single cross-survey systematic effect that could fully account for the discrepancy. In Section 2.1, we review the diverse range of methods used to infer $H_0$. Many of these techniques rely on the distance ladder to measure the Hubble flow, including refined SNIa analyses, Cepheid variable calibrations, TRGB and JAGB methods, SNII measurements, Mira variables, and the SBF technique. Additionally, CCs provide a direct means of measuring the Hubble parameter to comparable redshifts. Collectively, these approaches yield a consistently high value of $H_0$, a result reinforced by distance-ladder-independent methods such as maser-driven constraints and estimates based on the BTFR. Furthermore, higher-redshift techniques — including HII galaxy distance indicators, time-delay strong lensing, FRBs, QSOs and GRBs Hubble diagrams — further substantiate the discrepancy. Another promising avenue for constraining $H_0$ lies in GW-based measurements using standard sirens, which provide an independent approach free from electromagnetic systematics. This method continues to improve and has already delivered encouraging results, potentially adding new insights into the nature and expression of the Hubble tension. On the other hand, every CMB-based survey — including Planck, ACT, and SPT — consistently yields a significantly lower value of the Hubble constant, assuming a ΛCDM cosmological framework. This lower range of $H_0$ values is further reinforced through the combination of baryon acoustic oscillation data and constraints from BBN. The core of the Hubble tension thus lies in the stark contrast between low-redshift measurements, which suggest a higher $H_0$, and early-Universe

estimates derived from the CMB and similarly high-redshift probes, which favor a lower value.

The Hubble tension serves as a critical test of ΛCDM—or any alternative cosmological model — spanning from the primordial Universe to the present day. A closely related parameter that traces the expansion and structure formation history of the Universe is $S_8$, which encapsulates both the total matter density and the amplitude of matter fluctuations on scales of $8 h^{-1}$ Mpc. This parameter is widely regarded as an effective measure of cosmic structure growth and is examined in Section 2.2. Similar to the Hubble tension, a statistical discrepancy emerges in the observed values of $S_8$ when comparing CMB-based primary anisotropy measurements with local probes such as WL, galaxy clustering, and galaxy cluster abundance studies. The $S_8$ parameter is also closely connected to the $f\sigma_8$ parameter, which is constrained through RSD, as well as other structure growth parameters, including the growth index, growth parameter, and growth rate. CMB-based measurements yield a relatively high and stable estimate of $S_8$ across multiple experiments, including different data subsets from the Planck mission’s legacy release. In contrast, independent analyses from WL surveys, galaxy clustering, RSD, and galaxy count-based approaches predominantly indicate a lower $S_8$ value at a statistically significant level. When considered alongside the Hubble tension, the potential $S_8$ tension presents an even greater challenge to ΛCDM and alternative cosmological models, further testing their predictive power and ability to fully reconcile current observational data.

Additionally, several anomalies and challenges arising from the confrontation between ΛCDM and observational data have become increasingly apparent. These issues, described in Section 3, include the $A_{\text{lens}}$ anomaly, which suggests an excess lensing amplitude in the Planck data and a potential deviation from ΛCDM predictions. This is further compounded by a slight preference for a closed universe in spatial curvature parameter constraints within the ΛCDM framework. Other CMB anisotropy anomalies include the low quadrupole moment and its alignment with the octupole, hemispherical asymmetry, and the Cold Spot anomaly. Beyond the CMB, additional unresolved questions concern the exact nature of cosmological neutrino physics, potential deviations from the cosmological principle due to large-scale bulk flows, and anomalies in the primordial abundances of certain species in the early Universe. More broadly, discrepancies have emerged in Lyman-$\alpha$ measurements, the ISW effect, radio synchrotron background observations, and the possible existence of large cosmic voids.

The vast amount of observational data related to cosmic expansion, large-scale structure formation, and the evolution of fundamental parameters presents a formidable challenge for the data analysis and theoretical modeling community. Traditional implementations of MCMC methods are increasingly struggling to distinguish between competing cosmological scenarios due to the complexity of their parameter dependencies and the high dimensionality of their parameter spaces. In Section 3, novel approaches to MCMC methods are discussed alongside alternative data analysis techniques. Frequentist parameter inference through profile likelihoods offers an intriguing pathway to mitigating prior volume effects that can dominate posterior constraints in Bayesian approaches. However, this method is even more computationally demanding than standard MCMC, making it impractical for certain classes of models beyond ΛCDM. Similarly, extracting cosmological information from large-scale simulations has become computationally intractable using conventional methods, necessitating the development of novel tools. ML techniques, particularly deep generative models, have shown significant promise in constraining cosmological parameters with improved efficiency. More broadly, ML inference frameworks have begun replacing traditional MCMC techniques, leveraging various neural network architectures to refine parameter estimation. In parallel, model selection methodologies have incorporated GAs as a systematic approach for exploring complex model spaces against observational constraints. These rapidly evolving techniques are proving essential
<table><caption>**Table 7**

List of notation conventions used in the White Paper (unless otherwise stated).</caption><thead><tr><th>Definition</th><th>Meaning</th></tr></thead><tbody><tr><td>h = c = k<sub>B</sub> = 1</td><td>Natural units</td></tr><tr><td>κ<sup>2</sup> ≡ 8πG = M<sub>Pi</sub><sup>-2</sup></td><td>Gravitational constant</td></tr><tr><td>ln := log<sub>e</sub>, log := log<sub>10</sub></td><td>Logarithm conventions</td></tr><tr><td>( + + +)</td><td>Metric signature</td></tr><tr><td>g<sub>μν</sub></td><td>Metric tensor</td></tr><tr><td>G<sub>μν</sub> = R<sub>μν</sub> - 1/2 g<sub>μν</sub> R</td><td>Einstein tensor</td></tr><tr><td>Λ</td><td>Cosmological constant</td></tr><tr><td>ds<sup>2</sup> = -dt<sup>2</sup> + a<sup>2</sup>(t) [ (dθ<sup>2</sup> + sin<sup>2</sup>θdθdφ<sup>2</sup>) ]</td><td>Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime metric</td></tr><tr><td>a(t)</td><td>Scale factor</td></tr><tr><td>a<sub>0</sub> = 1</td><td>Scale factor today (set to unity)</td></tr><tr><td>t</td><td>Cosmic (proper) time</td></tr><tr><td>τ(t) = ∫<sub>0</sub><sup>t</sup> (dτ') / a(τ')</td><td>Conformal time</td></tr><tr><td>· ≡ d/dτ</td><td>Cosmic time derivative</td></tr><tr><td>' ≡ d/dτ</td><td>Conformal time derivative</td></tr><tr><td>T<sup>μν</sup> = 2(δ<sub>μν</sub> / √-g) δ<sub>εμν</sub></td><td>Energy-momentum tensor of the Lagrangian density L</td></tr><tr><td>z = -1 + 1/a</td><td>Cosmological redshift</td></tr><tr><td>H(z) = a/a</td><td>Hubble parameter</td></tr><tr><td>H<sub>0</sub></td><td>Hubble constant</td></tr><tr><td>h = H<sub>0</sub> / 100 km s<sup>-1</sup> Mpc<sup>-1</sup></td><td>Dimensionless reduced Hubble constant</td></tr><tr><td>ρ<sub>m</sub>, ρ<sub>b</sub>, ρ<sub>r</sub></td><td>Energy density of total matter, baryonic matter, and radiation</td></tr><tr><td>ρ<sub>DM</sub>, ρ<sub>DE</sub></td><td>Energy density of dark matter and dark energy</td></tr><tr><td>Ω<sub>m</sub></td><td>Present-day matter density parameter</td></tr><tr><td>Ω<sub>r</sub> = 2.469 × 10<sup>-5</sup> h<sup>-2</sup>(1 + 0.2271 N<sub>eff</sub>)</td><td>Present-day radiation density parameter</td></tr><tr><td>Ω<sub>DM</sub>, Ω<sub>DE</sub></td><td>Present-day density parameters of dark matter and dark energy</td></tr><tr><td>Ω<sub>CDM</sub></td><td>Present-day density parameters of cold dark matter</td></tr><tr><td>Ω<sub>m</sub>(z) = κ<sup>2</sup>ρ<sub>m</sub> / (3H<sup>2</sup>)</td><td>Matter density parameter</td></tr><tr><td>Ω<sub>r</sub>(z) = κ<sup>2</sup>ρ<sub>r</sub> / (3H<sup>2</sup>)</td><td>Relativistic content density parameter</td></tr><tr><td>Ω<sub>DE</sub>(z) = κ<sup>2</sup>ρ<sub>DE</sub> / (3H<sup>2</sup>)</td><td>Dark energy density parameter</td></tr><tr><td>ω ≡ ρ/ρ</td><td>Equation of state (EoS) parameter</td></tr><tr><td>c<sub>s</sub></td><td>Sound speed</td></tr><tr><td>r<sub>s</sub> ≡ ∫<sub>0</sub><sup>r</sup> c<sub>s</sub>(τ') dτ'</td><td>Sound horizon</td></tr><tr><td>r<sub>d</sub> ≡ r<sub>s</sub>(τ<sub>d</sub>)</td><td>Sound horizon at drag epoch</td></tr><tr><td>σ<sub>8</sub></td><td>Amplitude of mass fluctuations on scales of 8 h<sup>-1</sup> Mpc</td></tr><tr><td>S<sub>8</sub> = σ<sub>8</sub> √(Ω<sub>m</sub> / 0.3)</td><td>Weighted amplitude of matter fluctuations</td></tr></tbody></table>

in addressing the challenges posed by next-generation observatories, which are producing unprecedented volumes of data and introducing a vast array of potential new physics scenarios.

The increasingly robust expression of cosmic tensions — spanning the Hubble constant, large-scale structure growth, and various other anomalies — necessitates a reevaluation of potential new physics within both current and future observational surveys. The cosmology community has proposed a wide range of possible directions for addressing these challenges, which are reviewed in Section 4. Early-Universe modifications have the advantage of introducing exotic dynamics prior to recombination, beyond the reach of direct electromagnetic observations. However, while altering the sound horizon can help reconcile certain tensions, these modifications may introduce inconsistencies with the early growth of large-scale structure. Addressing this issue requires exploring different realizations of new physics in this sector alongside novel data analysis techniques, such as frequentist parameter inference. On the other hand, late-time modifications to cosmology have also shown promise in addressing cosmic tensions through diverse mechanisms, including additional fields, modifications to gravitational physics, and other extensions to the standard paradigm.

However, the significantly more detailed and structured nature of late-Universe observations places stringent constraints on the evolution of such models, restricting the amplitude of any new physics in this regime. An alternative to modifying gravity in the field equations is to reconsider the behavior of the matter sector, such as through interacting or decaying DM scenarios, or more intricate physics governing DM properties. Beyond standard modifications to cosmic evolution, alternative explanations have been explored, including the role of large cosmic voids, the influence of PMFs, and variations in the dynamics of cosmic inflation. The severity of these tensions has also revived interest in non-standard cosmological geometries that challenge aspects of the cosmological principle, though such proposals remain in early stages of development. Similarly, while quantum gravity theories have not yet demonstrated a direct resolution to cosmic tensions, the potential variation of fundamental constants has been shown to meaningfully impact both the inferred Hubble constant and the growth of large-scale structures, with broader implications across multiple areas of fundamental physics. Ultimately, reconciling early- and late-time cosmological observations, alongside non-standard phenomenology, may necessitate a combination of modifications to the concordance model.
However, it remains crucial to break the strong degeneracy among different classes of modified cosmologies and ensure that proposed models not only fit existing data but also yield new, testable predictions while preserving the well-established successes of the concordance framework across both astrophysical and cosmological scales.

The coming years will see an explosion of high-precision observational data from upcoming surveys, as reviewed in Section 5.1. New CMB experiments, such as LiteBIRD and CMB-S4, have the potential to detect primordial GWs and refine measurements of CMB anisotropies, which may provide key insights into fundamental physics. In parallel, large-scale structure surveys — including those conducted by Euclid, the Roman Space Telescope, and the Rubin Observatory — will probe the evolution of cosmic structure and the nature of DE in unprecedented detail. WL studies, RSD, and clustering analyses will provide complementary information on cosmic structure formation, while 21 cm intensity mapping from SKAO, FAST, and CHIME will open a new observational window into the cosmic dawn. Additionally, radio astronomy efforts, such as FRB surveys with UTMOST and MeerKAT, will offer independent constraints on cosmic expansion and structure evolution. Beyond electromagnetic probes, the next generation of GW observatories — including the LIGO-Virgo-KAGRA network, the ET, Cosmic Explorer, and the space-based LISA mission — will provide direct insight into gravitational radiation, potentially offering novel constraints on early-Universe physics and cosmic expansion. Additionally, advances in standard siren measurements may provide an independent means of resolving the Hubble tension. Meanwhile, improvements in the cosmic distance ladder, enabled by JWST, ELT, and other facilities, will refine local measurements of $H_0$ with increasing precision. As the volume of observational data continues to grow exponentially, computational advancements will play an increasingly critical role in extracting cosmological information. The limitations of traditional MCMC methods necessitate the development of alternative approaches, such as frequentist inference through profile likelihoods, deep generative models, and other ML techniques. These innovations have already shown promise in improving parameter estimation and accelerating statistical inference, while model selection algorithms, including GAs, offer systematic strategies for exploring vast cosmological parameter spaces. The integration of artificial intelligence and high-performance computing will be essential in processing and analyzing the unprecedented data streams expected from next-generation observatories.

The comprehensive review presented in this White Paper, along with the collaborative efforts that shaped it, reflects a growing consensus within the cosmology community on the key directions that must be pursued in the coming years. As detailed in Section 5.2, these efforts span observational challenges, advancements in data analysis techniques, and the theoretical development of new physics models. Crucially, resolving cosmic tensions will require a synergistic approach, combining observational precision, computational innovation, and theoretical creativity. The next decade of cosmology will be pivotal in shaping our understanding of the Universe, with the potential to refine the current paradigm or uncover new physics that reshapes our fundamental model of cosmic evolution.

## 6. Conventions

The White Paper spans research communities in observational, data analysis, and fundamental physics areas which observe vastly different notational traditions. A big effort was made to homogenize this notation across the breadth of communities in the separate sections of this project. These notation conventions are defined in Table 7. Any deviations from this notation convection are noted in the specific subsections in which they occur.

## 7. List of acronyms

<table><tr><td>ACT</td><td>Atacama Cosmology Telescope</td></tr><tr><td>AGN</td><td>Active Galactic Nucleus</td></tr><tr><td>AGB</td><td>Asymptotic Giant Branch</td></tr><tr><td>ANN</td><td>Artificial Neural Network</td></tr><tr><td>BAO</td><td>Baryon Acoustic Oscillations</td></tr><tr><td>BTFR</td><td>Baryonic Tully-Fisher Relation</td></tr><tr><td>BNN</td><td>Bayesian Neural Network</td></tr><tr><td>BBN</td><td>Big Bang Nucleosynthesis</td></tr><tr><td>BOSS</td><td>Baryon Oscillation Spectroscopic Survey</td></tr><tr><td>CC</td><td>Cosmic chronometers</td></tr><tr><td>CDM</td><td>Cold Dark Matter</td></tr><tr><td>CMB</td><td>Cosmic Microwave Background Radiation</td></tr><tr><td>CNN</td><td>Convolutional Neural Network</td></tr><tr><td>CPL</td><td>Chevallier-Polarski-Linder</td></tr><tr><td>DDE</td><td>Dynamical Dark Energy</td></tr><tr><td>DE</td><td>Dark Energy</td></tr><tr><td>DM</td><td>Dark Matter</td></tr><tr><td>eBOSS</td><td>Extended Baryon Oscillation Spectroscopic Survey</td></tr><tr><td>EDE</td><td>Early Dark Energy</td></tr><tr><td>EFTofLSS</td><td>Effective Field Theory of Large Scale Structure</td></tr><tr><td>ELT</td><td>Extremely Large Telescope</td></tr><tr><td>EoR</td><td>Epoch of Reionization</td></tr><tr><td>EoS</td><td>Equation of State</td></tr><tr><td>ESA</td><td>European Space Agency</td></tr><tr><td>ET</td><td>Einstein Telescope</td></tr><tr><td>DES</td><td>Dark Energy Survey</td></tr><tr><td>DESI</td><td>The Dark Energy Spectroscopic Instrument</td></tr><tr><td>FLRW</td><td>Friedmann-Lemaître-Robertson-Walker</td></tr><tr><td>FRB</td><td>Fast Radio Burst</td></tr><tr><td>CMB-S4</td><td>CMB-Stage 4</td></tr><tr><td>GA</td><td>Genetic Algorithm</td></tr><tr><td>GP</td><td>Gaussian processes</td></tr><tr><td>GR</td><td>General relativity</td></tr><tr><td>GRB</td><td>Gamma-ray burst</td></tr><tr><td>GUP</td><td>Generalized Uncertainty Principle</td></tr><tr><td>GW</td><td>Gravitational Wave</td></tr><tr><td>HST</td><td>Hubble Space Telescope</td></tr><tr><td>HSC</td><td>Hyper Suprime-Cam</td></tr><tr><td>IDE</td><td>Interacting Dark Energy</td></tr><tr><td>IDM</td><td>Interacting Dark Matter</td></tr><tr><td>IGM</td><td>Intergalactic Medium</td></tr><tr><td>ISM</td><td>Interstellar Medium</td></tr><tr><td>ISW</td><td>Integrated Sachs-Wolfe</td></tr><tr><td>LDE</td><td>Late Dark Energy</td></tr><tr><td>LF</td><td>Luminosity Function</td></tr><tr><td>LISA</td><td>Laser Interferometer Space Antenna</td></tr><tr><td>LMC</td><td>Large Magellanic Clouds</td></tr><tr><td>JAGB</td><td>J-region Asymptotic Giant Branch</td></tr><tr><td>JWST</td><td>James Webb Space Telescope</td></tr><tr><td>KiDS</td><td>Kilo-Degree Survey</td></tr><tr><td>LIGO</td><td>Laser Interferometer Gravitational Wave Observatory</td></tr><tr><td>LSS</td><td>Large Scale Structure</td></tr><tr><td>LSST</td><td>Legacy Survey of Space and Time</td></tr><tr><td>MG</td><td>Modified Gravity</td></tr><tr><td>MCMC</td><td>Markov chain Monte Carlo</td></tr><tr><td>ML</td><td>Machine Learning</td></tr><tr><td>MW</td><td>Milky Way galaxy</td></tr><tr><td>MOND</td><td>Modified Newtonian dynamics</td></tr></table>
<table><tr><td>NEDE</td><td>New Early Dark Energy</td></tr><tr><td>PMF</td><td>Primordial Magnetic Field</td></tr><tr><td>PDF</td><td>Probability Density function</td></tr><tr><td>RGB</td><td>Red Giant Branch</td></tr><tr><td>QSO</td><td>QSO</td></tr><tr><td>RSD</td><td>Redshift-Space Distortions</td></tr><tr><td>RVM</td><td>Running Vacuum Model</td></tr><tr><td>SBF</td><td>Surface Brightness Fluctuations</td></tr><tr><td>SGWB</td><td>Stochastic Gravitational Wave Background</td></tr><tr><td>SKAO</td><td>Square Kilometer Array Observatory</td></tr><tr><td>SMC</td><td>Small Magellanic Clouds</td></tr><tr><td>SN</td><td>Supernovae</td></tr><tr><td>SNIa</td><td>Type Ia supernovae</td></tr><tr><td>SNII</td><td>Type II supernovae</td></tr><tr><td>SPT</td><td>South Pole Telescope</td></tr><tr><td>SPT-3G</td><td>South Pole Telescope - 3rd Generation</td></tr><tr><td>SZ</td><td>Sunyaev-Zeldovich</td></tr><tr><td>TRGB</td><td>Tip of the Red Giant Branch</td></tr><tr><td>WDM</td><td>Warm Dark Matter</td></tr><tr><td>WL</td><td>Weak Lensing</td></tr><tr><td>WMAP</td><td>Wilkinson Microwave Anisotropy Probe</td></tr><tr><td>ZTF</td><td>Zwicky Transient Facility</td></tr></table>

### CRediT authorship contribution statement

**Eleonora Di Valentino:** Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization. **Jackson Levi Said:** Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This paper is based upon work from COST Action CA21136 Addressing observational tensions in cosmology with systematics and fundamental physics (CosmoVerse) supported by COST (European Cooperation in Science and Technology). EDV is supported by a Royal Society Dorothy Hodgkin Research Fellowship. JLS would also like to acknowledge funding from "Xjenza Malta" as part of the "Technology Development Programme" DTP-2024-014 (CosmicLearning) Project and the "XM-TÜBÂ° TAK R&I Programme" BridgingCosmology project. AGV is funded by "la Caixa" Foundation, Spain (ID 100010434) and the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 847648, with fellowship code LCF/BQ/PI23/11970027. AP acknowledges support from the Polish National Science Centre through the grant 2023/50/A/ST9/00579. AP is supported by National Science Foundation Grant No. 2308193. CvdB is supported by the Lancaster-Sheffield Consortium for Fundamental Physics under STFC grant: ST/X000621/1. CU was supported by UKRI STFC ST/W001020/1 and European Union ERC StG, LSS_BeyondAverage, 101075919. DE acknowledges support from the Swiss National Science Foundation (SNSF), Switzerland under grant agreement 200021_212576. EMT is supported by funding from the European Research Council (ERC) under the European Union's HORIZON-ERC-2022 (grant agreement no. 101076865). ENS acknowledges the contribution of the LISA CosWG.

This project has received funding from the European Research Council under the European Union's Horizon 2020 research and innovation programme (grant agreement 853291). FB acknowledges the support of the Royal Society through the University Research Fellowship. The work of FN is supported by VR Starting Grant 2022-03160 of the Swedish Research Council. GB is supported by the Spanish grants CIPROM/2021/054 (Generalitat Valenciana) and PID2023-151418NB-I00 funded by MCIU/AEI/10.13039/501100011033. IS acknowledges NASA, United States grants N4-ADAP24-0021 and 24-ADAP24-0074, and this research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP). JT is supported by a Ramón y Cajal contract by the Spanish Ministry for Science, Innovation and Universities with Ref. RYC2023-045660-I. JM would also like to acknowledge funding from "Xjenza Malta" as part of the "Technology Development Programme" DTP-2024-014 (CosmicLearning) Project. KS acknowledges support from the Australian Government through the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), through project number CE230100016. K.F.D. was supported by the PNRR-III-C9-2022-19 call, with project number 760016/27.01.2023, and funding from "Xjenza Malta" as part of the "XM-TÜBÂ° TAK R&I Programme" BridgingCosmology project. LZ is supported by the NAWA Ulam fellowship (No. BPN/ULM/2023/1/00107/U/00001) and the National Science Centre, Poland (research grant No. 2021/42/E/ST2/00031). LG acknowledges financial support from AGAUR, CSIC, MCIN and AEI 10.13039/50110 0011033 under projects PID2023-151307NB-I00, PIE 20215AT016, CEX2020-001058-M, ILINK23001, COOPB2304, and 2021-SGR-01270. LV acknowledges support by the National Natural Science Foundation of China (NSFC) through the grant No. 12350610240 "Astrophysical Axion Laboratories", and also thanks INFN through the "QGSKY" Iniziativa Specifica project. The work of LAA is supported by the US National Science Foundation Grant PHY-2412679. MA acknowledges the UK Science and Technology Facilities Council (STFC) under grant number ST/Y002652/1 and the Royal Society, United Kingdom under grant numbers RGSR222268 and ICAR1231094. MG acknowledges support from the European Union (ERC, RELiCS, project number 101116027) and the PRIN (Progetti di ricerca di Rilevante Interesse Nazionale) number 2022WJ9J33. MF is funded by the PRIN (Progetti di ricerca di Rilevante Interesse Nazionale) number 2022WJ9J33. MC, GR, and RH acknowledge support from the project "INAF-EDGE" (Large Grant 12-2022, P.I. L. Hunt), from the ASI-INAF agreement "Scientific Activity for the Euclid Mission" (n.2024-10-HH.0; WP8420) and from the INAF "Astrofisica Fondamentale" GO-grant 2024 (PI M. Cantiello). MM acknowledges support from MIUR, PRIN 2022 (grant 2022NY2ZRS 001) and from the grant ASI n. 2024-10-HH.0 "Attività scientifiche per la missione Euclid - fase E". RCN thanks the financial support from the CNPq under the project No. 304306/2022-3 and FAPERGS under the project No. 23/2551-0000848-3. RCB is supported by an appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government, and was also supported by the Korean Local Governments in Gyeongsangbukdo Province and Pohang City. RC acknowledges support from the CONAHCYT research grant CF2022-320152. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 947660). RIA is funded by the SNSF Eccellenza Professorial Fellowship PCEFP2_194638. SK acknowledges funding by the National Center for Science, Poland, grant no. 2023/49/B/ST9/02777. SL is supported by the National Science Foundation Graduate Research Fellowship Program under grant No. DGE2139757. SV acknowledges support from the Istituto Nazionale di Fisica Nucleare (INFN) through the Commissione Scientifica Nazionale 4 (CSN4) Iniziativa Specifica "Quantum Fields in Gravity, Cosmology and Black Holes"
(FLAG), and from the University of Trento and the Provincia Autonoma di Trento (PAT, Autonomous Province of Trento) through the UniTrento Internal Call for Research 2023 grant "Searching for Dark Energy off the beaten track" (DARKTRACK, grant agreement no. E63C22000500003). SP acknowledges the financial support from the Department of Science and Technology, Philippines (DST), Govt. of India under the Scheme "Fund for Improvement of S&T Infrastructure (FIST)" (File No. SR/FST/MS-I/2019/41). TT acknowledges support from the National Science Foundation, United States, the National Areonautics and Space Administration, and the Gordon and Betty Moore Foundation, United States. VP is supported by funding from the European Research Council (ERC) under the European Union's HORIZON-ERC-2022 (grant agreement no. 101076865) and from the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement no. 860881-HIDDEn. AD acknowledges the support of the European Union's Horizon 2021 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 101068013 (QGRANT). AK has been supported by a Lendület excellence grant by the Hungarian Academy of Sciences (MTA). This project has received funding from the European Union's Horizon Europe research and innovation programme under the Marie Skłodowska-Curie grant agreement number 101130774. Funding for this project was also available in part through the Hungarian Ministry of Innovation and Technology NRDI Office grant OTKA NN147550. ARL was supported by FCT through the Investigador FCT Contract CEECIND/02854/2017 and the research project PTDC/FIS-AST/0054/2021. AP is grateful for the support of Vicerrectoría de Investigación y Desarrollo Tecnológico (Vridt) at Universidad Católica del Norte through Núcleo de Investigación Geometría Diferencial y Aplicaciones, Resolución Vridt No - 096/2022 and Resolución Vridt No - 098/2022. AP was supported by the Proyecto Fondecyt Regular 2024, Folio 1240514, Etapa 2024. AB acknowledges support from the National Science Center, project no. UMO-2022/45/B/ST2/01067. ABR is supported by the Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), Grant No E-26/200.149/2025 é 200.150/2025 (304809) AJS received support from NASA, United States through STScI grants HST-GO-16773 and JWST-GO-2974. AM acknowledges the financial support by Conacyt-Mexico through the Post-doc Project I1200/311/2023. AB acknowledges the fellowship of the Brazilian research agency CNPq. AH is funded by the Carlsberg foundation. BSS acknowledges National Science Foundation awards AST-2307147, PHY-2207638, PHY-2308886 and PHY-2309064. B. L. acknowledges the support of the National Research Foundation of Korea, South Korea (NRF-2022R1F1A1076338), the Partenariat Hubert Curien STAR with the National Research Foundation of Korea (RS-2023-00259422), and of the Korea Institute for Advanced Study (KIAS) grant funded by the government of Korea. The research activities of BT is supported in part by the U.S. National Science Foundation under Grant PHY-2014104. CGB is supported by the Spanish Grant PID2023-149016NB-I00 (MINECO/AEI/FEDER, UE) and the Basque government Grant No. IT1628-22 (Spain). CM is supported by an FCT fellowship, grant number 2023.03984. CZ is supported by the China Scholarship Council for 1 year study at SISSA. CP acknowledges the financial support by the excellence cluster QuantumFrontiers of the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) under Germany's Excellence Strategy - EXC-2123 QuantumFrontiers - 390837967 and was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Germany - Project Number 420243324. D.B. acknowledges support from projects PID2021-122938NB-I00 funded by the Spanish "Ministerio de Ciencia e Innovación" and FEDER "A way of making Europe", PID2022-139841NB-I00 funded by the Spanish "Ministerio de Ciencia e Innovación" and SA097P24 funded by Junta de Castilla y León. DS acknowledges support from Bulgarian National Science Fund, Republic of Bulgaria grant

number KP-06-N58/5. DRG acknowledges support from grant PID2022-138607NB100, funded by MCIN/AEI/10.13039/501100011033. DB acknowledges funding from the Ministry of Science, Technological Development and Innovations of the Republic of Serbia, Project contract No. 451-03-136/2025-03/200017. The work of EG was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP). EF is supported by "Theoretical Astroparticle Physics" (TAsP), iniziativa specifica INFN and by the research grant number 2022E2J4RK "PANTHEON: Perspectives in Astroparticle and Neutrino THEory with Old and New messengers" under the program PRIN 2022 funded by the Italian Ministero dell'Università e della Ricerca (MUR). EDMF is supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. FA thanks CNPq and Fundação Carlos Chagas Filho de Amparo á Pesquisa do Estado do Rio de Janeiro (FAPERJ), Processo SEI 260003/014913/2023 for financial support. The work of FB was supported by the post-doctoral grant CIAPOS/2021/169. FP acknowledges partial support from the INFN grant InDark and from the Italian Ministry of University and Research (MUR), PRIN 2022 'EXSKALIBUR - Euclid-Cross-SKA: Likelihood Inference Building for Universe's Research', Grant No. 2022BBYB9, CUP C53D2300131 0006, and from the European Union - Next Generation EU. FP also acknowledges support from the FCT project "BEYLA - BEYond LAmbda" with ref. number PTDC/FIS-AST/0054/2021. FSNL acknowledges support from the Fundação para a Ciência e a Tecnologia (FCT) Scientific Employment Stimulus contract with reference CEECINST/00032/2018, and funding through the research grants UIDB/04434/2020, UIDP/04434/2020 and PTDC/FIS-AST/0054/2021. GL was funded by Agencia Nacional de Investigación y Desarrollo (ANID) through Proyecto Fondecyt Regular 2024, Folio 1240514, Etapa 2024. He also thanks Vicerrectorá de Investigación y Desarrollo Tecnológico (VRIDT) at Universidad Católica del Norte for support through Núcleo de Investigación Geometría Diferencial y Aplicaciones (Resolución VRIDT NÂ° 096/2022). GG acknowledges the financial support from the COSMOS network (www.cosmosnet.it) through the ASI (Italian Space Agency) Grants 2016-24-H.0 and 2016-24-H.1-2018. GDS acknowledges support from INAF-ASTROFIT fellowship and Istituto Nazionale di Fisica Nucleare (INFN), Naples Section, for specific initiatives QGSKY and Moonlight2, as well as GAIA DPAC funds from INAF and ASI (PI: M.Lattanzi). GJO acknowledges financial support from the Spanish Grants PID2020-116567GB-C21, PID2023-149560NB-C21 funded by MCIN/AEI/10.13039/501100011033, by CEX2023-001292-S funded by MCIU/AEI, and by i-COOP23096 funded by CSIC. GSDj acknowledges the support by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia under contract 451-03-137/2025-03/200124 and support by the ICTP - SEENET-MTP NT03 Project TECOM-GRASP. GCH acknowledges support through the ESA research fellowship programm. HAF was partially supported by National Science Foundation grant AST-1907404. The work of IDG was supported by the Estonian Research Council, Estonia grants MOB3JD1202, RVTT3, RVTT7, and by the CoE program TK202 "Fundamental Universe". The work of IAM is supported by the Basque Government, Spain Grant IT1628-22, by Grant PID2021-123226NB-I00 (funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe"). IDM acknowledges support from the grant PID2021-122938NB-I00 funded by MCIN/AEI/10.13039/501100011033 and from the grant SA097P24 funded by Junta de Castilla y León and by "ERDF A way of making Europe". JA acknowledges support from the Diputación General de Aragón-Fondo Social Europeo (DGA-FSE) Grant No. 2020-E21-17R of the Aragon Government. JG and BK have been supported in part by the Polish National Science Center (NCN) under grant 2020/37/B/ST2/02371. JR is supported by a Ramón y Cajal contract of the Spanish Ministry of Science and Innovation with Ref. RYC2020-028870-I. This research was further supported by the project PID2022-139841NB-I00 of MICIU/AEI/10.13039/501100011033 and FEDER, UE. JS is
supported by the Taiwan National Science & Technology Council. JARC is supported by the project PID2022-139841NB-I00 funded by MI-CIU/AEI/10.13039/501100011033 and by ERDF/EU. JJ acknowledge partial support from STSci, United States under grants HST-GO-16262 and JWST-GO-03055. JGB acknowledges support from the Spanish Research Project PID2021-123012NB-C43 [MICINN-FEDER], and the Centro de Excelencia Severo Ochoa Program, Spain CEX2020-001007-S at IFT. KL is a recipient of the John and Pat Hume Scholarship and acknowledges support from the Friedrich Naumann Foundation for Freedom and from the Swiss Study Foundation. The research activities of KRD are supported in part by the U.S. National Science Foundation through its employee IR/D program as well as by the U.S. Department of Energy under Grant DE-FG02-13ER41976/DE-SC0009913. LLG acknowledges support from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Grant No. 307636/2023-2 and from the Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro (FAPERJ) Grant No. E-26/204.598/2024. LY acknowledges support from YST Program of APCTP and Natural Science Foundation of Shanghai 24ZR1424600. LC acknowledges support from FCT - Fundação para a Ciência e a Tecnologia through the projects with DOI identifiers 10.54499/2023.11681.PEX and 10.54499/2024.00249.CERN. MB is supported by the Polish National Science Center through grants no. 2020/38/E/ST9/00395 and 2020/39/B/ST9/03494. MGE acknowledges the financial support of FONDECYT de Postdoctorado, NÂ° 3230801. MdC acknowledges support from INFN iniziativa specifica GeoSymQFT. The work of MR is supported by the European Union – Next Generation EU and by the Italian Ministry of University and Research (MUR) via the PRIN 2022 project n. 20228WHTYC. ME was supported by the Estonian Ministry of Education and Research (grant TK202, “Foundations of the Universe”), by Estonian Research Council, Estonia grant PRG2172, and by the European Union’s Horizon Europe research and innovation programme (EXCOSM, grant No. 101159513). The work of MBL, CGB & PM is supported by the Spanish Grant PID2023-149016NB-I00 (MINECO/AEI/FEDER, UE). This work is also supported by the Basque government Grant No. IT1628-22 (Spain). MC was supported by FCT through the Investigador FCT Contract No. CEECIND/02581/2018 and the research project PTDC/FIS-AST/0054/2021. MM acknowledges funding by the Agenzia Spaziale Italiana, Italy (ASI) under agreement no. 2018-23-HH.0 and support from INFN/Euclid Sezione di Roma. MASP acknowledges support from the FCT through the Fellowship UI/BD/154479/2022, through the Research Grants UIDB/04434/2020 and UIDP/04434/2020, and through the project with reference PTDC/FIS-AST/0054/2021 (“BEYond LAmbda”). MASP also acknowledges support from the MICINU through the project with reference PID2023-149560NB-C21. MAS received support from the CAPES scholarship. MK was funded through SASPRO2 project AGE of Gravity: Alternative Geometries of Gravity, which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 945478. MM acknowledges the support by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia under contract 451-03-137/2025-03/200124. MI acknowledges that this material is based upon work supported in part by the Department of Energy, Office of Science, under Award Number DE-SC0022184 and also in part by the U.S. National Science Foundation under grant AST2327245. NF acknowledge support from the Research grant TAsP (Theoretical Astroparticle Physics) funded by INFN, Italy. NF is supported by the European Union – Next Generation EU and by the Italian Ministry of University and Research (MUR) via the PRIN 2022 project n. 20228WHTYC. The Work of NEM. is supported in part by the UK Science and Technology Facilities research Council (STFC) under the research grant ST/X000753/1. NAN was financed by IBS, United States under the project code IBS-R018-D3, and acknowledges support from PSL/Observatoire de Paris. NS is supported by the Charles University Grant Agency (GAUK) - 94224.

PS is supported by Science and Technology Facilities Council, United Kingdom (STFC) training grant ST/X508287/1. PJ acknowledges funding from the Ministry of Science, Technological Development and Innovations of the Republic of Serbia, Project contract No. 451-03-136/2025-03/200002. RG acknowledges the support from the SNF 200020_175751 and 200020_207379 “Cosmology with 3D Maps of the Universe” research grant. RH work has been supported by the Spanish grants FPU19/03348 of MU, MCIN/AEI/10.13039/501100011033 grants PID2020-113644GB-I00, PID2023-148162NB-C22, by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grants HORIZON-MSCA-2021-SE-01/101086085-ASYMMETRY and H2020-MSCA-ITN-2019/860881-HIDDEn and by the Generalitat Valenciana grants PROMETEO/2019/083 and CIPROM/2022/69. RH acknowledges funding from the Italian National Institute of Astrophysics (INAF) through large grant PRIN 12-2022 “INAF-EDGE” (PI L. Hunt). RR acknowledges financial support from the STFC Consolidated Grant ST/X000583/1. RBN acknowledges funding by the Royal Society, United Kingdom through the University Research Fellowship Renewal URF R 221005. RK is supported by Project SA097P24 funded by Junta de Castilla y Leon. SB is supported by “Agencia Nacional de Investigación y Desarrollo” (ANID), Grant “Becas Chile postdoctorado al extranjero” No. 74220006. ST is supported by the National Science Centre, Poland (research grant No. 2021/42/E/ST2/00031). SSC acknowledges support from the Isitututo Nazionale di Fisica Nucleare (INFN) through the Commissione Scientifica Nazionale 4 (CSN4) Iniziativa Specifica “Quantum Fields in Gravity, Cosmology and Black Holes” (FLAG) and from the Fondazione Cassa di Risparmio di Trento e Rovereto (CARITRO Foundation) through a Caritro Fellowship (project “Inflation and dark sector physics in light of next-generation cosmological surveys”). SJL is supported by grant PIP 11220200100729CO CONICET and grant 20020170100129BA UBACYT. SP is supported by the international Gemini Observatory, a program of NSF NOIRLab, which is managed by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the U.S. National Science Foundation, on behalf of the Gemini partnership of Argentina, Brazil, Canada, Chile, the Republic of Korea, and the United States of America. SP acknowledges the financial support of the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fellowships 300936/2023-0 and 301628/2024-6. TP acknowledges the financial support from the Slovenian Research Agency (grants I0-0033, P1-0031, J1-8136, J1-2460 and Z1-1853). TB was supported by ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by European Union – NextGenerationEU. TS is supported by the Della Riccia foundation grant 2025 and the Galileo Galilei Institute Boost Fellowship 2024. TK was supported by the Estonian Research Council, Estonia grants CoE TK202 “Foundations of the Universe” and PRG2608 “Space - Time - Matter”. VM thanks CNPq (Brazil) and FAPES (Brazil) for partial financial support. VAM is supported by Generalitat Valenciana via the Excellence Grant 164CIPROM/2021/073, by the Spanish MICIN/AEI/10.13039/501100011033 and the EU/FEDER via grant PID2021-122134NB-C21, and by the Spanish MCIU/AEI via the Severo Ochoa project CEX2023-001292-S. VP acknowledges the support by the Ministry of Education and Science of the Federation of Bosnia and Herzegovina, under Project Number 05-35-2467-1/23. VK acknowledges financial support from Research Ireland Grant 21/PATH-S/9475 (MOREHIGGS) under the SFI-IRC Pathway Programme. Report number: DIAS-STP-25-05. VM acknowledges support from ANID FONDECYT Regular grant number 1231418, Millennium Science Initiative AIM23-0001, and Centro de Astrofísica de Valparaíso CIDI N21. VBJ acknowledges funding from the Ministry of Science, Technological Development and Innovations of the Republic of Serbia, Project contract No. 451-03-136/2025-03/200017. WY has been supported by the National Natural Science Foundation of China under Grant No. 12175096, and Liaoning Revitalization Talents Program under Grant
no. XLYC1907098. WY is supported via the research projects 'COLAB' funded by the National Science Center, Poland, under agreement number UMO-2020/39/B/ST9/03494. "YH is funded by NSFC under the grant No. 12347137 and the China Postdoctoral Science Foundation, China under Grant No. 2024M753076".

**Afternote:** The opinions and conclusions expressed herein are those of the authors, and do not represent any funding agencies.

## Data availability

The data that has been used is confidential.

## References

[1] CosmoVerse Network, CA21136 - Addressing observational tensions in cosmology with systematics and fundamental physics, CosmoVerse Network, https://www cost.eu/actions/CA21136.

[2] CosmoVerse Network, CA21136 - Addressing observational tensions in cosmology with systematics and fundamental physics, CosmoVerse Network, https://cosmoversetensions.eu/.

[3] E. Abdalla, et al., Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies, JHEAp 34 (2022) 49-211, arXiv:2203.06142 [astro-ph.CO].

[4] E. Di Valentino, et al., Snowmass2021 - Letter of interest cosmology intertwined I: Perspectives for the next decade, Astropart. Phys. 131 (2021) 102606, arXiv:2008.11283 [astro-ph.CO].

[5] E. Di Valentino, et al., Snowmass2021 - Letter of interest cosmology intertwined II: The Hubble constant tension, Astropart. Phys. 131 (2021) 102605, arXiv:2008.11284 [astro-ph.CO].

[6] E. Di Valentino, et al., Cosmology intertwined III: $f\sigma_8$ and $S_8$, Astropart. Phys. 131 (2021) 102604, arXiv:2008.11285 [astro-ph.CO].

[7] E. Di Valentino, et al., Snowmass2021 - Letter of interest cosmology intertwined IV: The age of the universe and its curvature, Astropart. Phys. 131 (2021) 102607, arXiv:2008.11286 [astro-ph.CO].

[8] CosmoVerse Network Seminars, CA21136 - Addressing observational tensions in cosmology with systematics and fundamental physics, CosmoVerse Network Seminars, https://cosmoversetensions.eu/for-scientists/cosmoverse-seminars/.

[9] CosmoVerse Network Conferences, CA21136 - Addressing observational tensions in cosmology with systematics and fundamental physics, CosmoVerse Network Conferences, https://cosmoversetensions.eu/category/event/conferences/.

[10] CosmoVerse Network School, CA21136 - Addressing observational tensions in cosmology with systematics and fundamental physics, CosmoVerse Network School, https://cosmoversetensions.eu/event/cosmoverschoolcorfu/.

[11] CosmoVerse Network Training Series, CA21136 - Addressing observational tensions in cosmology with systematics and fundamental physics, CosmoVerse Network Training Series, https://cosmoversetensions.eu/for-scientists/training-series/.

[12] CosmoVerse Network Training Series, CA21136 - Addressing observational tensions in cosmology with systematics and fundamental physics, CosmoVerse Network Training Series, https://cosmoversetensions.eu/for-scientists/journalclub/.

[13] G. Rácz, L. Dobos, R. Beck, I. Szapudi, I. Csabai, Concordance cosmology without dark energy, Mon. Not. R. Astron. Soc. 469 (1) (2017) L1–L5, arXiv:1607.08797 [astro-ph.CO].

[14] R. Beck, I. Csabai, G. Rácz, I. Szapudi, The integrated Sachs-Wolfe effect in the AvERA cosmology, Mon. Not. R. Astron. Soc. 479 (3) (2018) 3582–3591, arXiv:1801.08566 [astro-ph.CO].

[15] W.L. Freedman, et al., The Carnegie-Chicago Hubble Program. VIII. An independent determination of the Hubble constant based on the tip of the red giant branch, Astrophys. J. 882 (2019) 34, arXiv:1907.05922 [astro-ph.CO].

[16] G.S. Anand, et al., Tip of the red giant branch distances with JWST: An absolute calibration in NGC 4258 and first applications to type Ia Supernova hosts, Astrophys. J. 966 (1) (2024) 89, arXiv:2401.04776 [astro-ph.CO].

[17] A.J. Lee, W.L. Freedman, I.S. Jang, B.F. Madore, K.A. Owens, First JWST observations of JAGB stars in the SN Ia host Galaxies: NGC 7250, NGC 4536, NGC 3972, Astrophys. J. 961 (1) (2024) 132, arXiv:2312.02282 [astro-ph.GA].

[18] S. Li, A.G. Riess, S. Casertano, G.S. Anand, D.M. Scolnic, W. Yuan, L. Breuval, C.D. Huang, Reconnaissance with JWST of the J-region asymptotic giant branch in distance ladder galaxies: From irregular luminosity functions to approximation of the Hubble constant, Astrophys. J. 966 (1) (2024) 20, arXiv:2401.04777 [astro-ph.CO].

[19] C.D. Huang, A.G. Riess, W. Yuan, L.M. Macri, N.L. Zakamska, S. Casertano, P.A. Whitelock, S.L. Hoffmann, A.V. Filippenko, D. Scolnic, Hubble space telescope observations of Mira variables in the type Ia supernova host NGC 1559: An alternative candle to measure the Hubble constant, Astrophys. J. 889 (2020) 5, arXiv:1908.10883 [astro-ph.CO].

[20] C.D. Huang, et al., The Mira distance to M101 and a 4% measurement of H $\alpha$, Astrophys. J. 963 (2) (2024) 83, arXiv:2312.08423 [astro-ph.CO].

[21] J.P. Blakeslee, J.B. Jensen, C.-P. Ma, P.A. Milne, J.E. Greene, The Hubble constant from infrared surface brightness fluctuation distances, Astrophys. J. 911 (1) (2021) 65, arXiv:2101.02221 [astro-ph.CO].

[22] G.S. Anand, R.B. Tully, Y. Cohen, D.I. Makarov, L.N. Makarova, J.B. Jensen, J.P. Blakeslee, M. Cantiello, E. Kourkchi, G. Raimondo, The population II extragalactic distance scale: A TRGB distance to the Fornax cluster with JWST, Astrophys. J. 973 (2) (2024) 83, arXiv:2405.03743 [astro-ph.CO].

[23] T. de Jaeger, L. Galbany, A.G. Riess, B.E. Stahl, B.J. Shappee, A.V. Filippenko, W. Zheng, A 5 per cent measurement of the Hubble–Lemaître constant from Type II supernovae, Mon. Not. R. Astron. Soc. 514 (3) (2022) 4620–4628, arXiv:2203.08974 [astro-ph.CO].

[24] G. Csörnyei, C. Vogl, S. Taubenberger, A. Flörs, S. Blondin, M.G. Cudmani, A. Holas, S. Kressierer, B. Leibundgut, W. Hillebrandt, Consistency of Type IIP supernova sibling distances, Astron. Astrophys. 672 (2023) A129, arXiv:2302.03112 [astro-ph.SR].

[25] E. Kourkchi, R.B. Tully, H.M. Courtois, A. Dupuy, D. Guinet, Cosmicflows-4: the baryonic Tully–Fisher relation providing ~10 000 distances, Mon. Not. R. Astron. Soc. 511 (4) (2022) 616–6178, arXiv:2201.13023 [astro-ph.GA].

[26] A.G. Riess, et al., JWST validates HST distance measurements: Selection of supernova subsample explains differences in JWST estimates of local H $\alpha$, Astrophys. J. 977 (1) (2024) 120, arXiv:2408.11770 [astro-ph.CO].

[27] HST Collaboration, W.L. Freedman, et al., Final results from the Hubble Space Telescope key project to measure the Hubble constant, Astrophys. J. 553 (2001) 47–72, arXiv:astro-ph/0012376.

[28] Gaia Collaboration, Gaia Data Release 3. Summary of the content and survey properties, Astron. Astrophys. 674 (2023) A1, arXiv:2208.00211 [astro-ph.GA].

[29] G. Pietrzyński, et al., A distance to the Large Magellanic Cloud that is precise to one per cent, Nature 567 (7747) (2019) 200–203.

[30] D. Graczyk, G. Pietrzyński, I.B. Thompson, W. Gieren, B. Zgirski, S. Villanova, M. Górski, P. Wielgórski, P. Karczmarek, W. Narloch, B. Pilecki, M. Taormina, R. Smolec, K. Suchomska, A. Gallenne, N. Nardetto, J. Storm, R.-P. Kudritzki, M. Kaluszyński, W. Pych, A distance determination to the small magellanic cloud with an accuracy of better than two percent based on late-type eclipsing binary stars, Astrophys. J. 904 (1) (2020) 13, arXiv:2010.08754 [astro-ph.GA].

[31] M.J. Reid, D.W. Pesce, A.G. Riess, An improved distance to NGC 4258 and its implications for the Hubble constant, Astrophys. J. Lett. 886 (2) (2019) L27, arXiv:1908.05625 [astro-ph.GA].

[32] D. Scolnic, et al., The Pantheon+ analysis: The full data set and light-curve release, Astrophys. J. 938 (2) (2022) 113, arXiv:2112.03863 [astro-ph.CO].

[33] D. Brout, et al., The Pantheon+ analysis: Cosmological constraints, Astrophys. J. 938 (2) (2022) 110, arXiv:2202.04077 [astro-ph.CO].

[34] A.G. Riess, et al., A comprehensive measurement of the local value of the Hubble constant with 1 km/s/Mpc uncertainty from the Hubble Space Telescope and the SHOES Team, Astrophys. J. Lett. 934 (1) (2022) L7, arXiv:2112.04510 [astro-ph.CO].

[35] L. Breuval, A.G. Riess, S. Casertano, W. Yuan, L.M. Macri, M. Romaniello, Y.S. Murakami, D. Scolnic, G.S. Anand, I. Soszyński, Small magellanic cloud cepheids observed with the Hubble space telescope provide a new anchor for the SHOES distance ladder, Astrophys. J. 973 (1) (2024) 30, arXiv:2404.08038 [astro-ph.CO].

[36] L. Galbany, et al., An updated measurement of the Hubble constant from near-infrared observations of Type Ia supernovae, Astron. Astrophys. 679 (2023) A95, arXiv:2209.02546 [astro-ph.CO].

[37] V. Scowcroft, W.L. Freedman, B.F. Madore, A. Monson, S.E. Persson, J. Rich, M. Seibert, J.R. Rigby, The Carnegie Hubble program: the distance and structure of the SMC as revealed by mid-infrared observations of cepheids, Astrophys. J. 816 (2) (2016) 49, arXiv:1502.06995 [astro-ph.GA].

[38] I. Soszyński, A. Udalski, M.K. Szymański, D. Skowron, G. Pietrzyński, R. Poleski, P. Pietrukowicz, J. Skowron, P. Mróz, S. Kozłowski, Ł. Wyrzykowski, K. Ulaczyk, M. Pawlak, The OGLE collection of variable stars. Classical cepheids in the Magellanic system, Acta Astron. 65 (4) (2015) 297–312, arXiv:1601.01318 [astro-ph.SR].

[39] V. Ripepi, M.-R.L. Cioni, M.I. Moretti, M. Marconi, K. Bekki, G. Clementini, R. de Grijs, J. Emerson, M.A.T. Groenewegen, V.D. Ivanov, R. Molinaro, T. Muraveva, J.M. Oliveira, A.E. Piatti, S. Subramanian, J.T. van Loon, The VMC survey - XXV. The 3D structure of the small magellanic cloud from classical cepheids, Mon. Not. R. Astro. Soc. 472 (1) (2017) 808–827, arXiv:1707.04500 [astro-ph.GA].

[40] S.A. Zhevakin, Physical basis of the pulsation theory of variable stars, Ann. Rev. Astron. Astrophys. 1 (1963) 367–400.

[41] J.P. Cox, Theory of Stellar Pulsation. (PSA-2), Volume 2, vol. 2, Princeton University Press, 1980.

[42] H.S. Leavitt, E.C. Pickering, Periods of 25 variable stars in the small magellanic cloud, Harv. Obs. Circ. 173 (1912) 1–3.

[43] H. Shapley, Studies based on the colors and magnitudes in stellar clusters. IX. Three notes on cepheid variation, Astrophys. J. 49 (1919) 24–41.
[44] S.L. Hoffmann, et al., Optical identification of cepheids in 19 host galaxies of type Ia supernovae and NGC 4258 with the Hubble Space Telescope, Astrophys. J. 830 (1) (2016) 10, arXiv:1607.08650 [astro-ph.SR].

[45] L. Inno, N. Matsunaga, M. Romaniello, G. Bono, A. Monson, I. Ferraro, G. Iannicola, E. Persson, R. Buonanno, W. Freedman, W. Gieren, M.A.T. Groenewegen, Y. Ita, C.D. Laney, B. Lemasle, B.F. Madore, T. Nagayama, Y. Nakada, M. Nonino, G. Pietrzyński, F. Primas, V. Scowcroft, I. Soszyński, T. Tanabé, A. Udalski, New NIR light-curve templates for classical Cepheids, Astron. Astrophys. 576 (2015) A30, arXiv:1410.5460 [astro-ph.SR].

[46] L. Breuval, A.G. Riess, L.M. Macri, S. Li, W. Yuan, S. Casertano, T. Konchady, B. Trahin, M.J. Durbin, B.F. Williams, A. 1.3% distance to M33 from Hubble Space Telescope cepheid photometry, Astrophys. J. 951 (2) (2023) 118, arXiv: 2304.00037 [astro-ph.CO].

[47] R.I. Anderson, On cepheid distances in the $H_0$ measurement, 2024, http://dx.doi.org/10.48550/arXiv.2403.02801, arXiv e-prints, arXiv:2403.02801, arXiv:2403.02801 [astro-ph.SR].

[48] A.G. Riess, S. Casertano, W. Yuan, L.M. Macri, D. Scolnic, Large magellanic cloud cepheid standards provide a 1% foundation for the determination of the Hubble constant and stronger evidence for physics beyond ΛCDM, Astrophys. J. 876 (1) (2019) 85, arXiv:1903.07603 [astro-ph.CO].

[49] A.G. Riess, G. Narayan, A. Calamida, Calibration of the WFC3-IR count-rate nonlinearity, sub-percent accuracy for a factor of a million in flux, 2019, p. 1, Instrument Science Report WFC3 2019-1, 13 pages.

[50] A.G. Riess, G.S. Anand, W. Yuan, S. Casertano, A. Dolphin, L.M. Macri, L. Breuval, D. Scolnic, M. Perrin, R.I. Anderson, Crowded no more: The accuracy of the Hubble constant tested with high-resolution observations of cepheids by JWST, Astrophys. J. Lett. 956 (1) (2023) L18, arXiv:2307.15806 [astro-ph.CO].

[51] A.G. Riess, G.S. Anand, W. Yuan, S. Casertano, A. Dolphin, L.M. Macri, L. Breuval, D. Scolnic, M. Perrin, I.R. Anderson, JWST observations reject unrecognized crowding of cepheid photometry as an explanation for the Hubble tension at $8\sigma$ confidence, Astrophys. J. Lett. 962 (1) (2024) L17, arXiv:2401.04773 [astro-ph.CO].

[52] R.C. Kennicutt Jr., et al., The HST key project on the extragalactic distance scale. 13. The metallicity dependence of the cepheid distance scale, Astrophys. J. 498 (1998) 181, arXiv:astro-ph/9712055.

[53] S. Sakai, L. Ferrarese, R. Kennicutt, A. Saha, The effect of metallicity on cepheid - based distances, Astrophys. J. 608 (2004) 42-61, arXiv:astro-ph/0402499.

[54] L.M. Macri, K.Z. Stanek, D. Bersier, L. Greenhill, M. Reid, A new cepheid distance to the maser-host galaxy NGC 4258 and its implications for the Hubble constant, Astrophys. J. 652 (2006) 1133-1149, arXiv:astro-ph/0608211.

[55] V. Ripepi, G. Catanzaro, R. Molinaro, M. Gatto, G. De Somma, M. Marconi, M. Romaniello, S. Leccia, I. Musella, E. Trentin, G. Clementini, V. Testa, F. Cusano, J. Storm, Cepheid metallicity in the Leavitt Law (C-metal) survey - I. HARPS-N@TNG spectroscopy of 47 classical cepheids and 1 BL her variables, Mon. Not. R. Astr. Soc. 508 (3) (2021) 4047-4071, arXiv:2108.11391 [astro-ph.GA].

[56] A. Bhardwaj, et al., High-resolution spectroscopic metallicities of Milky Way cepheid standards and their impact on the Leavitt Law and the Hubble constant, Astrophys. J. Lett. 955 (1) (2023) L13, arXiv:2309.03263 [astro-ph.SR].

[57] E. Trentin, V. Ripepi, R. Molinaro, G. Catanzaro, J. Storm, G. De Somma, M. Marconi, A. Bhardwaj, M. Gatto, V. Testa, I. Musella, G. Clementini, S. Leccia, Cepheid metallicity in the Leavitt Law (C-MetalL) survey. IV. The metallicity dependence of cepheid period-luminosity relations, Astron. Astrophys. 681 (2024) A65, arXiv:2310.03603 [astro-ph.SR].

[58] L. Breuval, A.G. Riess, P. Kervella, R.I. Anderson, M. Romaniello, An improved calibration of the wavelength dependence of metallicity on the cepheid Leavitt Law, Astrophys. J. 939 (2) (2022) 89, arXiv:2205.06280 [astro-ph.GA].

[59] R.I. Anderson, H. Saio, S. Ekström, C. Georgy, G. Meynet, On the effect of rotation on populations of classical cepheids II. Pulsation analysis for metallicities 0.014, 0.006, and 0.002, Astron. Astrophys. 591 (2016) A8, arXiv:1604.05691 [astro-ph.SR].

[60] G. De Somma, M. Marconi, R. Molinaro, V. Ripepi, S. Leccia, I. Musella, An updated metal-dependent theoretical scenario for classical cepheids, Astrophys. J. Suppl. 262 (1) (2022) 25, arXiv:2206.11154 [astro-ph.SR].

[61] B.F. Madore, The period-luminosity relation. IV - Intrinsic relations and reddensions for the large magellanic cloud cepheids, Astrophys. J. 253 (1982) 575-579.

[62] M. Romaniello, et al., The iron and oxygen content of LMC Classical Cepheids and its implications for the extragalactic distance scale and Hubble constant - Equivalent width analysis with Kurucz stellar atmosphere models, Astron. Astrophys. 658 (2022) A29, arXiv:2110.08860 [astro-ph.CO]; Erratum: Astron. Astrophys. 662 (2022) C1.

[63] D. Zaritsky, R.C. Kennicutt, J.P. Huchra, H II regions and the abundance properties of spiral galaxies, Astrophys. J. 420 (1994) 87.

[64] A.G. Riess, W.-D. Li, P.B. Stetson, A.V. Filippenko, S. Jha, R.P. Kirshner, P.M. Challis, P.M. Garnavich, R. Chornock, Cepheid calibrations from the Hubble Space Telescope of the luminosity of two recent type Ia supernovae and a re-determination of the Hubble constant, Astrophys. J. 627 (2005) 579-607, arXiv:astro-ph/0503159.

[65] A.G. Riess, et al., Cepheid calibrations of modern type Ia supernovae: Implementations for the Hubble constant, Astrophys. J. Suppl. 183 (2009) 109-141, arXiv:0905.0697 [astro-ph.CO].

[66] L. Galbany, et al., Nearby supernova host galaxies from the CALIFA Survey: II. SN environmental metallicity, Astron. Astrophys. 591 (2016) A48, arXiv:1603.07808 [astro-ph.GA].

[67] P. Kervella, A. Gallenne, N. Remage Evans, L. Szabados, F. Arenou, A. Mérand, Y. Proto, P. Karczmarek, N. Nardetto, W. Gieren, G. Pietrzyński, Multiplicity of Galactic Cepheids and RR Lyrae stars from Gaia DR2. I. Binarity from proper motion anomaly, Astron. Astrophys. 623 (2019) A116, arXiv:1903.03632 [astro-ph.SR].

[68] P. Karczmarek, G. Hajdu, G. Pietrzyński, W. Gieren, W. Narloch, R. Smolec, G. Wiktorowicz, K. Belczynski, Synthetic population of binary cepheids. II. The effect of companion light on the extragalactic distance scale, Astrophys. J. 950 (2) (2023) 182, arXiv:2303.15664 [astro-ph.GA].

[69] R.I. Anderson, A.G. Riess, On cepheid distance scale bias due to stellar companions and cluster populations, Astrophys. J. 861 (1) (2018) 36, arXiv:1712.01065 [astro-ph.SR].

[70] B.J. Mochejska, L.M. Macri, D.D. Sasselov, K.Z. Stanek, The direct project: influence of blending on the cepheid distance scale. I. Cepheids in m31, Astron. J. 120 (2000) 810, arXiv:astro-ph/9908293.

[71] B. Follin, L. Knox, Insensitivity of the distance ladder Hubble constant determination to Cepheid calibration modelling choices, Mon. Not. R. Astron. Soc. 477 (4) (2018) 4534-4542, arXiv:1707.01175 [astro-ph.CO].

[72] L. Perivolaropoulos, F. Skara, Hubble tension or a transition of the cepheid Sna calibrator parameters? Phys. Rev. D 104 (12) (2021) 123511, arXiv:2109.04406 [astro-ph.CO].

[73] C. Hahn, T.K. Starkenburg, D. Anglés-Alcázar, E. Choi, R. Davé, C. Dickey, K.G. Iyer, A.H. Maller, R.S. Somerville, J.L. Tinker, L.Y.A. Yung, IQ collaboratory. III. The empirical dust attenuation framework-taking hydrodynamical simulations with a grain of dust, Astrophys. J. 926 (2) (2022) 122, arXiv:2106.09741 [astro-ph.GA].

[74] G.F. Benedict, B.E. McArthur, M.W. Feast, T.G. Barnes, T.E. Harrison, R.J. Patterson, J.W. Menzies, J.J. Bean, W.L. Freedman, Hubble space telescope fine guidance sensor parallaxes of galactic cepheid variable stars: Period-luminosity relations, Astron. J. 133 (2007) 1810-1827, arXiv:astro-ph/0612465; Erratum: Astron. J. 133 (2007) 2980.

[75] S. Casertano, et al., Parallax of galactic cepheids from spatially scanning the wide field camera 3 on the Hubble Space Telescope: The Case of SS Canis Majoris, Astrophys. J. 825 (1) (2016) 11, arXiv:1512.09371 [astro-ph.SR].

[76] A.G. Riess, et al., New parallaxes of galactic cepheids from spatially scanning the Hubble space telescope: Implications for the Hubble constant, Astrophys. J. 855 (2) (2018) 136, arXiv:1801.01120 [astro-ph.SR].

[77] L. Lindegren, U. Bastian, M. Biermann, A. Bombrun, A. de Torres, E. Gerlach, R. Geyer, J. Hernández, T. Hilger, D. Hobbs, S.A. Klioner, U. Lammers, P.J. McMillan, M. Ramos-Lerate, H. Steidelmüller, C.A. Stephenson, F. van Leeuwen, Gaia early data release 3. Parallax bias versus magnitude, colour, and position, Astron. Astrophys. 649 (2021) A4, arXiv:2012.01742 [astro-ph.IM].

[78] A.G. Riess, S. Casertano, W. Yuan, J.B. Bowers, L. Macri, J.C. Zinn, D. Scolnic, Cosmic distances calibrated to 1% precision with Gaia EDR3 parallaxes and Hubble Space Telescope photometry of 75 Milky Way Cepheids confirm tension with ΛCDM, Astrophys. J. Lett. 908 (1) (2021) L6, arXiv:2012.08534 [astro-ph.CO].

[79] S. Li, S. Casertano, A.G. Riess, A maximum likelihood calibration of the tip of the red giant branch luminosity from high latitude field giants using Gaia early data release 3 parallaxes, Astrophys. J. 939 (2) (2022) 96, arXiv:2202.11110 [astro-ph.GA].

[80] R.I. Anderson, L. Eyer, N. Mowlavi, Cepheids in open clusters: An 8-D all-sky census, Mon. Not. R. Astron. Soc. 434 (2013) 2238, arXiv:1212.5119 [astro-ph.GA].

[81] L. Breuval, et al., The Milky Way cepheid Leavitt Law based on Gaia DR2 parallaxes of companion stars and host open cluster populations, Astron. Astrophys. 643 (2020) A115, arXiv:2006.08763 [astro-ph.SR].

[82] A.G. Riess, L. Breuval, W. Yuan, S. Casertano, L.M. Macri, J.B. Bowers, D. Scolnic, T. Cantat-Gaudin, R.I. Anderson, M.C. Reyes, Cluster cepheids with high precision Gaia parallaxes, low zero-point uncertainties, and Hubble Space Telescope photometry, Astrophys. J. 938 (1) (2022) 36, arXiv:2208.01045 [astro-ph.CO].

[83] M.C. Reyes, R.I. Anderson, A 0.9% calibration of the galactic cepheid luminosity scale based on Gaia DR3 data of open clusters and cepheids, Astron. Astrophys. 672 (2023) A85, arXiv:2208.09403 [astro-ph.GA].

[84] W. Yuan, L.M. Macri, A.G. Riess, T.G. Brink, S. Casertano, A.V. Filippenko, S.L. Hoffmann, C.D. Huang, D. Scolnic, Absolute calibration of cepheid Period-Luminosity relations in NGC 4258, Astrophys. J. 940 (1) (2022) 64, arXiv:2203.06681 [astro-ph.GA].

[85] S. Li, A.G. Riess, M.P. Busch, S. Casertano, L.M. Macri, W. Yuan, A sub-2% distance to M31 from photometrically homogeneous near-infrared cepheid Period-Luminosity relations measured with the Hubble Space Telescope, Astrophys. J. 920 (2) (2021) 84, arXiv:2107.08029 [astro-ph.CO].
[86] A.L. Argon, L.J. Greenhill, J.M. Moran, M.J. Reid, K.M. Menten, M. Inoue, The IC133 water vapor maser in the galaxy M33: A geometric distance, Astrophys. J. 615 (2004) 702–719, arXiv:astro-ph/0407486.

[87] A.Z. Bonanos, et al., The first DIRECT distance determination to a detached eclipsing binary in M33, Astrophys. J. 652 (2006) 313–322, arXiv:astro-ph/0606279.

[88] M. Taormina, R.-P. Kudritzki, J. Puls, B. Pilecki, E. Sextl, G. Pietrzyński, M.A. Urbaneja, W. Gieren, Toward early-type eclipsing binaries as extragalactic milestones. II. NLTE spectral analysis and stellar parameters of the detached O-type system OGLE-LMC-ECL-06782 in the LMC, Astrophys. J. 890 (2) (2020) 137, arXiv:2001.04762 [astro-ph.SR].

[89] A. Salsi, N. Nardetto, D. Mourard, D. Graczyk, M. Taormina, O. Creevey, V. Hocdé, F. Morand, K. Perraut, G. Pietrzyński, G.H. Schaefer, Progress on the calibration of surface brightness-color relations for early- and late-type stars, Astron. Astrophys. 652 (2021) A26, arXiv:2106.01073 [astro-ph.SR].

[90] C.-C. Ngeow, A. Bhardwaj, J.-Y. Henderson, M.J. Graham, R.R. Laher, M.S. Medford, J. Purdum, B. Rusholme, Zwicky transient facility and globular clusters: The period-luminosity and period-wesenheit relations for Type II Cepheids, Astrophys. J. 164 (4) (2022) 154, arXiv:2208.03404 [astro-ph.SR].

[91] W. Narloch, G. Hajdu, G. Pietrzyński, W. Gieren, P. Wielgórski, B. Zgirski, P. Karczmarek, M. Górski, D. Graczyk, Period-luminosity relations for galactic classical cepheids in the sloan bands, Astrophys. J. 953 (1) (2023) 14, arXiv:2306.06326 [astro-ph.GA].

[92] F. Bresolin, W. Gieren, R.-P. Kudritzki, G. Pietrzyński, M.A. Urbaneja, G. Carraro, Extragalactic chemical abundances: do HII regions and young stars tell the same story? The case of the spiral galaxy NGC 300, Astrophys. J. 700 (2009) 309–330, arXiv:0905.2791 [astro-ph.CO].

[93] F. Bresolin, R.-P. Kudritzki, M.A. Urbaneja, The metallicity and distance of NGC 2403 from blue supergiants, Astrophys. J. 940 (1) (2022) 32, arXiv:2209.13135 [astro-ph.GA].

[94] C.-C. Ngeow, S.M. Kanbur, S. Nikolaev, J. Buonaccorsi, K.H. Cook, D.L. Welch, Further empirical evidence for the non-linearity of the period-luminosity relations as seen in the Large Magellanic cloud Cepheids, Mon. Not. R. Astron. Soc. 363 (2005) 831–846, arXiv:astro-ph/0507601.

[95] A. Sandage, G.A. Tammann, B. Reindl, New period-luminosity and period-color relations of classical Cepheids: III. Cepheids in SMC, Astron. Astrophys. 493 (2009) 471–479, arXiv:0810.1780 [astro-ph].

[96] M. Kodric, et al., Properties of M31. II: A cepheid disk sample derived from the first year of PS1 PAndromeda data, AJ 145 (2013) 106, arXiv:1301.6170 [astro-ph.CO].

[97] A. Bhardwaj, S.M. Kanbur, L.M. Macri, H.P. Singh, C.-C. Ngeow, E.E.O. Ishida, Large magellanic cloud near-infrared synoptic survey - III. A statistical study of non-linearity in the Leavitt Laws, Mon. Not. R. Astro. Soc. 457 (2) (2016) 1644–1665, arXiv:1601.00953 [astro-ph.GA].

[98] D. Kushnir, A. Sharon, A cepheid systematics-free test of $H_0$ to $\le 2.5\%$ accuracy using SH0ES photometry, 2024, arXiv:2404.16102 [astro-ph.CO].

[99] C. Kuo, J.A. Braatz, M.J. Reid, F.K.Y. Lo, J.J. Condon, C.M.V. Impellizzeri, C. Henkel, The megamaser cosmology project. V. An angular diameter distance to NGC 6264 at 140 Mpc, Astrophys. J. 767 (2013) 155, arXiv:1207.7273 [astro-ph.CO].

[100] C.Y. Kuo, J.A. Braatz, K.Y. Lo, M.J. Reid, S.H. Suyu, D.W. Pesce, J.J. Condon, C. Henkel, C.M.V. Impellizzeri, The megamaser cosmology project. VI. Observations of NGC 6323, Astrophys. J. 800 (1) (2015) 26, arXiv:1411.5106 [astro-ph.GA].

[101] B. Cooke, M. Elitzur, Water masers in late-type stars, Astrophys. J. 295 (1985) 175–182.

[102] K.Y. Lo, Mega-masers and galaxies, Annu. Rev. Astron. Astrophys. 43 (1) (2005) 625–676.

[103] A.L. Argon, L.J. Greenhill, M.J. Reid, J.M. Moran, E.M.L. Humphreys, Toward a new geometric distance to the active galaxy NGC4258. I. VLBI monitoring of water maser emission, Astrophys. J. 659 (2007) 1040–1062, arXiv:astro-ph/0701396.

[104] J. Kormendy, L.C. Ho, Coevolution (or not) of supermassive black holes and host galaxies, Ann. Rev. Astron. Astrophys. 51 (2013) 511–653, arXiv:1304.7762 [astro-ph.CO].

[105] J.R. Herrnstein, J.M. Moran, L.J. Greenhill, P.J. Diamond, M. Inoue, N. Nakai, M. Miyoshi, C. Henkel, A. Riess, A geometric distance to the galaxy NGC 4258 from orbital motions in a nuclear gas disk, Nature 400 (1999) 539–541, arXiv:astro-ph/9907013.

[106] C.Y. Kuo, J.A. Braatz, J.J. Condon, C.M.V. Impellizzeri, K.Y. Lo, I. Zaw, M. Schenker, C. Henkel, M.J. Reid, J.E. Greene, The megamaser cosmology project. III. Accurate masses of seven supermassive black holes in active galaxies with circumnuclear megamaser disks, Astrophys. J. 727 (2011) 20, arXiv:1008.2146 [astro-ph.CO].

[107] F. Gao, J.A. Braatz, M.J. Reid, J.J. Condon, J.E. Greene, C. Henkel, C.M.V. Impellizzeri, K.Y. Lo, C.Y. Kuo, D.W. Pesce, J. Wagner, W. Zhao, The megamaser cosmology project. IX. Black hole masses for three maser galaxies, Astrophys. J. 834 (1) (2017) 52, arXiv:1610.06802 [astro-ph.GA].

[108] M.J. Reid, J.A. Braatz, J.J. Condon, K.Y. Lo, C.Y. Kuo, C.M.V. Impellizzeri, C. Henkel, The megamaser cosmology project: IV. A direct measurement of the Hubble constant from UGC 3789, Astrophys. J. 767 (2013) 154, arXiv:1207.7292 [astro-ph.CO].

[109] F. Gao, J.A. Braatz, M.J. Reid, K.Y. Lo, J.J. Condon, C. Henkel, C.Y. Kuo, C.M.V. Impellizzeri, D.W. Pesce, W. Zhao, The megamaser cosmology project VIII. A geometric distance to NGC 5765b, Astrophys. J. 817 (2) (2016) 128, arXiv:1511.08311 [astro-ph.GA].

[110] D.W. Pesce, et al., The megamaser cosmology project. XIII. Combined Hubble constant constraints, Astrophys. J. Lett. 891 (1) (2020) L1, arXiv:2001.09213 [astro-ph.CO].

[111] M.J. Reid, J.A. Braatz, J.J. Condon, L.J. Greenhill, C. Henkel, K.Y. Lo, The megamaser cosmology project: I. VLBI observations of UGC 3789, Astrophys. J. 695 (2009) 287–291, arXiv:0811.4345 [astro-ph].

[112] J.A. Braatz, M.J. Reid, E.M.L. Humphreys, C. Henkel, J.J. Condon, K.Y. Lo, The megamaser cosmology Project. II. The angular-diameter distance to UGC 3789, Astrophys. J. 718 (2010) 657–665, arXiv:1005.1955 [astro-ph.CO].

[113] C.Y. Kuo, A. Constantin, J.A. Braatz, H.H. Chung, C.A. Witherspoon, D. Pesce, C.M.V. Impellizzeri, F. Gao, L. Hao, J.H. Woo, I. Zaw, Enhancing the H₂O megamaser detection rate using optical and mid-infrared photometry, Astrophys. J. 860 (2) (2018) 169, arXiv:1712.04204 [astro-ph.GA].

[114] C.Y. Kuo, J.Y. Hsiang, H.H. Chung, A. Constantin, Y.Y. Chang, E.d. Cunha, D. Pesce, W.T. Chien, B.Y. Chen, J.A. Braatz, I. Zaw, S. Matsushita, J.C. Lin, A more efficient search for H₂O megamaser galaxies: the power of X-ray and mid-infrared photometry, Astrophys. J. 892 (1) (2020) 18, arXiv:1911.10721 [astro-ph.GA].

[115] D.W. Pesce, J.A. Braatz, J.J. Condon, F. Gao, C. Henkel, E. Litzinger, K.Y. Lo, M.J. Reid, The megamaser cosmology project. VII. Investigating disk physics using spectral monitoring observations, Astrophys. J. 810 (1) (2015) 65, arXiv:1507.07904 [astro-ph.GA].

[116] A.E. Bragg, L.J. Greenhill, J.M. Moran, C. Henkel, Accelerations of water masers in ngc4258, Astrophys. J. 535 (2000) 73, arXiv:astro-ph/0001543.

[117] E.M.L. Humphreys, M.J. Reid, L.J. Greenhill, J.M. Moran, A.L. Argon, Toward a new distance to the active galaxy ngc 4258: II. Centripetal accelerations and investigation of spiral structure, Astrophys. J. 672 (2008) 800–816, arXiv:0709.0925 [astro-ph].

[118] J. Braatz, D. Pesce, J. Condon, M. Reid, H₂O megamaser cosmology with the ngvLAI, Bull. Am. Astron. Soc. 51 (3) (2019) 446.

[119] M.G. Lee, W.L. Freedman, B.F. Madore, The tip of the red giant branch as a distance indicator for resolved galaxies, Astrophys. J. 417 (1993) 553.

[120] J.B. Jensen, J.P. Blakeslee, M. Cantiello, M. Cowles, G.S. Anand, R.B. Tully, E. Kourkchi, G. Raimondo, The TRGB-SBF Project. III. Refining the hst surface brightness fluctuation distance scale calibration with JWST, 2025, arXiv:2502.15935 [astro-ph.CO].

[121] G.S. Anand, R.B. Tully, L. Rizzi, A.G. Riess, W. Yuan, Comparing tip of the red giant branch distance scales: An independent reduction of the Carnegie-Chicago Hubble program and the value of the Hubble constant, Astrophys. J. 932 (1) (2022) 15, arXiv:2108.00007 [astro-ph.CO].

[122] D. Scolnic, A.G. Riess, J. Wu, S. Li, G.S. Anand, R. Beaton, S. Casertano, R.I. Anderson, S. Dhawan, X. Ke, CATS: The Hubble constant from standardized TRGB and type Ia supernova measurements, Astrophys. J. Lett. 954 (1) (2023) L31, arXiv:2304.06693 [astro-ph.CO].

[123] S. Li, R.L. Beaton, The tip of the red giant branch distance ladder and the Hubble constant, 2024, arXiv:2403.17048 [astro-ph.CO].

[124] J.B. Jensen, et al., Infrared surface brightness fluctuation distances for massive and type Ia supernova host galaxies, Astrophys. J. Supp. 255 (2) (2021) 21, arXiv:2105.08299 [astro-ph.CO].

[125] J. Wu, D. Scolnic, A.G. Riess, G.S. Anand, R. Beaton, S. Casertano, X. Ke, S. Li, Comparative analysis of TRGBs (CATs) from unsupervised, multi-halo-field measurements: Contrast is key, Astrophys. J. 954 (1) (2023) 87, arXiv:2211.06354 [astro-ph.CO].

[126] R.I. Anderson, N.W. Koblishchke, L. Eyer, Small-amplitude red giants elucidate the nature of the tip of the red giant branch as a standard candle, Astrophys. J. Lett. 963 (2) (2024) L43, arXiv:2303.04790 [astro-ph.CO].

[127] D. Hatt, et al., The Carnegie-Chicago Hubble Program. II. The distance to IC 1613: The tip of the red giant branch and RR Lyrae Period-luminosity relations, Astrophys. J. 845 (2) (2017) 146, arXiv:1703.06468 [astro-ph.CO].

[128] S. Nikolaev, M.D. Weinberg, Stellar populations in the large magellanic cloud from 2mass, Astrophys. J. 542 (2000) 804–818, arXiv:astro-ph/0003012.

[129] B.F. Madore, W.L. Freedman, Astrophysical distance scale: The AGB J-band method. I. Calibration and a first application, Astrophys. J. 899 (1) (2020) 66, arXiv:2005.10792 [astro-ph.GA].

[130] R.I. Anderson, The span of space, Nat. Phys. 20 (11) (2024) 1841–1841.

[131] J. Tang, A. Bressan, P. Rosenfield, A. Slemer, P. Marigo, L. Girardi, L. Bianchi, New PARSEC evolutionary tracks of massive stars at low metallicity: testing canonical stellar evolution in nearby star-forming dwarf galaxies, Mon. Not. R. Astro. Soc. 445 (4) (2014) 4287–4305, arXiv:1410.1745 [astro-ph.SR].

[132] Y. Chen, A. Bressan, L. Girardi, P. Marigo, X. Kong, A. Lanza, PARSEC evolutionary tracks of massive stars up to 350 M☉ at metallicities 0.0001 $\le Z \le 0.04$, Mon. Not. R. Astro. Soc. 452 (1) (2015) 1068–1080, arXiv:1506.01681 [astro-ph.SR].
[133] M. Salaris, S. Cassisi, The tip of the red giant branch as a distance indicator: results from evolutionary models, Mon. Not. R. Astron. Soc. 289 (1997) 406, arXiv:astro-ph/9703186.

[134] M. Salaris, S. Cassisi, A. Weiss, Red giant branch stars: the theoretical framework, Publ. Astron. Soc. Pac. 114 (2002) 375, arXiv:astro-ph/0201387.

[135] M. Salaris, S. Cassisi, Evolution of Stars and Stellar Populations, Wiley, 2005.

[136] S. Cassisi, M. Salaris, Old Stellar Populations: How to Study the Fossil Record of Galaxy Formation, Wiley-VCH Verlag GmbH, 2013.

[137] A. Serenelli, A. Weiss, S. Cassisi, M. Salaris, A. Pietrinferni, The brightness of the red giant branch tip. theoretical framework, a set of reference models, and predicted observables, Astron. Astrophys. 606 (2017) A33, arXiv:1706.09910 [astro-ph.SR].

[138] L. Rizzi, R.B. Tully, D. Makarov, L. Makarova, A.E. Dolphin, S. Sakai, E.J. Shaya, Tip of the red giant branch distances. 2. Zero-point calibration, Astrophys. J. 661 (2007) 815-829, arXiv:astro-ph/0701518.

[139] I.S. Jang, M.G. Lee, The tip of the red giant branch distances to type Ia supernova host galaxies. IV. Color dependence and zero-point calibration, Astrophys. J. 835 (1) (2017) 28, arXiv:1611.05040 [astro-ph.GA].

[140] E. Farag, F.X. Timmes, M.T. Chidester, S. Anandagoda, D.H. Hartmann, Stellar neutrino emission across the Mass-Metallicity plane, Astrophys. J. Suppl. 270 (1) (2024) 5, arXiv:2310.13142 [astro-ph.SR].

[141] S. Cassisi, Modelling of red giant stars: The state-of-the-art, Eur. Phys. J. Web Conf. 160 (2017) 04002.

[142] I.D. Saltas, E. Tognelli, New calibrated models for the tip of the red giant branch luminosity and a thorough analysis of theoretical uncertainties, Mon. Not. R. Astron. Soc. 514 (2) (2022) 3058-3073, arXiv:2203.02499 [astro-ph.SR].

[143] Gaia Collaboration, T. Prusti, et al., The Gaia mission, Astron. Astrophys. 595 (Gaia Data Release 1) (2016) A1, arXiv:1609.04153 [astro-ph.IM].

[144] W.L. Freedman, Measurements of the Hubble constant: Tensions in perspective, Astrophys. J. 919 (1) (2021) 16, arXiv:2106.15656 [astro-ph.CO].

[145] B.F. Madore, W.L. Freedman, K. Owens, Astrophysical distance scale VII: A self-consistent, multi-wavelength calibration of the slopes and relative zero points for the run of luminosity with color of stars defining the tip of the red giant branch, 2023, arXiv:2311.05048 [astro-ph.GA].

[146] G. Csörnyei, R.I. Anderson, C. Vogl, S. Taubenberger, S. Blondin, B. Leibundgut, W. Hillebrandt, Reeling in the Whirlpool galaxy: Distance to M 51 clarified through Cepheids and the Type IIP supernova 2005cs, Astron. Astrophys. 678 (2023) A44, arXiv:2305.13943 [astro-ph.GA].

[147] N.W. Kobleschke, R.I. Anderson, Calibrating and standardizing the tip of the red giant branch in the small magellanic cloud using small-amplitude red giants, Astrophys. J. 974 (2) (2024) 181, arXiv:2406.19375 [astro-ph.SR].

[148] S. Li, S. Casertano, A.G. Riess, A Gaia data release 3 view on the tip of the red giant branch luminosity, Astrophys. J. 950 (2) (2023) 83, arXiv:2304.06695 [astro-ph.GA].

[149] J. Maŕz Apellániz, M. Pantaleoni González, R.H. Barbá, Validation of the accuracy and precision of Gaia EDR3 parallaxes with globular clusters, Astron. Astrophys. 649 (2021) A13, arXiv:2101.10206 [astro-ph.IM].

[150] Y. Huang, H. Yuan, T.C. Beers, H. Zhang, The parallax zero-point of Gaia early data release 3 from LAMOST primary red clump stars, Astrophys. J. Lett. 910 (1) (2021) L5, arXiv:2101.09691 [astro-ph.GA].

[151] F. Ren, X. Chen, H. Zhang, R. de Grijs, L. Deng, Y. Huang, Gaia EDR3 parallax zero-point offset based on W Ursae majoris-type eclipsing binaries, Astrophys. J. Lett. 911 (2) (2021) L20, arXiv:2103.16096 [astro-ph.SR].

[152] S. Khan, R.I. Anderson, A. Miglio, B. Mosser, Y.P. Elsworth, Investigating Gaia EDR3 parallax systematics using asteroseismology of cool giant stars observed by Kepler, K2, and TESS. II. Deciphering Gaia parallax systematics using red clump stars, Astron. Astrophys. 680 (2023) A105, arXiv:2310.03654 [astro-ph.SR].

[153] J. Soltis, S. Casertano, A.G. Riess, The parallax of ω centauri measured from Gaia EDR3 and a direct, geometric calibration of the tip of the red giant branch and the Hubble constant, Astrophys. J. Lett. 908 (1) (2021) L5, arXiv:2012.09196 [astro-ph.GA].

[154] S. Jang, A.P. Milone, E.P. Lagioia, M. Tailo, M. Carlos, E. Dondoglio, M. Martorano, A. Mohandasan, A.F. Marino, G. Cordoni, Y.W. Lee, Integrated photometry of multiple stellar populations in globular clusters, Astrophys. J. 920 (2) (2021) 129, arXiv:2107.14246 [astro-ph.GA].

[155] D.M. Skowron, J. Skowron, A. Udalski, M.K. Szymański, I. Soszyński, L. Wyrzykowski, K. Ulaczyk, R. Poleski, S. Kozłowski, P. Pietrukowicz, P. Mróz, K. Rybicki, P. Iwanek, M. Wrona, M. Gromadzki, OGLE-ing the magellanic system: Optical reddening maps of the large and small magellanic clouds from red clump stars, Astrophys. J. Suppl. 252 (2) (2021) 23, arXiv:2006.02448 [astro-ph.SR].

[156] D.J. Schlegel, D.P. Finkbeiner, M. Davis, Maps of dust IR emission for use in estimation of reddening and CMBR foregrounds, Astrophys. J. 500 (1998) 525, arXiv:astro-ph/9710327.

[157] E.F. Schlafly, D.P. Finkbeiner, Measuring reddening with SDSS Stellar spectra and recalibrating SFD, Astrophys. J. 737 (2011) 103, arXiv:1012.4804 [astro-ph.GA].

[158] R.I. Anderson, Relativistic corrections for measuring Hubble's constant to 1% using stellar standard candles, Astron. Astrophys. 658 (2022) A148, arXiv:2108.09067 [astro-ph.CO].

[159] J.E.G. Peek, B. Ménard, L. Corrales, Dust in the circumgalactic medium of low-redshift galaxies, Astrophys. J. 813 (1) (2015) 7, arXiv:1411.3333 [astro-ph.GA].

[160] B. Mendez, M. Davis, J. Moustakas, J. Newman, B.F. Madore, W.L. Freedman, Deviations from the local Hubble flow. 1. The tip of the red giant branch as a distance indicator, Astron. J. 124 (2002) 213, arXiv:astro-ph/0204192.

[161] D. Makarov, L. Makarova, L. Rizzi, R.B. Tully, A.E. Dolphin, S. Sakai, E.J. Shaya, Tip of the red giant branch distances. 1. optimization of a maximum likelihood algorithm, Astron. J. 132 (2006) 2729-2742, arXiv:astro-ph/0603073.

[162] B.F. Madore, V. Mager, W.L. Freedman, Sharpening the tip of the red giant branch, Astrophys. J. 690 (2009) 389-393, arXiv:0809.2598 [astro-ph].

[163] R.L. Beaton, G. Bono, V.F. Braga, M. Dall'Ora, G. Fiorentino, I.S. Jang, C.E. Martínez-Vázquez, N. Matsunaga, M. Monelli, J.R. Neeley, M. Salaris, Old-aged primary distance indicators, Space Sci. Rev. 214 (8) (2018) 113, arXiv:1808.09191 [astro-ph.GA].

[164] Euclid Collaboration, Y. Mellier, et al., Euclid. i. Overview of the Euclid mission, 2024, arXiv:2405.13491 [astro-ph.CO].

[165] M.J.B. Newman, K.B.W. McQuinn, E.D. Skillman, M.L. Boyer, R.E. Cohen, A.E. Dolphin, O.G. Telford, An empirical calibration of the tip of the red giant branch distance method in the near infrared. I. Hubble Space Telescope WFC3/IR F110W and F160W filters, Astrophys. J. 966 (2) (2024) 175, arXiv:2403.03086 [astro-ph.GA].

[166] M.J.B. Newman, K.B.W. McQuinn, E.D. Skillman, M.L. Boyer, R.E. Cohen, A.E. Dolphin, O.G. Telford, An empirical calibration of the tip of the red giant branch distance method in the near infrared. II. JWST NIRCam wide filters, Astrophys. J. 975 (2) (2024) 195, arXiv:2406.03532 [astro-ph.CO].

[167] E. Valenti, F.R. Ferraro, L. Origlia, The red giant branch in the near - infrared color - magnitude diagrams. 1: The calibration of photometric indices, Mon. Not. R. Astron. Soc. 351 (2004) 1204, arXiv:astro-ph/0403563.

[168] J.J. Dalcanton, et al., Resolved near-infrared stellar populations in nearby galaxies, Astrophys. J. Suppl. 198 (2012) 6, arXiv:1109.6893 [astro-ph.CO].

[169] P.-F. Wu, R.B. Tully, L. Rizzi, A.E. Dolphin, B.A. Jacobs, I.D. Karachentsev, Infrared tip of the red giant branch and distances to the Maffei/IC 342 group, Astron. J. 148 (2014) 7, arXiv:1404.2987 [astro-ph.GA].

[170] B.F. Madore, et al., The near-infrared tip of the red giant branch. I. A calibration in the isolated dwarf Galaxy IC 1613, Astrophys. J. 858 (1) (2018) 11, arXiv:1803.01278 [astro-ph.GA].

[171] T.J. Hoyt, W.L. Freedman, B.F. Madore, M. Seibert, R.L. Beaton, D. Hatt, I.S. Jang, M.G. Lee, A.J. Monson, J.A. Rich, The near-infrared tip of the red giant branch. II. An absolute calibration in the large magellanic cloud, Astrophys. J. 858 (1) (2018) 12, arXiv:1803.01277 [astro-ph.GA].

[172] M.J. Durbin, R.L. Beaton, J.J. Dalcanton, B.F. Williams, M.L. Boyer, MCR-TRGB: A multiwavelength-covariant, robust tip of the red giant branch measurement method, Astrophys. J. 898 (1) (2020) 57, arXiv:2006.08559 [astro-ph.GA].

[173] K.B.W. McQuinn, M. Boyer, E.D. Skillman, A.E. Dolphin, Using the tip of the red giant branch as a distance indicator in the near infrared, Astrophys. J. 880 (1) (2019) 63, arXiv:1904.01571 [astro-ph.GA].

[174] W.L. Freedman, B.F. Madore, I.S. Jang, T.J. Hoyt, A.J. Lee, K.A. Owens, Status report on the Chicago-Carnegie Hubble program (CCHP): Three independent astrophysical determinations of the Hubble constant using the James Webb space telescope, 2024, arXiv:2408.06153 [astro-ph.CO].

[175] Gaia Collaboration, Gaia data release 3. The galaxy in your preferred colours: Synthetic photometry from Gaia low-resolution spectra, Astron. Astrophys. 674 (2023) A33, arXiv:2206.06215 [astro-ph.SR].

[176] D.R. Weisz, et al., The JWST resolved stellar populations early release science program. II. Survey overview, Astrophys. J. Suppl. 268 (1) (2023) 15, arXiv:2301.04659 [astro-ph.GA].

[177] A.J. Lee, L. Rousseau-Nepton, W.L. Freedman, B.F. Madore, M.-R.L. Cioni, T.J. Hoyt, I.S. Jang, A. Javadi, K.A. Owens, The astrophysical distance scale. V. A 2% distance to the local group spiral M33 via the JAGB method, tip of the red giant branch, and Leavitt Law, Astrophys. J. 933 (2) (2022) 201, arXiv:2205.11323 [astro-ph.GA].

[178] J. Tonry, D.P. Schneider, A new technique for measuring extragalactic distances, Astron. J. 96 (1988) 807.

[179] J.L. Tonry, E.A. Ajhar, G.A. Luppino, Observations of surface-brightness fluctuations in virgo, Astron. J. 100 (1990) 1416.

[180] J.P. Blakeslee, A. Jordan, S. Mei, P. Cote, L. Ferrarese, L. Infante, E.W. Peng, J.L. Tonry, M.J. West, The ACS Fornax Cluster Survey. V. Measurement and recalibration of surface brightness fluctuations and a precise value of the Fornax-Virgo relative distance, Astrophys. J. 694 (2009) 556-572, arXiv:0901.1138 [astro-ph.CO].

[181] J.B. Jensen, J.P. Blakeslee, Z. Gibson, H.-c. Lee, M. Cantiello, G. Raimondo, N. Boyer, H. Cho, Measuring infrared surface brightness fluctuation distances with HST WFC3: Calibration and advice, Astrophys. J. 808 (1) (2015) 91, arXiv:1505.00400 [astro-ph.GA].