<figure><img src="image_47.png" /><figcaption>**Fig. 45.** SFR-stellar mass diagram. The points represent the photometric sample, divided into star-forming (in blue) and passive galaxies (in red). Galaxy type was assigned as a function of mass and redshift from the stellar mass function (SMF) by Peng et al. (2010) and Ilbert et al. (2013). The coloured contours highlight the spectroscopic sample (for the EWS in the case of star-forming galaxies in blue, and for the EDS in the case of passive galaxies, in red). The two insets show two examples of star-forming and passive galaxies as observed in the EDS, comprising both the blue and the red grisms, simulated from the MAMBO mock catalogue (Girelli 2021) taking into account all instrumental and observational effects.</figcaption></figure>

data available in the archives (e.g. XMM-Newton and Chandra), will provide measurements of the cosmological parameters with a precision of 2% on Ω_m and 5% on w₀, assuming an equation of state given by Eq. (1). The results from the *Euclid* quasar Hubble diagram will thus be highly complementary, in both physical and observational terms, to all the other cosmological tests that *Euclid* will enable.

## 9.6. Cosmology with cosmic chronometers

Passive galaxies are not only a powerful resource to set constraints on galaxy formation and evolution (Sect. 10.8), but can also be used to provide cosmological constraints when used as cosmic chronometers. As discussed in Moresco et al. (2022), the measurement of the differential age evolution within an interval $dt$ of the Universe using a redshift bin of width $dz$ can provide direct and cosmology-independent constraints on the expansion rate of the Universe, since by only assuming a FLRW metric it is possible to derive that $H(z) = -1/(1+z)dz/dt$. Very massive and passively evolving galaxies represent the ideal chronometers in the Universe, since many observational pieces of evidence indicate that they represent the oldest objects in the Universe at a given redshift, they experienced a synchronised formation, and they are a homogeneous population in terms of their physical properties. Hence, by measuring their differential ages as a function of redshift, it is possible to obtain an independent and complementary measurement of the Hubble parameter (for a detailed review on the cosmic chronometer method, see Moresco et al. 2022).

*Euclid* will detect thousands of passive galaxies at $1.5 < z < 3.2$ in the EDS (see Sect. 10.8), and from their spectra it will be possible to detect features that have been demonstrated to provide robust tracers of their differential age (in particular the feature at 4000 Å, the D4000 break). A test study using quiescent galaxies with strong D4000 breaks as cosmic chronometers to derive cosmological constraints was presented in Moresco (2015). In this work, only 29 high-redshift ($1.4 < z < 2.2$) massive

and passive galaxies ($19.7 \le H_{AB} \le 22.2$) were analysed, showing the potential of this method to constrain the expansion history of the Universe in a cosmology-independent way up to $z \sim 2.5$. Moreover, in Moresco et al. (2022) forecasts were presented showing how this method, applied to *Euclid* data, will be able to constrain the Hubble constant and the dark energy equation-of-state parameter with a precision of 4% and 30%, respectively. While these constraints are less precise than the ones obtained with the main cosmological probes in *Euclid*, they provide useful complementary information, that combined with the other approaches can contribute to maximise the scientific harvesting of *Euclid* data.

## 10. Non-cosmological science with Euclid

*Euclid*'s combination of data of unrivalled fidelity and volume will have a significant impact in other areas of astronomy, especially once combined with various complementary data. In this section we highlight some of the other science cases where we expect *Euclid* to have a major impact. This discussion updates and extends the relevant discussion in Laureijs et al. (2011) and highlights where the main challenges are. We refer to these as 'legacy' science cases to emphasise their expected long-lasting value over the coming decades.

For instance, the high spatial resolution, PSF stability, and photometric depth of *Euclid* offer unprecedented opportunities to study resolved stellar populations in the Milky Way and nearby galaxies out to beyond 5 Mpc. The ability to detect and characterise faint cool stars, either dwarf stars nearby in the Galactic disc or luminous evolved stars throughout the Local Volume, along with the contiguous FoVs of regions of the sky is expected to be transformative for a variety of science cases. Moreover, the *Euclid* surveys will provide imaging and spectroscopy of very large samples of galaxies. Indeed, the majority of sources in the final catalogues will be galaxies and this will enable a wide variety of extragalactic studies over a vast range in redshift. These include spatially resolved and integrated measures of star
formation in galaxies, detailed morphologies of galaxies, and the
detection and characterisation of transient phenomena, as well
as distant galaxies in the epoch of reionisation (EoR). Closer to
home, Euclid will also enable the study of objects in the Solar
System.

10.1. *The Milky Way and the Local Volume*

Starting with the Milky Way, major advances are expected in
studies of low-mass stars and star clusters. For example ultra-
cool dwarfs (UCDs) are the lowest-mass, coldest and faintest
products of star formation. Defined as objects with spectral
types M7 and later (Kirkpatrick 2005), they have masses of
*M* ≤ 0.1 *M*<sub>☉</sub>, and effective temperatures ≤ 2700 K. They encom-
pass the stellar-substellar limits, including the lowest mass stars
(late M and early L) as well as brown dwarfs and planetary mass
objects across the whole L-, T-, and Y-dwarf sequence. The EWS
is poised to dramatically increase the census of UCDs in the
solar vicinity (Solano et al. 2021; Martín et al. 2021), and spectra
from the NISP instrument will allow these objects to be clas-
sified into subtypes (Zhang et al. 2024). High-redshift quasars
are contaminants for this kind of study (cf. Sect. 10.5) but these
can be distinguished from UCDs through use of VIS photometry
and/or adoption of statistical modelling techniques (e.g. Euclid
Collaboration: Barnett et al. 2019). With large complete sam-
ples of UCDs, studies of the oldest Milky Way populations, the
structure of the Galactic disc, and the form of the substellar ini-
tial mass function will be possible. The sharp VIS PSF offers
the opportunity to resolve UCD binaries and study the binary
properties for an unprecedented number of systems. Moreover,
Euclid will provide a particularly exciting window on some of
the rarest low-mass objects currently known – the coolest low-
mass objects, the so-called Y dwarfs (e.g. Cushing et al. 2011),
and young planetary mass objects, both free-floating and in wide
binaries (e.g. Liu et al. 2013). A showcase of Euclid's capabil-
ities to detect planetary mass objects in star-forming regions is
provided by the Early Release Observations (ERO) programme
in Orion (Martín et al. 2025).

Euclid will observe many star clusters and star-forming
regions throughout the local disc and halo. Of special interest
are the roughly 25 globular clusters (GCs) that will lie within the
EWS footprint. Euclid will enable a variety of studies, such as
multiple population signatures at the end of the main sequence,
the present-day mass function and GC ages using the near-IR
colour-magnitude diagram (CMD) 'knee' – such studies have
thus far been possible for only a small handful of GCs (e.g.
Massari et al. 2016; Dondoglio et al. 2022). The wide-area cov-
erage will also facilitate unmatched studies of the peripheral
structures of GCs, including the search for very sparse tidal
features as demonstrated by the ERO data for NGC 6254 and
NGC 6397 (Massari et al. 2025). Even more detailed analysis
will be possible for the halo GC AM-1 which falls within the
EDS South. AM-1 lies at a Galactocentric radius of 120 kpc and
is one of the most distant GCs currently known in the Milky Way.
The multi-epoch imagery will permit an extremely deep CMD
study of AM-1, as well as a search for RR Lyrae variable stars
that can be used to accurately measure its distance, and hence
refine the measurement of its age (e.g. Dotter et al. 2008).

Our understanding of the assembly history of the Milky Way
has undergone a transformation in the last few years thanks to
the ESA Gaia mission. Results include the discovery of a signif-
icant accretion event early in the history of our Galaxy (Helmi
et al. 2018; Belokurov et al. 2018) and a large number of new
nearby stellar streams (e.g. Ibata et al. 2019). However, one of the

most fascinating and poorly understood components of the Milky
Way lies beyond Gaia's reach but will be accessible with Euclid
– the outer stellar halo. Euclid will detect main sequence stars
to Galactocentric radii of ≥ 100 kpc, providing the first detailed
window of the outer stellar halo with its repository of diverse
dwarf satellites, ancient GCs and copious tidal debris from past
accretion events (e.g. Johnston et al. 2008). The outer halo also
provides an excellent laboratory for hunting for clues about the
nature of dark matter. The existence of gaps, spurs, and peaks in
cold tidal streams could signify impacts with dark matter sub-
halos (e.g. Bonaca et al. 2019). The existence of many other
possible perturbing sources (e.g. the rotating bar, giant molec-
ular clouds, and spiral arms) in the inner halo of the Galaxy
has complicated work of this nature to date, but the outer halo
offers a much cleaner environment in which to characterise and
interpret the origins of these density variations.

Results from the Gaia mission have also brought to the fore
the importance of understanding how representative our Milky
Way is of the disk galaxy population at large. Indeed, the archae-
ological record in our nearest large neighbour, M31, suggests
a much more active accretion history than that experienced by
the Milky Way (e.g. Mackey et al. 2019), raising the possibil-
ity that our home galaxy may be unusual. Euclid is poised to
have an enormous impact by enabling studies of resolved stellar
populations in the halos of galaxies throughout the Local Vol-
ume. Thanks to the long dynamical timescales, these parts are
expected to contain the richest and best-preserved fossil record of
the accretion history of a galaxy (e.g. Johnston et al. 2008). The
resolved star approach is extremely powerful, having sensitivity
to surface-brightness levels well below ~ 30 mag arcsec⁻², but
has proved a challenge from the ground due to star-galaxy sep-
aration at faint magnitudes (e.g. Žemaitis et al. 2023). Euclid's
high-resolution imagery and stable PSF allows it to resolve lumi-
nous evolved stars, such as red giant and age-sensitive asymptotic
giant branch stars, in the low surface-brightness peripheries of
galaxies to distances of 5–7 Mpc (Hunt et al. 2025). This volume
encompasses several hundred systems, ranging from the small-
est dwarf galaxies to large spirals like the Milky Way. Systematic
studies will be possible of tidal streams and stellar halos across
the galaxy mass spectrum and in environments ranging from
the field to small groups. The detection and characterisation of
new dwarf satellites and halo GCs around these galaxies will
be achievable, as well as a search for free-floating GCs across
roughly a third of the sky (e.g. Mackey et al. 2016).

10.2. *Nearby galaxies and diffuse structures*

The superb ability of Euclid to detect low-surface brightness
(LSB) features of galaxies (Euclid Collaboration: Scaramella
et al. 2022; Euclid Collaboration: Borlaff et al. 2022) makes it
an ideal facility to study galaxy evolution, as exemplified by the
first applications presented in Cuillardre et al. (2025b), Marleau
et al. (2025), Kluge et al. (2025), and Hunt et al. (2025). In the
hierarchical paradigm of structure assembly, massive galaxies
and their host dark matter halos are assembled from smaller
ones, leaving observable signatures such as LSB stellar streams,
shells, and tidal remnants around galaxies. As shown in a
number of observational (Duc et al. 2015; Trujillo & Fliri 2016;
Spavone et al. 2017; Buitrago et al. 2017; Martínez-Delgado et al.
2023) and theoretical (Cooper et al. 2010; Martin et al. 2022;
Pérez-Montaño et al. 2022) works, the diffuse LSB light in the
outskirts of galaxies contains tidal streams, tails, shells, and
extended stellar halos; these features encode information about
the past merging history of galaxies and helps to reconstruct
their mass assembly through major or minor mergers (Conselice et al. 2003; Raj et al. 2020; Spavone et al. 2020).

Euclid's unrivalled combination of area, resolution, low background, wavelength coverage, and PSF stability has the potential to revolutionise these fields of research. Euclid will reach a photometric depth of $I_E = 29.5$ mag arcsec$^{-2}$ (measured as $3\sigma$ fluctuations in $10'' \times 10''$ boxes) in the EWS. This is equivalent to the deep surveys done so far from the ground over much smaller areas: hundreds of square degrees versus many thousands of square degrees for the EWS. Furthermore in the EDS, a gain of 2 magnitudes will in principle be achievable (Euclid Collaboration: Scaramella et al. 2022; Euclid Collaboration: Borlaff et al. 2022). In the NIR, a regime for which ground-based LSB studies are almost impossible, Euclid has no competitor, with expected $1\sigma$ EWS depths of $Y_E = 28.2$, $J_E = 28.4$, and $H_E = 28.4$ mag arcsec$^{-2}$ (Euclid Collaboration: Scaramella et al. 2022). These surface-brightness limits have been confirmed observationally by Cuillandre et al. (2025a) and Hunt et al. (2025).

Euclid will also reveal a population of low-surface-brightness and ultra-diffuse dwarf galaxies, both as satellites around massive hosts and as isolated field galaxies (e.g. van Dokkum et al. 2015; van der Burg et al. 2016; Marleau et al. 2021; Venhola et al. 2022). These populations are the most abundant galaxies by number at any redshift, and tend to be missed by large-scale surveys. They contribute to the faint end of the galaxy LF, which is poorly known in the environments that Euclid will probe. However, the detection of these LSB structures, some located towards foreground Galactic cirrus, is challenging and will require non-standard data reduction procedures. Euclid will provide the crucial NIR regime that, combined with deep multi-wavelength imaging from future synoptic facilities such as the Rubin Observatory or Roman telescopes, will constrain stellar populations and enable the characterization of LSB emission in and around dwarfs and more massive spirals and early-type galaxies. This is demonstrated by the census of dwarf galaxy satellites in the Perseus cluster of galaxies (Marleau et al. 2025) and around a nearby spiral galaxy (Hunt et al. 2025).

Detailed studies of semi-resolved stellar populations in nearby galaxies will be possible with the superb spatial resolution of Euclid's VIS and NISP imagers. The NIR wavelengths are crucial because they trace the bulk of the stellar mass in galaxies by directly sampling the peak of the SEDs of the cool, low-mass stars that dominate stellar populations. Spectral modelling of independent pixels in galaxy images will spatially resolve stellar mass densities, ages, metallicities, dust extinction, and other properties (e.g. Aburro'uf et al. 2022a,b), as well as their variations with environment and galaxy type. It may also help ameliorate the well-known degeneracies among age, metallicity, and dust extinction because of additional constraints from neighbouring pixels. With the EWS and EDS, exploiting the important NIR regime, it will be possible to construct a census of resolved galaxy demographics on a statistical basis never before possible.

Euclid's spatial resolution, sensitivity, and PSF stability also provide a new, photometrically uniform, view of extragalactic globular clusters (EGCs; e.g. Powalka et al. 2017). Euclid VIS spatial resolution in combination with VIS/NISP colours help to distinguish EGCs from foreground stars and background high-$z$ galaxies (Muñoz et al. 2014; Cantiello et al. 2020; Saifollahi et al. 2021, 2025), and identify EGCs around galaxies spanning a wide range of mass and environment, in particular EGCs belonging to LSB dwarf galaxies (Georgiev et al. 2009;

Lim et al. 2018; Müller et al. 2021; Saifollahi et al. 2022). Accumulating the statistics of EGCs around galaxies in the volume where Euclid can detect these faint point sources provides strong constraints on the dark matter halo mass assembled through hierarchical merging (e.g. Zaritsky 2022; Burkert & Forbes 2020). The EWS and EDS offer unprecedented statistical constraints on any systematic variations of EGC demographics with environment and galaxy mass concentration, as well as the populations of nuclear star clusters (Voggel et al. 2016; Carlsten et al. 2022). Furthermore, within the Local Universe, Euclid VIS images also resolve ultra-compact dwarf galaxies, thus helping to complete our current understanding of these systems in a high-density environment (e.g. Voggel et al. 2020; Wang et al. 2023).

Finally, Euclid has the potential to furnish definitive estimates of galaxy distances, in particular through surface brightness fluctuations (SBFs). SBF distance measurements have to be calibrated with respect to the galaxy stellar populations, that is, their age and metallicity, and have been typically applied to massive galaxies (e.g. Tonry et al. 2000; Mei et al. 2007; Blakeslee et al. 2009; Cantiello et al. 2018). It would be particularly important to apply the SBF methodology for distance estimates to dwarf galaxies, because they tend to be too faint for an emission line analysis that would provide a redshift. Dwarf galaxies make up the bulk of galaxy populations, but detecting them without being able to measure their distances makes demographic studies impossible. Euclid's sensitivity to the abundant dwarf galaxy population enables extending the SBF method to dwarf galaxies and massive galaxies in different environments, with statistics that will only be possible through the EWS. Although the PSF is somewhat undersampled in Euclid images, preliminary results show that the SBF signal can be detected even as far as the Perseus cluster (Cantiello et al., in prep.).

## 10.3. Galaxy structure and morphology

Unlike LSST or completed large ground-based imaging surveys, such as SDSS, KiDS, and DES, Euclid can reveal features in the surface brightness distribution for a considerable fraction of the galaxies it will image. With a PSF FWHM of 0.13 (see Sect. 5.2) Euclid's resolution will be similar to that of HST (Fig. 46). However, the EWS will cover an area that is over 1000 times larger than what HST has imaged since 1990, as well as covering several deeper fields. This will allow investigations into the structures and morphologies of galaxies, which can then be correlated and applied to determine the physical drivers of galaxy evolution with redshift, and to establish how the environment affects galaxy properties.

We know mostly from HST that galaxies in the early Universe were more morphologically peculiar, compact in size, and undergoing more star formation, compared with galaxies at $z=0$ (Conselice et al. 2005; Conselice 2014; Huertas-Company et al. 2016). JWST is transforming our view of this topic, with the discovery that disk galaxies are much more common at high redshifts than we had previously thought (Ferreira et al. 2022; Vega-Ferrero et al. 2024; Huertas-Company et al. 2024). Euclid will make a unique contribution to this research area by providing orders of magnitude more resolved galaxy structures in the distant Universe than what we could ever obtain with HST and JWST. This includes parametric and non-parametric morphological investigations of galaxy structure and how these properties evolve to the highest redshifts where Euclid can resolve galaxies. The benefit of Euclid is that the rarer, more massive galaxies can be studied in detail. Hence, we will be able
<figure><img src="image_48.png" /><figcaption>**Fig. 46.** Illustration of Euclid's capabilities to measure galaxy morphologies. Top panels: example of a simulated galaxy observed with VIS as compared to HST and Subaru/HSC. The horizontal black line indicates a 1" length. Middle panels: comparison of the bias (left column), dispersion (middle column) and outlier fraction (right column) of the effective radii (top row), axis ratio (middle row) and Sérsic index (bottom row) for the best-fit Sérsic profiles obtained with different state-of-the art surface brightness fitting codes applied to simulated Euclid galaxies as a function of $I_E$. Sérsic parameters can be obtained with errors smaller than ~10% down to a $I_E$=24. Bottom panels: accuracy of deep learning based morphological classifications on simulated Euclid observations of galaxies trained on human based labels. The confusion matrices show the accuracy for identifying spiral arms (left) and clumpy galaxies (right). Figure adapted from Euclid Collaboration: Aussel et al. (2024) and Euclid Collaboration: Bretonnière et al. (2023).</figcaption></figure>

to examine the structures of the most massive and largest systems up to $z \sim 6$.

There are several ways in which the morphological properties of galaxies measured by Euclid will be investigated. One of the main methods for characterising galaxy morphology is to use the Sérsic fitting method, whereby a predetermined profile is

fit to galaxy light distributions. As discussed in Sect. 7.4, such fits are performed by the main pipeline. The output of this gives the size of each galaxy, as well as its Sérsic index $n_{Ser}$ (Sérsic 1963), with $n_{Ser} = 1$ being an exponential disk and $n_{Ser} = 4$ a de Vaucouleurs profile. The Sérsic modelling can be made more complex by adding further components to model the surface-brightness profiles of both bulges and disks, which is usually referred as bulge/disk decomposition. Euclid will be able to measure single Sérsic parameters with around 10% accuracy down to an apparent magnitude of $I_E < 23$, which roughly corresponds to 450 million galaxies with a median redshift of $z \sim 1.5$. For bulge-disc decomposition, the same 10% accuracy is reached for galaxies with $I_E < 21$ (Euclid Collaboration: Merlin et al. 2023; Euclid Collaboration: Bretonnière et al. 2023). These measurements will be critical to examine how scaling laws, such as the size-mass and size-environment relations, evolve with redshift, with unprecedented statistics. With Euclid we can determine accurate sizes from both Sérsic fits and Petrosian radii (Petrosian 1976), and use these to examine in great detail how galaxy sizes have changed with time, over a wide range in stellar mass.

The analysis pipeline will also provide non-parametric descriptions of galaxy structure, without the recourse to a predetermined parametric model, which is used in the Sérsic fitting. As discussed in Sect. 7.4, this includes the CAS parameters (Conselice 2003), as well as the Gini and M20 parameters (Lotz et al. 2004) as part of the standard Euclid pipeline. These parameters can then be used to examine the formation histories of galaxies, as well as the morphological properties of galaxies as a function of redshift (e.g. Conselice et al. 2003; Conselice 2014). These non-parametric measurements will allow us to measure structural evolution in a quantitative way, as opposed to simple visual estimates. Moreover, it allows us to find galaxies that are undergoing mergers to trace the merger history of galaxies, and thereby measure the role of merging in galaxy formation and evolution.

In recent years, deep learning has also been extensively used to provide morphological classifications of galaxies (see Huertas-Company & Lanusse 2023, for a review). This is particularly useful for providing detailed morphological descriptions of the internal structure of galaxies (e.g. clumps, bars) for samples that are too large to be visually inspected. Euclid Collaboration: Bretonnière et al. (2022) estimated that the EWS will be able to resolve the internal morphological structure of galaxies down to a surface brightness of $22.5 \text{ mag arcsec}^{-2}$, and the EDS down to $24.9 \text{ mag arcsec}^{-2}$, which roughly corresponds to 250 million galaxies at the end of the mission. This magnitude limit is typically brighter than for the Sérsic fits because internal features need to be detected. The Euclid photometric pipeline will provide neural network-based morphologies for this sample, first using existing labels from several Galaxy Zoo projects (e.g. Lintott et al. 2008) and subsequently complemented with classifications done on Euclid images (Euclid Collaboration: Aussel et al. 2024; see also Fig. 46). These detailed morphologies will enable a large variety of scientific analyses aiming at constraining the physical processes that drive the structural evolution of galaxies, for instance by comparing to predictions from simulations.

## 10.4. Active galaxies across redshift

Active galaxies have compact regions at their centres with characteristics indicating that their luminosity is not produced by stars but is the result of the accretion of matter onto a supermassive black hole (SMBH) at the centre of its host galaxy. While all
local massive galaxies show some level of AGN activity (Sabater et al. 2021), phenomenology caused by a high accretion rate onto the central black hole is seen in less than 10% of massive galaxies, and is thought to be short-lived (500 Myr to a few Gyr).

Type 1, or unobscured AGN, typically show broad emission lines ($\mathrm{FWHM} > 1000 \mathrm{km s}^{-1}$) and power-law continuum emission originating from the accretion disk, while Type 2, or obscured AGN, typically show extreme emission line ratios compared to the normal galaxy population and continuum emission with host galaxy features. In orientation-based unification models (e.g. Antonucci 1993; Urry & Padovani 1995; Netzer 2015), Type 2 AGN have been described as obscured Type 1 AGN with the broad-line emitting region and accretion disk being hidden behind a partially opaque torus. According to this simple scheme, Type 1 and 2 AGN should have similar distributions in terms of redshift, luminosity, host galaxy properties, and black hole mass. By contrast, in AGN evolutionary scenarios (e.g. Hopkins et al. 2008; Hickox et al. 2009), obscured Type 2 AGN may represent an earlier evolutionary phase compared to unobscured systems, and thus have different physical properties. The transition from obscured to unobscured accretion in AGN is postulated to occur through an outflow phase, during which energetic feedback is deposited in the host galaxy, impacting the formation of new stars (for a review see Harrison et al. 2018). Given their transient nature, comprehensive studies necessitate very large sample sizes to decipher their evolutionary paths, link to their host galaxies, clustering tendencies, and large-scale environments.

The unique combination of spatial resolution, depth and wide area coverage of *Euclid* will allow us to explore the AGN population like never before using both photometric and spectroscopic selection criteria. *Euclid*'s spatial resolution will provide critical observational constraints on AGN morphology and merger rate of their host galaxies. The depth of the NIR observations will allow for the first time the detailed study of Type 1 and Type 2 AGN sub-populations and their co-evolution with galaxies during the so-called 'Cosmic Noon' ($1 < z < 3$) and beyond. Finally, due to the depth and wide area coverage, rare and extreme states, such as red quasars, will benefit from detailed analysis of their morphologies and large-scale environment.

The most luminous Type 1 AGN, namely quasars, can be identified using *Euclid* photometry alone or in combination with multi-band coverage from optical surveys, such as LSST. We estimate that $4 \times 10^7$ ($2.4 \times 10^5$) AGN will be detectable (at $5\sigma$) in at least one *Euclid* filter in the EWS (EDS), corresponding to a surface density of $3-5 \times 10^5$ AGN per square degree (Fig. 47 open downwards triangles; Selwood et al., in prep.). This large sample will include about 30% Type 1 and 70% Type 2 AGN, based on population studies in the X-rays (Fotopoulou et al. 2016; Merloni et al. 2014). A colour selection using *u* band in combination with the *i*, *r*, or *z* filter, reaches completeness and purity ~ 81% (77%) and 92% (91%) for the EWS (EDS), respectively (Bisigello et al., in prep.). As shown in Fig. 47, this corresponds to a total of $8.1 \times 10^6$ ($3.5 \times 10^4$) AGN in the EWS (EDS) identified as AGN, by using *Euclid* and LSST colours (filled triangles). This simple colour selection will provide quasar surface densities that are better or even better with current AGN surveys, from X-rays (e.g. XMM-SERVS, Chen et al. 2018), optical (e.g. DES Yang & Shen 2023) and mid-infrared (e.g. WISE 75% completeness – C75, Assef et al. 2018). On the other hand, the identification of Type 2 AGN is challenging with *Euclid* and optical filters alone. Longer wavelength observations, in combination with more sophisticated methods, are therefore necessary.

<figure><img src="image_49.png" /><figcaption>**Fig. 47.** AGN surface density ($\mathrm{deg}^{-2}$) versus survey area ($\mathrm{deg}^2$) for EWS and EDS compared with wide field and medium area surveys in different wavebands (according to the legend). Unfilled downwards triangles show the surface density of AGN detected in at least one *Euclid* band (at $5\sigma$), while filled upwards triangles represent the surface density of AGN selected by using a simple colour criterion with *Euclid* and LSST colours, in both EWS and EDS.</figcaption></figure>

The identification of AGN in *Euclid* will also rely on spectroscopic data. Type 1 AGN will be classified through broad emission-line detection, while Type 2 AGN will be identified by using the narrow emission-line [N II]6584/H$\alpha$ versus [O III]5007/H$\beta$ diagnostic diagram, called the Baldwin-Phillips-Terlevich (BPT) diagram (Baldwin et al. 1981). A notable challenge for the BPT AGN identification using *Euclid* spectroscopy is the limited spectral resolution ($R \approx 450$), leading to the blending of key emission lines ($H\alpha$ and [N II]6548,6584) and a restricted availability of diagnostic narrow emission lines in specific redshift ranges within the EWS and EDS (Euclid Collaboration: Lusso et al. 2024).

With *Euclid* we will use BPT diagrams to classify and characterise Type 2 AGN within the narrow redshift range $1.5 < z < 1.8$ ($1 < z < 1.8$) in the EWS (EDS), which corresponds approximately to the peak of star-formation activity. Additionally, bright Type 2 AGN will be identified through the detection of high-ionisation emission lines, such as [Ne v]3426 (Mignoli et al. 2013) at $1.7 < z < 4.4$ and C IV at $z > 4.9$ in the EDS (e.g. Mignoli et al. 2019). Furthermore, spectroscopic redshifts will be available for millions of *Euclid* AGN. We expect to determine spectroscopic redshifts for around 90% of the Type 2 AGN in the redshift range $0.9 < z < 1.8$ down to an emission line flux of about $3 \times 10^{-16} \mathrm{erg cm}^{-2} \mathrm{s}^{-1}$ for the integrated $H\alpha$+[N II], whilst the same redshift completeness percentage occurs for an emission line flux more than a factor of two higher for Type 1 AGN, namely $8.5 \times 10^{-16} \mathrm{erg cm}^{-2} \mathrm{s}^{-1}$ (Euclid Collaboration: Lusso et al. 2024).

*Euclid*'s exceptionally extensive AGN data set presents a unique opportunity to constrain the LF of AGN in the near-infrared, over larger magnitude and redshift ranges, and larger area than previously employed to generate NIR galaxy LFs (Bell et al. 2003; Cirasuolo et al. 2007). The AGN LF and its evolution with time are key observational quantities for understanding the origin of SMBHs and accretion onto them (Aird et al. 2013; Shankar et al. 2013; Schulze et al. 2015). Additionally, the measurement of the SMBH mass serves as a key parameter for studies aimed at establishing scaling relations between black holes and host galaxy properties. These scaling relations are vital
for testing black hole feedback mechanisms (e.g. Steinborn et al. 2015) and cosmological hydrodynamical simulations of structure formation that investigate the relationship between galaxy and black hole growth (e.g. DeGraf et al. 2015). The AGN LF and the SMBH demography (Euclid Collaboration: Lusso et al. 2024) will be important observational products of Euclid, along with the AGN clustering, which links the evolution of growing SMBHs and the large-scale cosmic structure (Allevato et al. 2019), and the study of AGN close pairs and galaxy mergers.

## 10.5. Galaxies and quasars in the epoch of reionisation

Euclid's combination of optical and NIR instruments makes it ideally suited for identifying galaxies and quasars at high redshifts, taken here to be $z \ge 7$. Whilst other telescopes can reach these distant redshifts, most notably HST and JWST, Euclid has the advantage that it covers a large area of the sky and therefore can find rarer but brighter sources. The data from Euclid will be sufficiently deep such that it will probe into the EoR whereby all sources at these redshifts will exhibit Lyα breaks (Gunn & Peterson 1965), redshifted to an observed wavelength of $\lambda_α \approx \{0.97 + 0.12(z-7)\}$ µm. Such sources would be detectable in Euclid's NISP images and grism spectra but will be VIS dropouts, so they could potentially be identifiable using Euclid data in isolation. The difficulty is that the vast majority of optical dropouts are not high-redshift sources, so the reliable selection of these sources represents a significant data analysis challenge (even with access to external data sets); however, the potential Euclid science return from high-redshift galaxies and quasars justifies this effort.

Euclid will cover 50 deg² to depths of about 26.4 AB magnitudes (5σ point source limit) in the NIR filters in the EDS fields, which means that it probes a unique parameter space in the selection of $z > 7$ galaxies. Previously, space-based NIR telescopes have been limited in their ability to select the brightest and hence rarest sources due to their small FoVs: the Wide Field Camera 3 (WFC3) on HST has an FoV of 4.5 arcmin² and the Near-InfraRed Camera (NIRCAM) on JWST has an FoV of 9.7 arcmin². Even with large efforts to produce mosaics, these cover $\lesssim 1$ deg². Hence, while the study of ultra-high-redshift galaxies was undoubtedly revolutionised with the deep NIR surveys of HST and JWST, which allow galaxy candidates to be identified up to $z \approx 11-13$, the identified galaxies are typically limited to $L < L^*$ (with $L^*$ being the knee in the rest-frame UV LF; see review by Stark 2016). In the traditional 'dropout' formalism, galaxies will be selected with Euclid via the Lyman-break as $I_E$ dropouts at $z \approx 7$, $Y_E$-dropouts at $z \approx 8.5$, and $J_E$-dropouts at $z \approx 11.5$, and Euclid can in principle detect sources up to $z \approx 15$ because the $H_E$ band extends up to 2 µm. Importantly, the higher resolution of the Euclid imaging will aid in the identification of the main contaminants, brown dwarfs (cf. Sect. 10.1), since the galaxies are expected to be resolved at these bright magnitudes. Moreover, contamination fractions from $z < 6$ galaxies can be reduced from up to 40% to less than 5% with the inclusion of deep optical photometry, such as LSST (Euclid Collaboration: van Mierlo et al. 2022).

These luminous galaxies provide signposts to the most ionised regions of the neutral IGM at $z > 7$, while also representing a challenge to theoretical models and being key candidates for multi-tracer follow-up, for example with Atacama Large Millimeter/Sub-millimetre Array (ALMA) and JWST. Recent results from JWST (e.g. Naidu et al. 2022; Donnan et al. 2023; Finkelstein et al. 2023) have revealed a surprising abundance of luminous sources, of which several have shown unusual spectral

features (e.g., GNz11; Oesch et al. 2016; Bunker et al. 2023). These results highlight the huge potential of Euclid-selected high-$z$ sources in understanding the earliest stages of galaxy formation and reionisation.

Much of this work in the deep fields will be aided by observations from the Cosmic Dawn Survey (Sect. 4.4), which provides matching depth $u$-band from CFHT, griz-bands from HSC on Subaru, and 3.6µm and 4.5µm from Spitzer/IRAC as described in more detail in Sect. 4.4. The science goals of this survey are primarily focused on the high-redshift Universe, but will also facilitate many aspects of legacy science for the Euclid mission. Leveraging the deep wide area data from the Cosmic Dawn Survey will provide robust measurements of the galaxy stellar mass function to $z = 8$ and the UV luminosity function to $z = 10$. Other science goals include mapping the topology of reionisation, studying the formation of large-scale structure, quantifying the prevalence of high-redshift protoclusters, and characterising the first quenched galaxies. The survey data have immediate value for studying galaxy formation and evolution, and that legacy value will only increase as more data are collected.

Previous work on smaller scales shows the potential of Euclid discoveries. Degree-scale ground-based surveys from UKIRT and VISTA have provided the first view of the LF at $L > L^*$ for $z = 7-10$, showing an excess of sources over the predictions of HST surveys and revealing an apparent lack of evolution in the number density of the brightest sources (e.g. Bowler et al. 2020; Harikane et al. 2022). With the unique combination of space-based, wide-area, deep NIR imaging provided by Euclid, the number of rare luminous galaxies will be increased by factors of 100–1000 over current samples, providing key constraints on the bright end of the LF. Integrating the current best-fit LFs leads to predictions of thousands of sources from the deep fields, down to an absolute UV magnitude of $M_{UV} = -21$. This allows the shape at the bright end – which depends sensitively on astrophysical effects such as dust, scattering, and lensing – to be unambiguously determined. If the slope of the bright end continues as a power law beyond observational limits, there is the possibility of detecting a substantial number of extremely bright galaxies with NISP $m_{AB} \lesssim 24.0$ within the EWS (approximately 2000 versus 50 for a double-power law or Schechter function, respectively, at $z = 7$; Bowler et al. 2017). These additional objects will not only be useful for deriving the LF, but can be used to study the structures, stellar masses, and star-forming properties of these early systems and to compare them to lower redshift systems, as well as with galaxies at lower masses studied with HST and JWST.

High-redshift quasars are much more luminous than comparably distant galaxies (and, unlike γ-ray bursts, are non-transient) and so are among the most useful probes of the high-redshift universe. As described in the review by Fan et al. (2023), spectroscopic observations of high-redshift quasars probe the growth of the first SMBHs, provide several unique constraints on cosmological reionisation, and also give a record of the evolution of elemental chemical abundances. Luminous high-redshift quasars are expected to be extremely rare: while the redshift range $6 \le z \le 7$ is reasonably well explored, with approximately 300 quasars known, just eight bright quasars have so far been spectroscopically confirmed to be at $z > 7$ (Fan et al. 2023), along with some more speculative fainter detections at even higher redshifts using JWST (Maiolino et al. 2024; Bogdán et al. 2024). It is in this regime that Euclid should be able to make a transformational contribution, thanks primarily to the large area coverage of the EWS (Sect. 4.1). The headline prediction given in Laureijs et al. (2011) was that Euclid imaging data would be expected to
include 55 $z > 8.1$ quasars brighter than $J_E = 22.5$, sufficient to completely revolutionise this field. Euclid Collaboration: Barnett et al. (2019) then presented a more realistic simulation, which explored the impact of a range of contaminants (M, L, and T dwarfs, as well as early-type galaxies at $1 \lesssim z \lesssim 2$), different selection methods, the availability of external optical data (from LSST), and uncertainty about the evolution of the quasar LF.

While these simulations showed that the *Euclid* data should be able to produce complete high-redshift quasar samples to a greater depth of $J_E \approx 23$ (particularly if it is possible to cross-match to LSST optical data, this is outweighed by the steeper decrease in quasar numbers with redshift found by Jiang et al. (2016). So the realistic predictions from Euclid Collaboration: Barnett et al. (2019), given in full in Table 3 of that paper, are broadly that the EWS photometry<fnref n="30" /> will yield approximately 100 robust quasar candidates with $7.0 \le z \le 7.5$, around 25 quasars beyond the current record of $z \approx 7.5$ (Bañados et al. 2018; Yang et al. 2020; Wang et al. 2021), and perhaps 10 quasars at $z \ge 8.0$.

While the *Euclid* photometry will be necessary to identify (candidate) $z > 7$ quasars, confirmation and characterisation will (in contrast to most other projects described in this paper) come primarily from external follow-up observations. Most important will be NIR spectroscopy; hence there is a particular utility to finding the brightest sources with $M_{1450} \lesssim -26$, corresponding to $J_E \lesssim 21$. Even one such detection at $z \ge 8$ (plausible in DR1) would represent major progress in this field; the full EWS should yield a well-characterised population of quasars out to at least $z > 8$, with the observational frontier possibly pushed back as far as $z \approx 9$.

## 10.6. Galaxy evolution and environment

While it is largely agreed that the cosmic environment in which a galaxy evolves strongly correlates with its measured properties (e.g. Darvish et al. 2017), we still need to understand all the physical processes that drive its evolution as well as their relative importance. Dressler (1980) showed that, at least in the local Universe, galaxies in denser environments are more likely to be elliptical galaxies, whilst systems found within regions of lower density are generally galaxies with spiral and irregular morphologies. Furthermore, in the local Universe, with the exception of radio-bright galaxies that preferentially reside at the centres of clusters (see Magliocchetti 2022, for a review), AGN are observed to avoid massive structures (e.g. Popesso & Biviano 2006).

A wide diversity of other properties are observed to correlate with various measures of environment as well. For instance, on average, high-density regions are mostly populated by redder, brighter, more metal rich, and less star-forming galaxies, while the opposite is true for low-density regions (e.g. Kauffmann et al. 2004; Blanton et al. 2006; Winkel et al. 2021). Additionally, ‘green valley’ galaxies, likely to be transitioning from star-forming to quiescent phases, have a lower specific star-formation rate in groups and clusters than in the field (e.g. Jian et al. 2020). Another example is the positive (negative) correlation between the star-formation rate (H I gas deficiency) of galaxies, at fixed mass, and their distance to the closest filamentary structure (Malavasi et al. 2017; Laigle et al. 2018; Kraljic et al. 2018; Gouin et al. 2020, Crone Odekon et al. 2018), or the

recent evidence that galaxies that are strongly connected to the cosmic web form fewer stars and are more pressure supported than those that are weakly connected. (Kraljic et al. 2020). Furthermore, a bimodality in the central surface brightness of disks is found for galaxies in voids, filaments and knots, but not in sheets (Sorce et al. 2016). All these findings seem to hold at least out to $z \sim 1$ (e.g. Cucciati et al. 2010; Jian et al. 2020).

At higher redshifts the situation is less clear, although there seems to be increasing evidence for a reversal of at least some of the scaling relations mentioned above. As an example, it has been found that at $z \sim 1.5-2$ more AGN reside within dense regions than in the field (e.g. Martini et al. 2013). However, the exact details of the processes leading to such observed correlations at $z > 1$ are still unknown. Evolutionary paths followed by galaxies are extremely complex, especially because several processes are at play in an intertwined way. For instance, McGee et al. (2009); De Lucia et al. (2012); Verdugo et al. (2012) and Sarron et al. (2019) showed that galaxies are probably preprocessed in groups (filaments) before falling into clusters where they finish their transition to passive states.

Given its extremely wide area coverage, *Euclid* will probe all environments in which galaxies are found, even the most extreme ones, over the widest redshift range to date. Indeed, it will be able to measure properties (such as redshifts, stellar masses, star-formation rates, presence and relevance of a central AGN) for billions of galaxies in regions of varying density out to $z \sim 2$ and, in the three deep fields, even out to $z \sim 3$.

In order to exploit the exquisite quality of *Euclid* data for environmental studies, we have developed several codes for the reconstruction and characterisation of the observed density field traced by *Euclid* galaxies at all scales. These all deal with the search of overdense structures such as high-z clusters and protoclusters. We also optimised existing codes for the detection of cosmic filaments (e.g. Sousbie 2011) in order to work with both photometric and spectroscopic samples. These codes will complement those already used for the detection of voids (e.g. VIDE, Sutter et al. 2015; Contarini et al. 2022) clusters (AMICO and PZWav, Euclid Collaboration: Adam et al. 2019), allowing the reconstruction and investigation of the full density field at all scales. This will permit us to shed light on the link between galaxy and AGN formation and evolution and their environments out to $z \sim 3$.

Furthermore, the codes developed for the investigation of the clustering properties of *Euclid* galaxies both in configuration space (two- and three-point correlation functions) and in Fourier space (power spectra and bispectra, cf. Sect. 7.7.1) will also be used to relate the properties (stellar mass, colour, luminosity, star-formation rate, metallicity, star-formation history, black hole type, accretion, luminosity, etc.) of the galaxies and AGN observed by *Euclid* with the LSST they trace. This will permit the establishment of a direct connection with the dark halos inhabited by these sources, via the so-called bias function (e.g. Mo & White 1996; Scoccimarro et al. 2001).

## 10.7. Star-forming galaxies across time

The combination of photometry and spectroscopy will enable detailed investigations into the physical properties of star-forming galaxies, such as stellar populations, star-formation rates, and dust attenuation, as well as their evolutionary processes and the interplay between star formation and black hole accretion at the peak of AGN activity and star-formation history, during Cosmic Noon.

<footnote n="30">³⁰ It is also possible that the brightest high-redshift quasars could be identified from the *Euclid* grism spectra directly. Unfortunately, the simulations described by Roche et al. (2012) are no longer relevant because of the subsequent reduction in the capabilities of the grisms, and no updated studies of this possibility have been published to date.</footnote>
In the EWS Euclid will map 2000–4800 Hα emitters per deg² in the redshift range 0.9 < z < 1.8 at a flux limit of 2 × 10⁻¹⁶ erg cm⁻² s⁻¹, totalling 28–67 million sources in the EWS, while in the EDS we will amass about 32 000–48 000 Hα emitters per deg² (i.e. a total of 1.6–2.4 million) at a flux limit of 5 × 10⁻¹⁷ erg cm⁻² s⁻¹, in the broader redshift range 0.4 < z < 1.8 enabled by the addition of the blue grism (Pozzetti et al. 2016). For these galaxies it is not only possible to obtain robust spectroscopic redshifts, but we will also be able to study a wide range of properties. First of all, the SFR, which can be estimated from the intensity of the Hα emission line (e.g. Kennicutt 1998b), corrected for dust attenuation using Hα/Hβ, when Hβ is available or statistically otherwise: with such a sample of tens of millions of Hα emitters we will be able to analyse in detail the tight correlation between SFR and stellar mass, the so-called galaxy main sequence (MS), down to a few M☉ yr⁻¹ at z ~ 1 in the EWS, as shown in Fig. 45. In particular, with the EWS sample we will be able to probe the most massive part (log₁₀ M*/M☉ > 10) of the MS with unprecedented statistics at these redshifts, and help provide the physical explanation for the observed turnover in the MS shape and its evolution (e.g. Popesso et al. 2023). Additionally, the EDS will allow us to explore the fainter end of SFR-stellar mass space. Moreover, thanks to the wider wavelength range due to the availability of the blue grism, multiple spectral lines will be available for individual galaxies (e.g. Hβ, [O III]5007, and [O II]3727), enabling us to recover dust attenuation and gas-phase metallicities, and to put solid constraints on a variety of scaling relations (e.g. the fundamental metallicity relation and mass-attenuation Maiolino & Mannucci 2019). In the EWS we expect to find about 440 [OIII]5007 emitters per deg² (resulting in a total of about 6 × 10⁶ over the entire EWS area) in the range 1.5 < z < 2.3 (Bagley et al. 2020). Finally, a complementary sample of Paβ emitters would also be mapped at low redshift (z < 0.48), similar to Cleri et al. (2022) with HST grism G141.

Euclid photometric information, complemented by ground-based data, will also be used to derive the physical properties of galaxies (Euclid Collaboration: Bisigello et al. 2023). In particular we will be able to classify galaxies from their photometric SED (Bisigello et al. 2020) and compute the stellar mass function (SMF) of galaxies of different classes to derive its differential evolution and infer the history of cosmic mass assembly. The enormous EWS area will enable the study of the evolution of the number density of rare populations, like massive star-forming galaxies, in order to relate them to the mass growth and buildup of passive galaxies, while assessing the contribution due to mergers, thanks to the exquisite morphological information that the Euclid high resolution will provide (cf. Sect. 10.3). By comparing the SMFs of galaxies classified with different methods (i.e. using their morphology or colours), it will also be possible to understand the timescale of the morphological transformation and stellar population ageing (e.g. Pozzetti et al. 2010) that lead to the present-day galaxies and to derive constraints on the quenching mechanisms (Peng et al. 2010) responsible for turning off star formation.

The combination of physical and morphological properties will provide constraints on the size-mass relation of blue star-forming galaxies and insights on the connection between the compactness of galaxies, their light profiles, and the efficiency of the star-formation process, leading to an understanding of the range of properties of the blue cloud galaxies quenched by internal mechanisms (Hamadouche et al. 2022). To explore the parameter space sampled by the EWS and EDS even further, we will consider samples of galaxies sharing similar

properties, for instance by reducing the high-dimensional photometric space of colours and fluxes with machine-learning algorithms (e.g. SOMs, as in Davidzon et al. 2022, see also Sect. 7.6.1). The spectra of these groups of galaxies can then be analysed with stacking techniques to improve the signal and eventually study the MS at 0.9 < z < 1.82 at SFRs as low as 0.1 M☉ yr⁻¹ in the EWS, and ~0.01 M☉ yr⁻¹ in the EDS. Similarly, SED fitting will be performed on the photometric composite SEDs with high S/N to analyse the physical properties and their evolution especially of faint galaxies. Taking advantage of the 3-dimensional distribution of galaxies (see Sect. 10.6), we will study how the physical properties of galaxies depend on the environments they inhabit.

The source-subtracted cosmic infrared background (CIB) fluctuations uncovered in deep Spitzer data (e.g. Kashlinsky et al. 2005, 2012) are coherent with the unresolved cosmic X-ray background (CXB; Cappelluti et al. 2013, 2017; Mitchell-Wynne et al. 2016; Li et al. 2018), which could be caused by a new population (Helgason et al. 2014) containing a fraction of black holes in excess of what appears in the known galaxy populations. As discussed in Kashlinsky et al. (2018), Euclid will play an important role in directly resolving the nature of the CIB at near-IR wavelengths, because the source-subtracted CIB measurements in the three Euclid near-IR bands over the EWS can be cross-correlated with the unresolved CXB from eROSITA to constrain model predictions (Kashlinsky et al. 2019).

In the far-IR, a statistical characterisation of star-formation processes across cosmic epochs can be obtained from a joint analysis of Euclid data and maps of the far-IR CIB, which probes the unresolved emission of dusty star-forming galaxies since the epoch of reionisation (Dole et al. 2006). Maps of the far-IR CIB can be extracted from multi-frequency CMB observations through component separation or from direct observation at relevant frequencies, such as those of Herschel, which is, however, hard to extract due to residual Galactic foreground contamination in far-IR CIB maps (Planck Collaboration XVIII 2014; Maniyar et al. 2019; McCarthy et al. 2023). Instead, the cross-correlation of CIB maps of Planck, Herschel, or future ground-based instruments (such as the Cerro Chajnantor Atacama Telescope) with the Euclid observables (galaxy or QSOs clustering and cosmic shear) can be used to constrain models of star-formation history, its efficiency across time, and the connection to host halo mass and environment (Jego et al. 2023a,b). Euclid's NIR images from both the EWS and EDS can be used to create background maps (after masking the detected sources) and directly cross-correlating with CIB maps from the same external sources to extract additional complementary information (Lim et al. 2023).

## 10.8. Passive galaxies and galaxy quenching

Massive ($M_* > 10^{11} M_☉$), quiescent galaxies are key systems for understanding galaxy formation, but they are rare and it is therefore challenging to assemble large samples. Euclid spectroscopy can play a unique role in studying these systems in the EDS at high redshifts. Indeed, due to the rapid decline of their number densities at $z > 1.5$ (Weaver et al. 2023), finding and observing over the widest possible redshift range is a crucial yet difficult task.

Much work has been done out to $z \sim 1$, but the peak of star-formation activity and the assembly of passive galaxies is at $z > 1$ (Ilbert et al. 2010, 2013; Madau & Dickinson 2014). The study of the number densities of massive passive galaxies at high redshift – that is the galaxy SMF – is crucial for understanding how the evolution proceeds from star-forming to passive galaxies, that
is when galaxies are quenched, and when and how they assemble their mass, which is still a challenge for models of galaxy formation. The EDS with the BG will be truly unique for finding and spectroscopically identifying, at the continuum limit $H_E < 21$ (22), the rarest and most massive quiescent galaxies at $z > 1.4$, with $\log_{10}(M_*/M_\odot) > 11.3$ (11). The evolution of the luminosity and mass functions of passive galaxy types can be followed in different environments (e.g. Cucciati et al. 2016, show the possibility to measure galaxy environments in the EDS over the redshift range $0.9 < z < 1.7$, see also Sect. 10.6). Therefore, the *Euclid* deep BG data can be used to probe the assembly of the red sequence out to $z \sim 2$.

The BG provides a fundamental complement to the RG for the identification of a large sample of quiescent galaxies based on the identification of the Balmer or D4000 break. We consider for the BG the wavelength range 0.926–1.366 µm, and 1.206–1.892 µm for the RG (50% peak transmission wavelengths) and a reference EDS area of 50 deg². The blue limit of $BG_E$, around 0.926 µm, allows us to detect the D4000 break starting at $z \sim 1.5$ and up to $z \approx 2.2$, while the RG allows its detection only in the redshift range $2.2 < z < 3.2$, where the expected number of passive galaxies is significantly smaller.

To obtain quantitative estimates of the expected numbers of passive galaxies, we have used the COSMOS2020 catalogue (Weaver et al. 2022) to derive the number density of passive galaxies expected for different $H_E$ limits. We have selected passive/quiescent galaxies using the colour-colour selection (NUV $-r$) versus $(r-J)$ and derived the redshift distributions $(dN/dz)$ for different $H_E$ limits. At the $BG_E$ limit, about 5000 passive galaxies will be detectable at $z > 1.5$ within the sensitivity limits of NISP continuum spectroscopy over 50 square degrees at $H_E=21$ in the EDS, and over 30000 at $H_E=22$.

The red grism extends the possibility of detecting passive galaxies, through the D4000 detection at $z > 2.2$, but only at $H_E < 23$. A typical example is shown in Fig. 45. Keeping in mind the drop in the number of passive galaxies above $z = 1.5$, the importance of having a blue grism is clear, since it allows for the detection of more than 5000 massive quiescent galaxies with $H_E < 21$ and approximately $4 \times 10^4$ (10⁵) galaxies with $H_E < 22$ (23) in 50 deg². These numbers are to be contrasted with the several hundreds of spectroscopically confirmed objects in the RG.

*Euclid* will not only provide a huge sample of passive/quiescent galaxies compared to what has been available before, but will also be fundamental for finding and spectroscopically identifying the rarest and most massive passive galaxies ($>10^{11} M_\odot$) with unparalleled statistics. This is because their number density (10–100 deg⁻²) makes their identification difficult with NIR instruments with a small FoV from space (e.g. JWST or HST), while from the ground strong sky residuals limit the sensitivity (e.g. VLT+MOONS or SUBARU+PFS). Only JWST can compete with *Euclid* in this area, but will provide much smaller samples.

At high redshift ($z > 1.5$), which is the most active period of galaxy assembly, but where ground-based spectroscopy is inefficient, *Euclid* will truly revolutionise the field and will be a unique facility for galaxy evolution analysis. The large number of passive galaxies provided in the EDS with the BG plus RG can be used to follow in detail the growth of this fundamental class of rare galaxies that remain a challenge for models of galaxy formation.

The detection of passive galaxy spectroscopic pairs could be used to evaluate the dry galaxy merger contribution to the assembly of massive passive galaxies. Galaxy mergers are, indeed, an

<figure><img src="image_50.png" /><figcaption>**Fig. 48.** Predicted signal-to-noise ratio of the weak gravitational lensing signal (the tangential shear) per angular bin produced by NISP-detected $H\alpha$ emitters selected in five redshifts bins. Even at such high redshifts, the combination of *Euclid* image quality, depth, and area results in a strong detection.</figcaption></figure>

essential part of the evolution of galaxies in any hierarchical cosmological model, but current observational constraints on the merger rate cannot distinguish between models due to the small existing samples (Duncan et al. 2019; Conselice et al. 2022).

*Euclid*'s BG plus RG spectra in the EDS will allow us to study, using spectral fitting techniques, the evolution of massive and passive galaxies in terms of the physical properties of their stellar populations (such as ages, metallicities, dust content, and velocity dispersions), with extraordinary statistics compared with present and future ground-based data sets. High-S/N (S/N > 10) spectra are needed to reconstruct physical properties (see, e.g. Citro et al. 2016) with high accuracy; we can perform such a study on the brightest subsample or on stacked spectra.

## 10.9. The galaxy-halo connection from gravitational lensing

Science with galaxy-galaxy lensing (GGL) focuses on the relation between galaxies, their baryonic properties (luminosity, stellar mass, etc.), and their dark matter halo properties (mass, density profile, shape, and environment), that is, the galaxy-halo connection. We will exploit the precise lensing signal around foreground galaxies with the aim to constrain the halo mass as a function of luminosity and/or stellar mass and to distinguish between central and satellite galaxies. The lens samples will be split by various properties, such as rest-frame colour, redshift, and size to explore the variation in the stellar mass-halo mass relation (SHMR) as a function of galaxy type and to quantify the evolution of this relation up to $z < 1.9$. The *Euclid* data should be able to constrain this from the GGL signal alone, but the analysis may need to include additional priors, for instance from the luminosity or stellar mass function. For this, we will use lens samples obtained from *Euclid* photometric redshifts, from large ground-based spectroscopic surveys such as DESI (DESI Collaboration 2024), as well as from *Euclid* spectroscopy. In the particular case of NISP emission-line galaxies detected in spectroscopy with *Euclid*, we will model their HODs, and use this information to build mock galaxy catalogues for the cosmological analysis. As shown in Fig. 48, although at quite high redshift, we expect a GGL signal of S/N > 10 in five redshift bins in the range $0.9 < z < 1.9$ and down to 1 arcmin scale.

We also anticipate HOD constraints with galaxy-galaxy-galaxy lensing (G3L; Schneider & Watts 2005; Simon et al. 2008), which encompasses the correlation between the positions of pairs of lens galaxies with the shear of a source galaxy (shear-lens-G3L), and the correlation between the shears of pairs of
sources with the position of individual lenses (shear-shear-lens G3L). G3L depends on HOD parameters in a way that is different than for the second-order statistic GGL. Hence, similarly to HODs for cosmological inference (see Sect. 9), combining GGL and G3L can reduce parameter degeneracies in the HOD that define the occupancy of central and satellite galaxies (such as minimal halo masses for galaxy formation and satellite fractions) and improve constraining power. Moreover, G3L can probe the correlations between different lens samples, for example, red-sequence and blue-cloud galaxies (Linke et al. 2022).

While G3L has been detected in smaller and shallower ground-based surveys (Simon et al. 2013; Linke et al. 2020), *Euclid* will provide an immense improvement in the S/N due to its larger area and higher galaxy number density. This is particularly important for the shear-shear-lens G3L, whose signal is about two orders of magnitude lower than shear-lens-lens G3L (Simon et al. 2013).

Measuring the radial mass density profiles of galaxies is important because baryonic cooling and feedback effects likely alter this from the standard dark matter-only halo density profile (Sonnenfeld et al. 2018). Empirically determining the profile is critical for both understanding galaxy formation and for its impact on cosmology. This is possible through careful measurement and modelling of the excess surface density, derived from the GGL tangential shear. Moreover, by combining weak and strong lensing, we can obtain tight constraints over the whole profile, provided that the selection function for strong lenses can be quantified.

Measuring the flattening of the dark matter halo is also possible with GGL. We will use the quadrupole moment of the tangential shear referenced to the major axis of the light, correcting for spurious signal caused by cosmic shear, large-scale alignments between galaxy shapes, and the tidal field of the matter, as well as additive PSF systematics. The measurements will be conducted for lens galaxies split, for example, according to colour or luminosity/stellar mass, to facilitate the comparison to predictions from simulations. With GGL alone, it is not possible to measure the ellipticity of a halo independently from the misalignment between the orientation of the halo and its central galaxy (e.g. Bett 2012). To break this degeneracy and so constrain the halo ellipticities, we will combine GGL with shear-shear-lens G3L, which is sensitive to the overall halo ellipticity (Simon et al. 2012; Adhikari et al. 2015; Shirasaki & Yoshida 2018).

Finally, we will use GGL to assess the link between galaxy content, galaxy halos, and their large-scale environments, extending the work described in Sect. 10.6. For example, we expect that satellite galaxies will have tidally stripped halos (e.g. Sifón et al. 2018), which will become increasingly truncated as they spiral into their host group or cluster. Moreover, we will explore larger-scale structures such as filaments between galaxies (Epps & Hudson 2017), a form of G3L (lens-lens-shear), and weak lensing by cosmic voids and the galaxies within them.

## 10.10. Clusters as testbeds for astrophysical processes

Clusters of galaxies are powerful testbeds for various astrophysical phenomena, from AGN heating to tidal stripping; this is because almost all of the matter in them can be probed. The dark matter is so densely concentrated that it can be traced by strong and weak gravitational lensing (e.g. Bradač et al. 2005; Umetsu et al. 2016). The intracluster medium is visible through X-ray and sub-millimetre observations and carries information

about the thermal and chemical enrichment history (e.g. Voit 2005). Member galaxies, although representing a minor contribution to the total and baryonic mass budget, trace the dynamics of the system and retain memory of the formation and evolutionary path in their morphologies and colours. Additionally, the diffuse glow of intracluster light, situated between the cluster galaxies, enables the tracking of stars that have been stripped from previous galaxy mergers and interactions (Montes 2022). However, due to the rarity and size of clusters, our knowledge of their physical properties is limited to relatively small samples, primarily focused on core regions and predominantly at $z \lesssim 1$.

*Euclid* will be transformational, since it only needs to be combined with a probe of the gas (e.g. from eROSITA, XMM-Newton, Chandra, Planck, ACT, or SPT) to provide a comprehensive view of the state of the clusters. The high-resolution VIS images enable the mass distribution to be mapped using weak lensing, the combination of the spectra and galaxy positions will reveal the dynamical state of the cluster, and the low sky-background in the NIR means intracluster light can be observed out to $z \sim 2$.

*Euclid* will be able to measure the weak lensing masses of nearly 3000 massive clusters with a relative uncertainty of less than 30% (Euclid Collaboration: Sereno et al. 2024, also see Köhlinger et al. 2015). Weak lensing analyses of individual clusters or stacked samples will accurately probe the mass distribution from the inner and virial region, with accurate measurements of the inner slope and concentration (Sereno et al. 2016; Euclid Collaboration: Giocoli et al. 2024), to the cluster boundaries and beyond, constraining the splashback radius (the radius at which accreted matter reaches its first orbital apocentre after turnaround) and the infalling region (Umetsu & Diemer 2017; Contigiani et al. 2019; Giocoli et al. 2024), and the correlated matter in the cluster environment (Sereno et al. 2018; Giocoli et al. 2021; Ingoglia et al. 2022).

With the redshifts, the masses, and the dynamical states of the clusters provided by *Euclid* observations, the properties of the gas and the baryon budget will be readily predicted from theories of gravitational collapse (Voit 2005). Any deviation from these predictions and comparisons with state-of-the-art simulations will be used to quantify the impact of non-gravitational physics such as gas cooling and feedback from supernovae and AGN, as well as to probe hydrodynamical phenomena induced by hierarchical structure formation, such as the process of mass and energy accretion and distribution through shocks, turbulence, and bulk motions (Kravtsov & Borgani 2012), plus the relative importance of cosmic rays and magnetic fields (Brunetti & Jones 2014). These astrophysical phenomena are the reason that the galaxy-halo connection is so complex and our poor understanding of these phenomena limit our ability to constrain cosmology with both primary *Euclid* probes (see Sects. 2.2 and 8.2.1) as well as with cluster counts.

As mentioned in Sect. 10.2, *Euclid* will have an unrivalled ability to measure low-surface brightness features in the infrared, with $Y_E$, $J_E$, and $H_E$ depths of $28.4 \ \text{mag arcsec}^{-2}$ (Euclid Collaboration: Scaramella et al. 2022), which are sufficient to observe intracluster light out to 100 kpc in $z \sim 2$ protoclusters (Werner et al. 2023) and to the splashback radius in clusters to $z \gtrsim 0.6$ (Gonzalez et al. 2021). Intracluster stars, freed from their host galaxies, are expected to follow the global distribution of dark matter in clusters and may act as a luminous tracer of the dark matter distribution (Montes & Trujillo 2019), which is especially important for the $z > 1$ clusters where mass measurements from weak gravitational lensing cannot be made.
## 10.11. Protoclusters

Galaxy clusters in the local Universe are dominated by elliptical galaxies that were formed in the early Universe at $z > 2$, often in short-lived intense starbursts (e.g. Bower et al. 1992). Therefore, understanding how clusters assembled their mass in the early Universe is of critical importance, because their precursors are expected to contribute significantly to the star-formation rate density at high redshifts (Chiang et al. 2017).

Although different definitions are used in the literature, Overzier (2016) suggests to define a protocluster as ‘a non-virialised structure in the distant Universe that will finally collapse into a typical local galaxy cluster, a virialised system of a mass larger than $10^{14} M_\odot$. Although a common definition is useful in many respects, we acknowledge that the very nature of protoclusters (i.e. being defined based on their future fate) prevents a robust and univocal operational definition.

The study of galaxy protoclusters in the distant Universe has been an emerging research field in the past decade (for a review, see Overzier 2016) and is now reaching maturity, with an increasing number of systematic searches, complemented by serendipitous discoveries. Both the EWS and EDS, together with the exquisite optical/NIR imaging data sets, offer a unique opportunity to search for protoclusters in a systematic way and make a big leap forward in this research field (Böhringer et al., in prep.). To this end, we have developed several tools tailored for the detection of galaxy protoclusters, including fine-tuned variations of the two official cluster-selection algorithms AMICO (Bellagamba et al. 2018) and PZWav (Gonzalez 2014, also see Sect. 7.7.4). All these codes have been applied to real data and Euclid-like simulations to study the properties of protoclusters as they will be observed in the Euclid surveys and to test the synergies with other available data-sets. With such a study we aim to provide guidelines for the detection of these objects, the interpretation of the results, and pave the way for follow-up observations. More generally, we will study both the physical properties of the protoclusters as whole objects, and the properties of their members. This will allow us to make a complete census of protoclusters at several stages of evolution (which will require a careful synergy with theoretical simulations) and to understand and to understand the physics behind the correlation of galaxy properties with environment (see Sect. 10.6).

For the detection of protoclusters we adopt two strategies: (1) a blind search exploring the entire wealth of data; and (2) a search around possible signposts, such as sub-millimetre galaxies (e.g. Planck Collaboration Int. XXVII 2015; Planck Collaboration Int. XXXIX 2016; Calvi et al. 2023) and/or high-z radio galaxies (e.g. Kurk et al. 2000; Pentericci et al. 2000). In this way it will be possible to study, with rich statistics, any possible differences and biases between the two methods. For the protocluster detection, we will rely mostly on photometric redshifts, based mainly on optical and NIR imaging (see Sect. 7.6.1). Protoclusters could also be revealed through overdensities in the spectroscopic redshift data, out to $z = 1.8$ using $H\alpha$ and perhaps also out to $z = 2.7$ through the [O III]4959,5007 doublet. For specific areas on the sky, far-IR and (sub)mm observations are also available, and we will use these observations to reveal the progenitors of elliptical galaxies dominating local galaxy clusters, the dusty starbursts (for a review, see Alberts & Noble 2022).

## 10.12. Transient objects

Exploration of the time domain is a rapidly growing area of modern astronomy. In particular, time-domain astronomy in the NIR

is an unexplored frontier. Although the majority of the EWS will be visited only once, some fields such as the EDFs and self-calibration field are planned to be observed repeatedly, and hence they can be used to search for transient objects.

Transient surveys in the NIR can identify transients that are obscured by dust absorption. It has been suggested that a significant fraction of transients, such as supernovae (SNe) and tidal disruption events (TDEs), have been missed by optical transient surveys because of strong absorption in their host galaxies (e.g. Kool et al. 2018; Panagiotou et al. 2023). Measuring the rates of dust-obscured transients will allow us to estimate the true event rates of transients that are essential information to uncover their nature. In addition, some transients are known to be intrinsically bright in NIR and such transients can be explored by Euclid. For example, the extragalactic infrared transient survey conducted by Spitzer revealed that there is a population of unusual infrared transients without optical counterparts (Kasliwal et al. 2017). Thanks to the combination of simultaneous VIS and NISP data, Euclid will be able to carry out a census of transients that are intrinsically luminous in NIR in nearby galaxies to understand their origins.

NIR transient surveys also allow us to discover high-redshift transients. For example, Euclid can discover hundreds of Type Ia SNe at $1 \le z \le 1.5$, which could lead to a significant improvement in cosmological parameter estimation if Euclid can perform a dedicated transient survey for 6 months (Astier et al. 2014). Although such a survey is not currently planned, such a dedicated transient survey could be conducted with Euclid if there is time available later in the mission. However, even with the current survey plan, long-lasting luminous transients, such as superluminous SNe and pair-instability SNe, can be discovered out to $z \sim 3.5$ in the EDFs (Inserra et al. 2018; Moriya et al. 2022). High-redshift superluminous SNe and pair-instability SNe allow us to constrain properties of massive stars (expected to be the progenitors of such SNe) at high redshifts (Moriya et al. 2022; Tanikawa et al. 2023). High-redshift superluminous SNe may also provide additional cosmological parameter constraints (Inserra et al. 2018).

As an indication of the expected numbers of SNe detectable with Euclid, the weekly observations of the self-calibration field (with an area of approximately 3 deg$^2$) obtained during the PV phase can yield around 40 Type Ia SNe discoveries, of which about 10 are expected to be at $z > 1$. A similar number of core-collapse SNe is also expected to be discovered. During regular operations, the self-calibration field will be observed monthly. Such long-term monthly observations over the full duration of the survey should enable the discovery of around 500 Type Ia SNe at $z > 1$ and around 200 core-collapse SNe at $z > 1$. In addition, up to dozens of superluminous SNe and pair-instability SNe out to $z \sim 4$ may be discovered during the long-term self-calibration field observations, depending on their unknown event rates.

An example of an early Euclid discovery of a transient object is shown in Fig. 49. The object with coordinates RA = 09h59m39.872s, Dec = +02°35′54″129 (J2000.0) was discovered in Euclid observations of the COSMOS field taken on 21–23 November 2023. The object, a likely SN, brightened significantly during this period, enabling a clear detection in $I_E$ difference images. Subsequent analysis shows that the object is also clearly detected in the three Euclid NIR bands. Given that there is no previously known transient reported at this position, this is a new discovery by Euclid and it is officially named as AT 2023adqt. The host galaxy (SDSS J095940.08+023554.6) has a spectroscopic redshift of $z = 0.246$ (Knobel et al. 2012).
<figure><img src="image_51.png" /></figure>

**Fig. 49.** Top row: the left panel shows a section of a VIS image acquired on 21 November 2023 centred on RA = 09°59′39.872s, Dec = +02°35′54.′129 (J2000.0), the location of the SN candidate AT 2023adqt (internally called Euclid_SNT_2023B). It is close to the galaxy SDSS J095940.08+023554.6 (z = 0.246; Knobel et al. 2012), which is the likely host. The right panel shows this galaxy in a deep stacked image in the r-band obtained by the SUDARE program in 2011 using the VLT Survey Telescope (VST, Cappellaro et al. 2015). No source is visible on the SN position. Middle row: the SN candidate is clearly visible on two VIS $I_E$ band images acquired on 21 November 2023 and 23 November 2023 as well as in the corresponding difference image. Bottom row: the SN candidate is not visible in the NISP $J_E$ band image on 21 November 2023, but it appears on 23 November 2023. The difference image clearly shows the SN candidate.

Photometry of the transient object yields a brightness of $I_E = 23.64 \pm 0.06$, $Y_E = 25.18 \pm 0.10$, $J_E = 24.60 \pm 0.09$ and $H_E = 24.94 \pm 0.15$ on 23 November 2023. Its optical to NIR colours are consistent with the rise of a SN at the same redshift, although at this stage it is not possible to determine the SN type. The clear detection and deep NIR photometry, enabling detection even when significantly far from peak brightness, demonstrate Euclid 's power for the detection and study of transient objects.

Euclid can also provide important information on transients discovered by the LSST (Guy et al. 2022). As the Euclid survey fields overlap with some LSST fields, some transients are likely to be observed by both Euclid and the LSST. In such a case, Euclid can provide complementary NIR photometry information to LSST. Such NIR data can be used to constrain dust production in and around transients, for example. The joint detection of thousands of Type Ia SNe by Euclid and LSST would provide a valuable contribution to our understanding of the impact of dust on Type Ia SN cosmology (Bailey et al. 2023). Euclid will also provide some spectroscopic measurements of SNe after scene modelling (e.g. Lezmy et al. 2022). For transients discovered by LSST and other facilities, the EWS and EDS can provide essential information such as morphology, infrared photometry, and spectroscopy of their host galaxies. Furthermore, red supergiant progenitors of Type II SNe discovered by LSST or other transient surveys may be identified in the Euclid images taken before their explosion.

## 10.13. Demographics of cool exoplanets

From 2027 the NASA Roman mission is expected to undertake the Roman Galactic Exoplanet Survey (RGES, Penny et al. 2019), a statistical census of the cool exoplanet regime using the microlensing effect. The cool exoplanet census will be pivotal for testing planet formation models (Burn et al. 2021), and the RGES census will complement that of hot exoplanets obtained by Kepler (Borucki et al. 2010). RGES is the key science driver for the Galactic Bulge Time Domain Survey (GBTDS), one of the three Roman core community surveys that will each occupy around 25% of the first 5 years of Roman mission.

The RGES is designed to find around 1400 cool exoplanets down to the mass of Mars (Penny et al. 2019), and to be able to make direct mass measurements for at least half of its sample. Direct planet mass measurements can be achieved through a number of approaches, including: direct measurement of the lens host flux; measurements of finite-source magnification effects in the lightcurve; and measurements of PSF distortion arising from relative proper motion between the foreground lensed host and background magnified source star. Together with the event duration, such measurements provide the means to break what would otherwise be a three-way degeneracy between the planet mass, distance, and transverse speed.

However, many Roman events will have insufficient data to fully break the mass-distance-speed degeneracy, and others may have relatively poor precision due to the challenging measurement of lens-source relative proper motion. Due to the very close alignment of lens and source on the sky, measurements of proper motion rely on the detection of PSF skewness, the measurement precision of which improves with the cube of the observation time baseline (Bennett et al. 2007).

At the time of writing, Euclid precursor imaging of the Roman fields is under active consideration. The GBTDS area can be covered by nine Euclid pointings, taking up to 42 hours of time if executed using four standard ROS cycles for each pointing (see Sect. 4.1). Due to pointing restrictions imposed by the solar aspect angle, the GBTDS can only be accessed by Euclid near the spring and autumn equinox for periods of up to 23 days. If these observations by Euclid can be scheduled during the first year of operations, this would extend the proper motion sensitivity baseline for Roman from 5 years to 8 years and so improve the planet mass measurement precision by a factor $(8/5)^3 \approx 4$ for events that rely on proper motion measurements (Bachelet et al. 2022; Kerins et al. 2023).

## 10.14. Solar system objects

The number of Solar System objects (SSOs) for which the composition can be characterised, has recently increased significantly, thanks to low-resolution reflectance spectroscopy obtained by Gaia for more than 60 000 objects (Gaia Collaboration 2018; Tanga et al. 2023; Gaia Collaboration 2023a). The next Gaia release will increase this sample further, and the upcoming LSST is expected to discover and characterise 5–6 million SSOs with broadband photometry in the optical (LSST Science Collaboration 2009). This avalanche of optical data should be contrasted with the shortage of observations in the NIR.

To date, the largest corpus of NIR broad-band colours for 34 998 SSOs was extracted from the ESO Visible and Infrared Survey Telescope for Astronomy (VISTA) VHS survey (Popescu et al. 2016). Decades of targeted spectral observations in the NIR raised the sample to only about 3000 low-resolution
spectra covering the 0.9–2.4 µm range (see Mahlke et al. 2022). Low-resolution spectroscopy or broad-band photometry in the near-infrared is, however, crucial to disentangle among several compositions that are otherwise degenerate with only visible data (e.g. DeMeo et al. 2009). The $Y_E$, $J_E$, and $H_E$ filters of the Euclid NISP photometer (Fig. 11) offer an important complement to visible colours to characterise the surface composition of SSOs (Carry 2018). However, the geometry of the observations implies high phase angles. Hence, it will be necessary to account for possible phase effects which may affect colours (Mahlke et al. 2021; Alvarez-Candal 2024).

Characterising the distribution of compositions of SSOs is key for understanding the formation of our Solar System (DeMeo & Carry 2014). Among the thousands of exoplanet systems discovered to date<fnref n="31" />, the Solar System with its external giant planets is more an exception than the rule (most systems are composed of multiple super-Earth planets, e.g. Raymond et al. 2020). Several models have been put forward to explain the peculiar orbital architecture of the Solar System (e.g. Walsh et al. 2011; Raymond & Izidoro 2017). These models succeed in reproducing the dynamical architecture of terrestrial and giant planets, but often diverge in the dynamical, and more importantly compositional, distribution of SSOs.

The current distribution of orbits and compositions is, however, an evolved version of the primordial distribution, resulting from planetary formation. Collisions break up bodies, injecting fragments into orbit that enhance the fraction of bodies sharing the same composition on similar orbits. These clumps of fragments are called ‘dynamical families’ (Hirayama 1918). It is crucial to distinguish between collisional fragments and planetsimals (Delbo et al. 2017) to debias the current distribution of compositions and access the primordial distribution. An additional complication results from the secular, non-gravitational, dynamical evolution of SSOs which spread structures through the Yarkovsky effect (due to the delayed thermal emission of the incoming solar illumination, Bottke et al. 2001). The Yarkovsky effect results from a complex interplay of the physical properties of SSOs (diameter, spin orientation, surface reflectivity, etc). As such, deciphering the early history of the Solar System requires the characterisation of the composition of numerous SSOs and of their physical properties.

There are millions of SSOs with apparent magnitudes within the depth of the EWS and observable almost at any time on the celestial sphere (Grav et al. 2011). Because the main Euclid cosmological survey avoids low ecliptic latitudes (Fig. 14), the fraction of SSOs in the survey is, however, small. Nevertheless, considering an early design of the Euclid survey, it is predicted that about 150 000 objects will be serendipitously observed over the course of the mission (Carry 2018). Conversely, the SSOs detected by Euclid will belong to populations with large inclination to the ecliptic plane (Carruba & Machuca 2011; Novaković et al. 2011; Terai & Itoh 2011; Chen et al. 2016; Saifollahi et al. 2023), often missed by discovery surveys more typically focusing on the ecliptic (see reports of biases against high inclination by Mahlke et al. 2018; Carry et al. 2021).

The sequence of observations, with four repetitions of VIS-$Y_E$, $J_E$, and $H_E$ exposures (Sect. 4.1), is fortunately well matched to the detection of SSOs from their motion between frames. While objects from the outer Solar System (Kuiper-belt objects or Centaurs) will appear as point sources, objects closer to the Earth (Jupiter Trojans, asteroids, or near-Earth objects) will produce long trails on Euclid frames (up to tens of pixels,

Carry 2018). Therefore, two different methods are used to detect SSOs: those optimised for slow-moving point sources (Nucita et al., in prep.) and those for fast-moving trailed sources (Pöntinen et al. 2020, 2023).

Going beyond the basic detections, Euclid's observing sequence allows us to determine the intrinsic colours of SSOs, without any bias introduced by the light curve due to their irregular spinning shapes (Popescu et al. 2016; Carry 2018). The SSOs detected by Euclid, once combined with colours in the visible (from, e.g. LSST), will provide a large reference sample to study the distribution of compositions in the Solar System. In addition to merging colours at the catalogue level, the quasi-simultaneous observations of SSOs by Euclid and LSST would provide a direct and accurate measurement of their distances, and hence dramatically improve the quality of their orbits (Granvik et al. 2007; Rhodes et al. 2017). While such observations may happen by pure coincidence, scheduling them would rely on coordination with LSST (Snodgrass et al. 2018; Guy et al. 2022).

Euclid's sequence of observations will also provide hour-long light curves, critical for the determination of physical properties (rotation period and obliquity mainly). While photometry that is sparse in time (in which the time interval between measure is larger than the period of the signal) can be successfully used to determine the physical properties of SSOs (Kaasalainen 2004), the rate of objects for which solutions are found remains limited (under 50%, see Durech & Hanuš 2023). The combination of a partial light curve to the sparse photometry allows us to reject degenerate solutions, efficiently improving the solutions (Durech et al. 2015). Euclid light curves, along with the NISP spectroscopic measurements, will thus be particularly powerful when used together with LSST photometry.

## 11. Conclusions and outlook

Euclid was successfully launched on 1 July 2023 into an orbit around L2, which provides the thermally stable environment that is needed to achieve its main objective, namely to measure the growth of structure over a significant fraction of the age of the Universe with unprecedented precision. Comparison of the measurements with models of structure formation can shed light on the origin of the accelerated expansion of the Universe, test for deviations from GR, examine scenarios for inflation, and robustly explore many other aspects of the ΛCDM model.

Euclid can achieve its challenging objectives because it is optimised to measure galaxy clustering and weak gravitational lensing, while ensuring that observational sources of bias remain subdominant. As discussed in Sect. 4, the EWS will cover 14 000 deg² of extragalactic sky, combining near-infrared spectroscopy and photometry with diffraction-limited visual imaging, while the EDS will yield deep observations that cover 53 deg². Additional deep observations, primarily designed for calibration purposes, provide further opportunities to study the distant Universe. To obtain all these data within its nominal mission span of six years, the spacecraft contains two instruments with a common FoV of about 0.54 deg². The VIS instrument (Sect. 3.4; Euclid Collaboration: Cropper et al. 2025) provides the high-resolution optical imaging needed for accurate shape measurements of about 1.5 billion galaxies. It is complemented by NISP (Sect. 3.5; Euclid Collaboration: Jahnke et al. 2025), which provides near-IR imaging and spectroscopy over the same area.

The performance of the spacecraft and the instruments is excellent, but as discussed in Sect. 5, several anomalies were

<footnote n="31">³¹ https://exoplanetarchive.ipac.caltech.edu</footnote>
discovered during commissioning. Fortunately, all of these can
be mitigated. The discovery of high levels of stray light for a wide
range of AA values led to a complete overhaul of the observ-
ing plan. The main consequence of a more restricted range in
spacecraft orientation is a modest reduction in survey speed.

After an initial performance and verification phase, a period
of 24 hours was devoted to carrying out observations of targets
that could highlight the broad astrophysical potential of *Euclid*.
The first results from these ERO data are presented in an accom-
panying series of papers (Cuillandre et al. 2025a,b; Martín et al.
2025; Massari et al. 2025; Hunt et al. 2025; Saifollahi et al. 2025;
Kluge et al. 2025; Atek et al. 2025; Weaver et al. 2025). These
provide concrete validations of the wide range of science objec-
tives listed in this paper, for example highlighting the potential
for the study of LSB features, or the study of UCD and GC
populations.

On 14 February 2024, the scientific survey started and *Euclid* commenced its journey to explore the dark Universe, at a rate of about 10 deg² per day. First public releases are planned in early 2025 (a single visit over the EDFs) and mid-2026 (about 2500 deg² of the EWS). The resulting high-quality data products that will be released, described in Sect. 7, will allow us to determine cosmological parameters with unprecedented precision using the primary probes (Sect. 8), and this can be improved further with additional probes (Sect. 9). Importantly, the impact of *Euclid* is not limited to cosmology, and some other applications of the data were highlighted in Sect. 10.

The data obtained to date show that *Euclid* is on track to ful-
fil the many science goals described in this paper. What we have
outlined here, has largely focused on studies where the *Euclid*
data play a dominant role; however, we expect a far greater
impact when combining *Euclid* with other data. For instance,
cross-correlations with data sets at completely different wave-
lengths, as well as joint analyses with other spectroscopic and
imaging surveys, will continue to add value. The deep, high-
resolution space-based data covering a large fraction of the
extragalactic sky will also enable studies in a huge array of
astrophysics topics. While many of these have been described
in this paper, there is also the exciting possibility for *Euclid*
enabling discoveries about our Universe that were completely
unanticipated. The EWS and EDS images and catalogues will be
an exceptional database of astronomical sources for decades to
come and will be a gold mine for detecting new rare or unknown
astronomical phenomena.

Acknowledgements. The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of *Euclid*, in particular the Agenzia Spaziale Italiana, the Austrian Forschungsförderungsgesellschaft funded through BMK, the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches Zentrum für Luft- und Raumfahrt, the DTU Space and the Niels Bohr Institute in Denmark, the French Centre National d'Etudes Spatiales, the Fundação para a Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de Ciencia, Innovación y Universidades, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Nederlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Research Council of Finland, the Romanian Space Agency, the State Secretariat for Education, Research, and Innovation (SERI) at the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete and detailed list is available on the *Euclid* web site (http://www.euclid-ec.org).

References

Abazajian, K. N., Adshead, P., Ahmed, Z., et al. 2016, arXiv e-prints
[arXiv:1610.02743]

Abbott, T., Abdalla, F. B., Allam, S., et al. 2016, Phys. Rev. D, 94, 022001

Abbott, T. M. C., Abdalla, F. B., Alarcon, A., et al. 2018a, Phys. Rev. D, 98, 043526

Abbott, T. M. C., Abdalla, F. B., Allam, S., et al. 2018b, ApJS, 239, 18

Abbott, T. M. C., Abdalla, F. B., Alarcon, A., et al. 2019, Phys. Rev. D, 100, 023541

Abbott, T. M. C., Adamów, M., Aguena, M., et al. 2021, ApJS, 255, 20

Abbott, T. M. C., Aguena, M., Alarcon, A., et al. 2022, Phys. Rev. D, 105, 023520

Abbott, T. M. C., Aguena, M., Alarcon, A., et al. 2023, Phys. Rev. D, 107, 023531

Abdalla, F. B., Amara, A., Capak, P., et al. 2008, MNRAS, 387, 969

Abdurro'uf, Lin, Y.-T., Hirashita, H., et al. 2022a, ApJ, 926, 81

Abdurro'uf, Lin, Y.-T., Hirashita, H., et al. 2022b, ApJ, 935, 98

Acebron, A., Schuldt, S., Grillo, C., et al. 2023, A&A, 680, L9

Ade, P., Aguirre, J., Ahmed, Z., et al. 2019, J. Cosmology Astropart. Phys., 02, 056

Adhikari, S., Chue, C. Y. R., & Dalal, N. 2015, J. Cosmology Astropart. Phys., 01, 009

Aihara, H., AlSayyad, Y., Ando, M., et al. 2022, PASJ, 74, 247

Aihara, H., Arimoto, N., Armstrong, R., et al. 2018, PASJ, 70, S4

Aird, J., Coil, A. L., Moustakas, J., et al. 2013, ApJ, 775, 41

Aker, M., Beglarian, A., Behrens, J., et al. 2022, Nat. Phys., 18, 160

Akeson, R., Armus, L., Bachelet, E., et al. 2019, arXiv e-prints
[arXiv:1902.05569]

Alam, S., Ata, M., Bailey, S., et al. 2017, MNRAS, 470, 2617

Alam, S., Aubert, M., Avila, S., et al. 2021, Phys. Rev. D, 103, 083533

Alberts, S., & Noble, A. 2022, Universe, 8, 554

Albrecht, A., Bernstein, G., Cahn, R., et al. 2006, arXiv e-prints
[astro-ph/0609591]

Albrecht, A., Amendola, L., Bernstein, G., et al. 2009, arXiv e-prints
[arXiv:0901.0721]

Alcock, C., & Paczynski, B. 1979, Nature, 281, 358

Allen, S. W., Evrard, A. E., & Mantz, A. B. 2011, ARA&A, 49, 409

Allevato, V., Viitanen, A., Finoguenov, A., et al. 2019, A&A, 632, A88

Alonso, D., Fabbian, G., Storey-Fisher, K., et al. 2023, J. Cosmology Astropart. Phys., 11, 043

Alvarez-Candal, A. 2024, A&A, 685, A29

Amara, A., & Réfrégier, A. 2007, MNRAS, 381, 1018

Amara, A., & Réfrégier, A. 2008, MNRAS, 391, 228

Amendola, L., Appleby, S., Avgoustidis, A., et al. 2018, Liv. Rev. Relativ., 21, 2

Amon, A., Gruen, D., Troxel, M. A., et al. 2021, Phys. Rev. D, 105, 023514

Anderson, L., Aubourg, E., Bailey, S., et al. 2012, MNRAS, 427, 3435

Andreon, S. 2016, A&A, 587, A158

Angulo, R. E., Zennaro, M., Contreras, S., et al. 2021, MNRAS, 507, 5869

Antilogus, P., Astier, P., Doherty, P. E., Guyonnet, A., & Regnault, N. 2014, J. Instrum., 9, C03048

Antonucci, R. 1993, ARA&A, 31, 473

Aricò, G., Angulo, R. E., Hernández-Monteagudo, C., et al. 2020, MNRAS, 495, 4800

Aricò, G., Angulo, R. E., Contreras, S., et al. 2021, MNRAS, 506, 4070

Arnold, C., Li, B., Giblin, B., Harnois-Déraps, J., & Cai, Y.-C. 2022, MNRAS, 515, 4161

Asgari, M., & Heymans, C. 2019, MNRAS, 484, L59

Asgari, M., Lin, C.-A., Joachimi, B., et al. 2021, A&A, 645, A104

Assef, R. J., Stern, D., Noirot, G., et al. 2018, ApJS, 234, 23

Astier, P., Balland, C., Brescia, M., et al. 2014, A&A, 572, A80

Atek, H., Richard, J., Jauzac, M., et al. 2015, ApJ, 814, 69

Atek, H., Gavazzi, R., Weaver, J., et al. 2025, A&A, 697, A15 (Euclid on Sky SI)

Bachelet, E., Specht, D., Penny, M., et al. 2022, A&A, 664, A136

Bacon, D. J., Refregier, A. R., & Ellis, R. S. 2000, MNRAS, 318, 625

Bagley, M. B., Scarlata, C., Mehta, V., et al. 2020, ApJ, 897, 98

Bahcall, N. A., & Fan, X. 1998, ApJ, 504, 1

Bailey, A. C., Vincenzi, M., Scolnic, D., et al. 2023, MNRAS, 524, 5432

Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5

Balestra, I., Mercurio, A., Sartoris, B., et al. 2016, ApJS, 224, 33

Ballardini, M., Akrami, Y., Finelli, F., et al. 2024, A&A, 683, A220

Ballinger, W. E., Peacock, J. A., & Heavens, A. F. 1996, MNRAS, 282, 877

Bañados, E., Venemans, B. P., Mazzucchelli, C., et al. 2018, Nature, 553, 473

Bargiacchi, G., Benetti, M., Capozziello, S., et al. 2022, MNRAS, 515, 1795

Baron, M. 2024, PhD thesis, Université Claude Bernard Lyon I, France, https://theses.hal.science/tel-04610414

Baron, M., Sassolas, B., Frugier, P. A., et al. 2022, SPIE Conf. Ser., 12180, 121804V

Baron, M., Sassolas, B., Pinard, L., & Ealet, A. 2023, Opt. Express, 31, 32968

Barreira, A., Krause, E., & Schmidt, F. 2018, J. Cosmology Astropart. Phys., 06, 015

Bartelmann, M. 2010, Class. Quantum Grav., 27, 233001

Bartelmann, M., & Schneider, P. 2001, Phys. Rep., 340, 291

Bartelmann, M., Narayan, R., Seitz, S., & Schneider, P. 1996, ApJ, 464, L115

Barthelemy, A., Codis, S., Uhlemann, C., Bernardeau, F., & Gavazzi, R. 2020, MNRAS, 492, 3420
Bassett, B. A., Tsujikawa, S., & Wands, D. 2006, *Rev. Mod. Phys.*, **78**, 537

Battaglieri, M., Belloni, A., Chou, A., et al. 2017, arXiv e-prints [arXiv:1707.04591]

Beauchamps, S. G., Lacasa, F., Tutusaus, I., et al. 2022, A&A, **659**, A128

Becker, M. R., Troxel, M. A., MacCrann, N., et al. 2016, *Phys. Rev. D*, **94**, 022002

Behroozi, P. S., Wechsler, R. H., & Wu, H.-Y. 2013, ApJ, **762**, 109

Bell, E. F., McIntosh, D. H., Katz, N., & Weinberg, M. D. 2003, ApJS, **149**, 289

Bellagamba, F., Roncarelli, M., Maturi, M., & Moscardini, L. 2018, MNRAS, **473**, 5221

Belokurov, V., Erkal, D., Evans, N. W., Koposov, S. E., & Deason, A. J. 2018, MNRAS, **478**, 611

Bennett, D. P., Anderson, J., & Gaudí, B. S. 2007, ApJ, **660**, 781

Bennett, J. J., Buldgen, G., De Salas, P. F., et al. 2021, J. Cosmology Astropart. Phys., **04**, 073

Benson, B. A., Ade, P. A. R., Ahmed, Z., et al. 2014, SPIE Conf. Ser., **9153**, 91531P

Bergamini, P., Schuldert, S., Acebron, A., et al. 2024, A&A, **682**, L2

Bernardeau, F., van Waerbeke, L., & Mellier, Y. 1997, A&A, **322**, 1

Bernardeau, F., Colombi, S., Gaztañaga, E., & Scoccimarro, R. 2002, Phys. Rep., **367**, 1

Bernardeau, F., Nishimichi, T., & Taruya, A. 2014, MNRAS, **445**, 1526

Bernstein, G. 2002, PASP, **114**, 98

Bernstein, G. M. 2009, ApJ, **695**, 652

Bernstein, G., & Jain, B. 2004, ApJ, **600**, 17

Bertin, E. 2010, *Swarp: Resampling and Co-adding* FITS Images Together, Astrophysics Source Code Library [record ascl:1010.068]

Bertin, E., Mellier, Y., Radovich, M., et al. 2002, in Astronomical Data Analysis Software and Systems XI, eds. D. A. Bohlender, D. Durand, & T. H. Handley, ASP Conf. Ser., **281**, 228

Bertin, E., Schefer, M., Apostolakos, N., et al. 2020, in Astronomical Data Analysis Software and Systems XXIX, eds. R. Pizzo, E. R. Deul, J. D. Mol, J. de Plaa, & H. Verkouter, ASP Conf. Ser., **527**, 461

Betoule, M., Kessler, R., Guy, J., et al. 2014, A&A, **568**, A22

Bett, P. 2012, MNRAS, **420**, 3303

Beutler, F., Seo, H.-J., Ross, A. J., et al. 2017, MNRAS, **464**, 3409

Beutler, F., Castorina, E., & Zhang, P. 2019, J. Cosmology Astropart. Phys., **03**, 040

Bianchi, D., Gil-Marín, H., Ruggeri, R., & Percival, W. J. 2015, MNRAS, **453**, L11

Bianchini, F., & Reichardt, C. L. 2018, ApJ, **862**, 81

Biesiadzinski, T., Lorenzon, W., Newman, R., et al. 2011, PASP, **123**, 958

Bisigello, L., Kuchner, U., Conselice, C. J., et al. 2020, MNRAS, **494**, 2337

Blakeslee, J. P., Jordán, A., Mei, S., et al. 2009, ApJ, **694**, 556

Blandford, R. D., Saust, A. B., Brainerd, T. G., & Villumsen, J. V. 1991, MNRAS, **251**, 600

Blanton, M. R., Eisenstein, D., Hogg, D. W., & Zehavi, I. 2006, ApJ, **645**, 977

Blazek, J. A., MacCrann, N., Troxel, M. A., & Fang, X. 2019, *Phys. Rev. D*, **100**, 103506

Bleem, L. E., Salder, B., de Haan, T., et al. 2015, ApJS, **216**, 27

Bocquet, S., Dietrich, J. P., Schrabback, T., et al. 2019, ApJ, **878**, 55

Bogdán, Á., Goulding, A. D., Natarajan, P., et al. 2024, Nat. Astron., **8**, 126

Boldrin, M., Giocoli, C., Meneghetti, M., & Moscardini, L. 2012, MNRAS, **427**, 3134

Boldrin, M., Giocoli, C., Meneghetti, M., et al. 2016, MNRAS, **457**, 2738

Bolliet, B., Colin Hill, J., Ferraro, S., Kusiak, A., & Krolewski, A. 2023, J. Cosmology Astropart. Phys., **03**, 039

Bonaca, A., Hogg, D. W., Price-Whelan, A. M., & Conroy, C. 2019, ApJ, **880**, 38

Bonici, M., Carbone, C., Davini, S., et al. 2023, A&A, **670**, A47

Borgani, S., Rosati, P., Tozzi, P., et al. 2001, ApJ, **561**, 13

Borucki, W. J., Koch, D., Basri, G., et al. 2010, Science, **327**, 977

Bosch, J., Armstrong, R., Bickerton, S., et al. 2018, PASJ, **70**, S5

Bosch, J., AlSayyad, Y., Armstrong, R., et al. 2019, in Astronomical Data Analysis Software and Systems XXVII, eds. P. J. Teuben, M. W. Pound, B. A. Thomas, & E. M. Warner, ASP Conf. Ser., **523**, 521

Bose, B., Cataneo, M., Tröster, T., et al. 2020, MNRAS, **498**, 4650

Bottke, W. F., Yokrouhlický, D., Broz, M., Nesvorný, D., & Morbidelli, A. 2001, Science, **294**, 1693

Boucaud, A., Bocchio, M., Abergel, A., et al. 2016, A&A, **596**, A63

Bougoin, M., Mallet, F., Lavenac, J., et al. 2019, SPIE Conf. Ser., **11180**, **11180P**

Bower, R. G., Lucey, J. R., & Ellis, R. S. 1992, MNRAS, **254**, 601

Bowler, R. A. A., Dunlop, J. S., McLure, R. J., & McLeod, D. J. 2017, MNRAS, **466**, 3612

Bowler, R. A. A., Jarvis, M. J., Dunlop, J. S., et al. 2020, MNRAS, **493**, 2059

Boyle, A., Uhlemann, C., Friedrich, O., et al. 2021, MNRAS, **505**, 2886

Bradač, M., Schneider, P., Lombardi, M., & Erben, T. 2005, A&A, **437**, 39

Bradshaw, E. J., Almaini, O., Hartley, W. G., et al. 2013, MNRAS, **433**, 194

Bridle, S., & King, L. 2007, New J. Phys., **9**, 444

Bridle, S., Balan, S. T., Bethge, M., et al. 2010, MNRAS, **405**, 2044

Brown, M. L., Taylor, A. N., Hambly, N. C., & Dye, S. 2002, MNRAS, **333**, 501

Brown, M. L., Castro, P. G., & Taylor, A. N. 2005, MNRAS, **360**, 1262

Brunetti, G., & Jones, T. W. 2014, Int. J. Mod. Phys. D, **23**, 1430007

Brunner, H., Liu, T., Lamer, G., et al. 2022, A&A, **661**, A1

Bruzual, G., & Charlot, S. 2003, MNRAS, **344**, 1000

Buitrago, F., Trujillo, I., Curtis-Lake, E., et al. 2017, MNRAS, **466**, 4888

Bulbul, E., Liu, A., Kluge, M., et al. 2024, A&A, **685**, A106

Bunker, A. J., Saxena, A., Cameron, A. J., et al. 2023, A&A, **677**, A88

Burger, P. A., Porth, L., Heydenreich, S., et al. 2024, A&A, **683**, A103

Burkert, A., & Forbes, D. A. 2020, AJ, **159**, 56

Burn, R., Schlecker, M., Mordasini, C., et al. 2021, A&A, **656**, A72

Calvi, R., Castignani, G., & Dannerbauer, H. 2023, A&A, **678**, A15

Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, **533**, 682

Caminha, G. B., Suyu, S. H., Grillo, C., & Rosati, P. 2022, A&A, **657**, A83

Cantiello, M., Jensen, J. B., Blakeslee, J. P., et al. 2018, ApJ, **854**, L31

Cantiello, M., Venhola, A., Grado, A., et al. 2020, A&A, **639**, A136

Cappellaro, E., Botticella, M. T., Pignata, G., et al. 2015, A&A, **584**, A62

Cappelluti, N., Kashlinsky, A., Arendt, R. G., et al. 2013, ApJ, **769**, 68

Cappelluti, N., Arendt, R., Kashlinsky, A., et al. 2017, ApJ, **847**, L11

Carlsten, S. G., Greene, J. E., Beaton, R. L., & Greco, J. P. 2022, ApJ, **927**, 44

Carlstrom, J. E., Holder, G. P., & Reese, E. D. 2002, ARA&A, **40**, 643

Carrilho, P., Moretti, C., & Pourtsidou, A. 2023, J. Cosmology Astropart. Phys., **01**, 028

Carron, J. 2013, A&A, **551**, A88

Carruba, V., & Machuca, J. F. 2011, MNRAS, **418**, 1102

Carry, B. 2018, A&A, **609**, A113

Carry, B., Thuillot, W., Spoto, F., et al. 2021, A&A, **648**, A96

Casas, S., Cardone, V. F., Sapone, D., et al. 2023, A&A, submitted [arXiv:2306.11053]

Castignani, G., & Benoist, C. 2016, A&A, **595**, A111

Castro, T., Borgani, S., Dolag, K., et al. 2021, MNRAS, **500**, 2316

Cataneo, M., Rapetti, D., Schmidt, F., et al. 2015, *Phys. Rev. D*, **92**, 044009

Chambers, K. C., Magnier, E. A., Metcalfe, N., et al. 2016, arXiv e-prints [arXiv:1612.05560]

Chaves-Montero, J., Hernández-Monteagudo, C., Angulo, R. E., & Emberson, J. D. 2021, MNRAS, **503**, 1798

Chen, Y.-T., Lin, H. W., Holman, M. J., et al. 2016, ApJ, **827**, L24

Chen, C. T. J., Brandt, W. N., Luo, B., et al. 2018, MNRAS, **478**, 2132

Chen, S.-F., Lee, H., & Dvorkin, C. 2021, J. Cosmology Astropart. Phys., **05**, 030

Cheng, S., & Ménard, B. 2021, MNRAS, **507**, 1012

Cheng, S., Ting, Y.-S., Ménard, B., & Bruna, J. 2020, MNRAS, **499**, 5902

Chiang, Y.-K., Overzier, R. A., Gebhardt, K., & Henriques, B. 2017, ApJ, **844**, L23

Chipman, R., Lam, W.-S., & Young, G. 2019, Polarized Light and Optical Systems (CRC Press)

Chisari, N. E., Mead, A. J., Joudaki, S., et al. 2019, Open J. Astrophys., **2**, 4

Chiu, I. N., Klein, M., Mohr, J., & Bocquet, S. 2023, MNRAS, **522**, 1601

Chon, G., Challinor, A., Prunet, S., Hivon, E., & Szapudi, I. 2004, MNRAS, **350**, 914

Cimatti, A., Robberto, M., Baugh, C., et al. 2009, *Exp. Astron.*, **23**, 39

Cirasuolo, M., McLure, R. J., Dunlop, J. S., et al. 2007, MNRAS, **380**, 585

Citro, A., Pozzetti, L., Moresco, M., & Cimatti, A. 2016, A&A, **592**, A19

Clarke, A., Hall, D., Murray, N., Holland, A., & Burt, D. 2012, SPIE Conf. Ser., **8453**, **845311**

Cleri, N. J., Trump, J. R., Backhaus, B. E., et al. 2022, ApJ, **929**, 3

Clowe, D., Bradač, M., Gonzalez, A. H., et al. 2006, ApJ, **648**, L109

Coe, D., Fuselier, E., Benítez, N., et al. 2008, ApJ, **681**, 814

Cole, S., Percival, W. J., Peacock, J. A., et al. 2005, MNRAS, **362**, 505

Colless, M., Dalton, G., Maddox, S., et al. 2001, MNRAS, **328**, 1039

Collett, T. E. 2015, ApJ, **811**, 20

Collett, T. E., & Bacon, D. J. 2016, MNRAS, **456**, 2210

Collister, A. A., & Lahav, O. 2005, MNRAS, **361**, 415

Conselice, C. J. 2003, ApJS, **147**, 1

Conselice, C. J. 2014, ARA&A, **52**, 291

Conselice, C. J., Bershady, M. A., Dickinson, M., & Papovich, C. 2003, AJ, **126**, 1183

Conselice, C. J., Blackburne, J. A., & Papovich, C. 2005, ApJ, **620**, 564

Conselice, C. J., Mundy, C. J., Ferreira, L., & Duncan, K. 2022, ApJ, **940**, 168

Contarini, S., Verza, G., Pisani, A., et al. 2022, A&A, **667**, A162

Contigiani, O., Hoekstra, H., & Bahé, Y. M. 2019, MNRAS, **485**, 408

Cooke, R. J., Pettini, M., & Steidel, C. C. 2018, ApJ, **855**, 102

Cooper, A. P., Cole, S., Frenk, C. S., et al. 2010, MNRAS, **406**, 744

Cooper, M. C., Griffith, R. L., Newman, J. A., et al. 2012, MNRAS, **419**, 3018

Costanzi, M., Rozo, E., Simet, M., et al. 2019, MNRAS, **488**, 4779

Costanzi, M., Saro, A., Bocquet, S., et al. 2021, Phys. Rev. D, **103**, 043522

Coulton, W. R., Armstrong, R., Smith, K. M., Lupton, R. H., & Spergel, D. N. 2018, AJ, **155**, 258
Crittenden, R. G., Natarajan, P., Pen, U.-L., & Theuns, T. 2002, ApJ, 568, 20

Croft, R. A. C., & Dailey, M. 2011, arXiv e-prints [arXiv:1112.3108]

Crone Odekon, M., Hallenbeck, G., Haynes, M. P., et al. 2018, ApJ, 852, 142

Cropper, M., Hoekstra, H., Kitching, T., et al. 2013, MNRAS, 431, 3103

Cropper, M., Pottinger, S., Niemi, S., et al. 2016, SPIE Conf. Ser., 9904, 99040Q

Cropper, M., Pottinger, S., Azzollini, R., et al. 2018, SPIE Conf. Ser., 10698, 1069828

Cucciati, O., Iovino, A., Kovač, K., et al. 2010, A&A, 524, A2

Cucciati, O., Marulli, F., Cimatti, A., et al. 2016, MNRAS, 462, 1786

Cuillardre, J.-C., Bertin, E., Bolzonella, M., et al. 2025a, A&A, 697, A6 (Euclid on Sky SI)

Cuillardre, J.-C., Bolzonella, M., Boselli, A., et al. 2025b, A&A, 697, A11 (Euclid on Sky SI)

Cushing, M. C., Kirkpatrick, J. D., Gelino, C. R., et al. 2011, ApJ, 743, 50

Cutri, R. M., Skrutskie, M. F., van Dyk, S., et al. 2003, VizieR Online Data Catalog: II/246

Cypriano, E. S., Amara, A., Voigt, L. M., et al. 2010, MNRAS, 405, 494

Czekaj, M. A., Robin, A. C., Figueras, F., Luri, X., & Haywood, M. 2014, A&A, 564, A102

Dakin, J., Hannestad, S., & Tram, T. 2022, MNRAS, 513, 991

Dalal, N., Doré, O., Huterer, D., & Shirokov, A. 2008, Phys. Rev. D, 77, 123514

d'Amico, G., Gleyzes, J., Kokron, N., et al. 2020, J. Cosmology Astropart. Phys., 05, 005

D'Amico, G., Lewandowski, M., Senatore, L., & Zhang, P. 2025, Phys. Rev. D, 111, 063514

Darvish, B., Mobasher, B., Martin, D. C., et al. 2017, ApJ, 837, 16

Davidzon, I., Jegatheesan, K., Ilbert, O., et al. 2022, A&A, 665, A34

Davis, M., Guhathakurta, P., Konidaris, N. P., et al. 2007, ApJ, 660, L1

Dawson, K. S., Schlegel, D. J., Ahn, C. P., et al. 2013, AJ, 145, 10

Dawson, K. S., Kneib, J.-P., Percival, W. J., et al. 2016, AJ, 151, 44

de Jong, J. T. A., Verdoes Kleijn, G. A., Boxhoorn, D. R., et al. 2015, A&A, 582, A62

De Lucia, G., Weinmann, S., Poggianti, B. M., Aragón-Salamanca, A., & Zaritsky, D. 2012, MNRAS, 423, 1277

Debackere, S. N. B., Schaye, J., & Hoekstra, H. 2020, MNRAS, 492, 2285

DeDeo, S., Spergel, D. N., & Trac, H. 2005, arXiv e-print [astro-ph/0511060]

DeGraf, C., Di Matteo, T., Treu, T., et al. 2015, MNRAS, 454, 913

Delbo, M., Walsh, K., Bolin, B., Avdellidou, C., & Morbidelli, A. 2017, Science, 357, 1026

DeMeo, F. E., & Carry, B. 2014, Nature, 505, 629

DeMeo, F. E., Binzel, R. P., Slivan, S. M., & Bus, S. J. 2009, Icarus, 202, 160

DES Collaboration (Abbott, T. M. C., et al.) 2020, Phys. Rev. D, 102, 023509

Desai, S., Armstrong, R., Mohr, J. J., et al. 2012, ApJ, 757, 83

Desai, S., Mohr, J. J., Bertin, E., Kümmel, M., & Wetzstein, M. 2016, Astron. Comput., 16, 67

DESI Collaboration (Aghamousa, A., et al.) 2016, arXiv e-prints [arXiv:1611.00036]

DESI Collaboration (Adame, A. G., et al.) 2024, AJ, 167, 62

Desjacques, V., Jeong, D., & Schmidt, F. 2018, Phys. Rep., 733, 1

Dey, A., Schlegel, D. J., Lang, D., et al. 2019, AJ, 157, 168

Di Giorgio, A. M., Leutenegger, P. H., Bonati, A., et al. 2010, SPIE Conf. Ser., 7731, 77312W

Di Giorgio, A. M., Bastia, P., Liu, S. J., et al. 2012, SPIE Conf. Ser., 8442, 844233

Di Valentino, E., Anchordoqui, L. A., Akarsu, Ö., et al. 2021, Astropart. Phys., 131, 102604

Diego, J. M., Protopapas, P., Sandvik, H. B., & Tegmark, M. 2005, MNRAS, 360, 477

Dimauro, P., Huertas-Company, M., Daddi, E., et al. 2018, MNRAS, 478, 5410

Dole, H., Lagache, G., Puget, J. L., et al. 2006, A&A, 451, 417

Dondoglio, E., Milone, A. P., Renzini, A., et al. 2022, ApJ, 927, 207

Donnan, C. T., McLeod, D. J., Dunlop, J. S., et al. 2023, MNRAS, 518, 6011

Dotter, A., Sarajedini, A., & Yang, S.-C. 2008, AJ, 136, 1407

Dressler, A. 1980, ApJ, 236, 351

Drinkwater, M. J., Byrne, Z. J., Blake, C., et al. 2018, MNRAS, 474, 4151

Duc, P.-A., Cuillardre, J.-C., Karabal, E., et al. 2015, MNRAS, 446, 120

Duncan, K., Conselice, C. J., Mundy, C., et al. 2019, ApJ, 876, 110

Duncan, C. A. J., Harnois-Déraps, J., Miller, L., & Langedijk, A. 2022, MNRAS, 515, 1130

Durech, J., & Hanuš, J. 2023, A&A, 675, A24

Durech, J., Carry, B., Delbo, M., Kaasalainen, M., & Viikinkoski, M. 2015, Asteroid Models from Multiple Data Sources (Univ. Arizona Press), 183

Eggemeier, A., Camacho-Quevedo, B., Pezzotta, A., et al. 2022, MNRAS, 519, 2962

Eisenhardt, P. R. M., Brodwin, M., Gonzalez, A. H., et al. 2008, ApJ, 684, 905

Eisenstein, D. J., & Hu, W. 1998, ApJ, 496, 605

Eisenstein, D. J., Zehavi, I., Hogg, D. W., et al. 2005, ApJ, 633, 560

Eisenstein, D. J., Seo, H.-J., Sirko, E., & Spergel, D. N. 2007, ApJ, 664, 675

Elvin-Poole, J., Crocce, M., Ross, A. J., et al. 2018, Phys. Rev. D, 98, 042006

Endicott, J., Darby, S., Bowring, S., et al. 2012, SPIE Conf. Ser., 8453, 845304

Epps, S. D., & Hudson, M. J. 2017, MNRAS, 468, 2605

Er, X., Hoekstra, H., Schrabback, T., et al. 2018, MNRAS, 476, 5645

Eriksen, M., & Hoekstra, H. 2018, MNRAS, 477, 3433

Euclid Collaboration (Adam, R., et al.) 2019, A&A, 627, A23

Euclid Collaboration (Barnett, R., et al.) 2019, A&A, 631, A85

Euclid Collaboration (Knabenhans, M., et al.) 2019, MNRAS, 484, 5509

Euclid Collaboration (Martinet, N., et al.) 2019, A&A, 627, A59

Euclid Collaboration (Blanchard, A., et al.) 2020, A&A, 642, A191

Euclid Collaboration (Desprez, G., et al.) 2020, A&A, 644, A31

Euclid Collaboration (Guglielmo, V., et al.) 2020, A&A, 642, A192

Euclid Collaboration (Paykari, P., et al.) 2020, A&A, 635, A139

Euclid Collaboration (Ilbert, O., et al.) 2021, A&A, 647, A117

Euclid Collaboration (Pocino, A., et al.) 2021, A&A, 655, A44

Euclid Collaboration (Borlaff, A. S., et al.) 2022, A&A, 657, A92

Euclid Collaboration (Bretonnière, H., et al.) 2022, A&A, 657, A90

Euclid Collaboration (Ilić, S., et al.) 2022, A&A, 657, A91

Euclid Collaboration (Lepori, F., et al.) 2022, A&A, 662, A93

Euclid Collaboration (Moneti, A., et al.) 2022, A&A, 658, A126

Euclid Collaboration (Saglia, R., et al.) 2022, A&A, 664, A196

Euclid Collaboration (Scaramella, R., et al.) 2022, A&A, 662, A112

Euclid Collaboration (Schirmer, M., et al.) 2022, A&A, 662, A92

Euclid Collaboration (van Mierlo, S. E., et al.) 2022, A&A, 666, A200

Euclid Collaboration (Ajani, V., et al.) 2023, A&A, 675, A120

Euclid Collaboration (Bisigello, L., et al.) 2023, MNRAS, 520, 3529

Euclid Collaboration (Bretonnière, H., et al.) 2023, A&A, 671, A102

Euclid Collaboration (Gabarra, L., et al.) 2023, A&A, 676, A34

Euclid Collaboration (Merlin, E., et al.) 2023, A&A, 671, A101

Euclid Collaboration (Paterson, K., et al.) 2023, A&A, 674, A172

Euclid Collaboration (Schirmer, M., et al.) 2023, A&A, 675, A142

Euclid Collaboration (Lusso, E., et al.) 2024, A&A, 685, A108

Euclid Collaboration (Sciotti, D., et al.) 2024, A&A, 691, A318

Euclid Collaboration (Aussel, B., et al.) 2024, A&A, 689, A274

Euclid Collaboration (Congedo, G., et al.) 2024, A&A, 691, A319

Euclid Collaboration (Deshpande, A. C., et al.) 2024, A&A, 684, A138

Euclid Collaboration (Giocoli, C., et al.) 2024, A&A, 681, A67

Euclid Collaboration (Leuzzi, L., et al.) 2024, A&A, 681, A68

Euclid Collaboration (Paltani, S., et al.) 2024, A&A, 681, A66

Euclid Collaboration (Sereno, M., et al.) 2024, A&A, 689, A252

Euclid Collaboration (Serrano, S., et al.) 2024, A&A, 690, A103

Euclid Collaboration (Tanidis, K., et al.) 2024, A&A, 683, A17

Euclid Collaboration (Castander, F., et al.) 2025, A&A, 697, A5 (Euclid on Sky SI)

Euclid Collaboration (Hormuth, K., et al.) 2025, A&A, 697, A4 (Euclid on Sky SI)

Euclid Collaboration (Cropper, M., et al.) 2025, A&A, 697, A2 (Euclid on Sky SI)

Euclid Collaboration (Archidiacono, M., et al.) 2025, A&A, 693, A58

Fan, X., Bañados, E., & Simcoe, R. A. 2023, ARAA, 61, 373

Fang, X., Blazek, J. A., McEwen, J. E., & Hirata, C. M. 2017, J. Cosmology Astropart. Phys., 02, 030

Fang, X., Krause, E., Eifler, T., et al. 2024, MNRAS, 527, 9581

Farren, G. S., Sherwin, B. D., Bolliet, B., et al. 2023, arXiv e-prints [arXiv:2311.04213]

Feldman, H. A., Kaiser, N., & Peacock, J. A. 1994, ApJ, 426, 23

Fenech Conti, I., Herbonnet, R., Hoekstra, H., et al. 2017, MNRAS, 467, 1627

Ferreira, L., Adams, N., Conselice, C. J., et al. 2022, ApJ, 938, L2

Fidler, C., Rampf, C., Tram, T., et al. 2015, Phys. Rev. D, 92, 123517

Fienup, J. R. 1982, Appl. Opt., 21, 2758

Fienup, J. R. 1999, J. Opt. Soc. Am. A, 16, 1831

Finkelstein, S. L., Bagley, M. B., Ferguson, H. C., et al. 2023, ApJ, 946, L13

Flaugher, B., Diehl, H. T., Honscheid, K., et al. 2015, AJ, 150, 150

Fortuna, M. C., Hoekstra, H., Joachimi, B., et al. 2021, MNRAS, 501, 2983

Fosalba, P., Gaztañaga, E., Castander, F. J., & Manera, M. 2008, MNRAS, 391, 435

Fosalba, P., Gaztañaga, E., Castander, F. J., & Crocce, M. 2015, MNRAS, 447, 1319

Fotopoulou, S., Buchner, J., Georgantopoulos, I., et al. 2016, A&A, 587, A142

Froustey, J., Pitrou, C., & Volpe, M. C. 2020, J. Cosmology Astropart. Phys., 12, 015

Frusciante, N., & Perenon, L. 2020, Phys. Rep., 857, 1

Frusciante, N., Pace, F., Cardone, V. F., et al. 2024, A&A, 690, A133

Fumagalli, A., Costanzi, M., Saro, A., Castro, T., & Borgani, S. 2024, A&A, 682, A148

Furusawa, H., Kosugi, G., Akiyama, M., et al. 2008, ApJS, 176, 1

Gaia Collaboration (Prusti, T., et al.) 2016, A&A, 595, A1

Gaia Collaboration (Spoto, F., et al.) 2018, A&A, 616, A13

Gaia Collaboration (Galluccio, L., et al.) 2023a, A&A, 674, A35
Gaia Collaboration (Vallenari, A., et al.) 2023b, A&A, 674, A1

Galli, E., Di Giorgio, A. M., Pezzuto, S., et al. 2014, SPIE Conf. Ser., 9152, 91520Y

Gao, L., Navarro, J. F., Cole, S., et al. 2008, MNRAS, 387, 536

Garilli, B., Guzzo, L., Scodeggio, M., et al. 2014, A&A, 562, A23

Gaspar Venancio, L. M., Laureijs, R., Lorenzo, J., et al. 2014, SPIE Conf. Ser., 9143, 91430I

Gaspar Venancio, L. M., Carminati, L., Lorenzo Alvarez, J., et al. 2016, SPIE Conf. Ser., 9904, 99040V

Gatti, M., Sheldon, E., Amon, A., et al. 2021, MNRAS, 504, 4312

Gatti, M., Jain, B., Chang, C., et al. 2022, Phys. Rev. D, 106, 083509

Gavazzi, R., Treu, T., Koopmans, L. V. E., et al. 2008, ApJ, 677, 1046

Genolet, L., Bozzo, E., Paltani, S., et al. 2016, SPIE Conf. Ser., 9904, 99040U

George, K., Vassallo, T., Mohr, J., et al. 2020, in Astronomical Data Analysis Software and Systems XXIX, eds. R. Pizzo, E. R. Deul, J. D. Mol, J. de Plaa, & H. Verkouter, ASP Conf. Ser., 527, 701

Georgiev, I. Y., Puzia, T. H., Hilker, M., & Goudfrooij, P. 2009, MNRAS, 392, 879

Ghirardini, V., Bulbul, E., Artis, E., et al. 2024, A&A, 689, A298

Giacconi, R., Rosati, P., Tozzi, P., et al. 2001, ApJ, 551, 624

Giannantonio, T., Fosalba, P., Cawthon, R., et al. 2016, MNRAS, 456, 3213

Giavalisco, M., Ferguson, H. C., Koekemoer, A. M., et al. 2004, ApJ, 600, L93

Gilman, D., Birrer, S., Nierenberg, A., et al. 2020, MNRAS, 491, 6077

Gilmore, J., & Natarajan, P. 2009, MNRAS, 396, 354

Giocoli, C., Baldi, M., & Moscardini, L. 2018, MNRAS, 481, 2813

Giocoli, C., Marulli, F., Moscardini, L., et al. 2021, A&A, 653, A19

Giocoli, C., Palmucci, L., Lesci, G. F., et al. 2024, A&A, 687, A79

Giovanelli, R., & Haynes, M. P. 1991, ARA&A, 29, 499

Girelli, G. 2021, PhD thesis, Alma Mater Studiorum Università di Bologna, Italy, http://amsdottorato.unibo.it/9820/

Giri, S. K., & Schneider, A. 2021, J. Cosmology Astropart. Phys., 12, 046

Gonsalves, R. A. 1982, Opt. Eng., 21, 829

Gonzalez, A. 2014, in Building the Euclid Cluster Survey – Scientific Program, 7

Gonzalez, A. H., George, T., Connor, T., et al. 2021, MNRAS, 507, 963

González Delgado, R. M., Rodríguez-Martín, J. E., Díaz-García, L. A., et al. 2022, A&A, 666, A84

Górski, K. M., Hivon, E., Banday, A. J., et al. 2005, ApJ, 622, 759

Gouin, C., Aghanim, N., Bonjean, V., & Douspis, M. 2020, A&A, 635, A195

Granata, G., Bergamini, P., Grillo, C., et al. 2023, A&A, 679, A124

Grandis, S., Mohr, J. J., Costanzi, M., et al. 2021, MNRAS, 504, 1253

Granvik, M., Muinonen, K., Jones, L., et al. 2007, Icarus, 192, 475

Grav, T., Jedicke, R., Denneau, L., et al. 2011, PASP, 123, 423

Grillo, C., Rosati, P., Suyu, S. H., et al. 2018, ApJ, 860, 94

Grupp, F., Prieto, E., Geis, N., et al. 2014, SPIE Conf. Ser., 9143, 91432X

Gunn, J. E., & Peterson, B. A. 1965, ApJ, 142, 1633

Guy, L. P., Cuillardre, J.-C., Bachelet, E., et al. 2022, https://doi.org/10.5281/zenodo.5836022

Guzzo, L., Pierleoni, M., Meneux, B., et al. 2008, Nature, 451, 541

Guzzo, L., Scodeggio, M., Garilli, B., et al. 2014, A&A, 566, A108

Gwyn, S. D. J. 2008, PASP, 120, 212

Haiman, Z., Mohr, J. J., & Holder, G. P. 2001, ApJ, 553, 545

Hall, A. 2021, MNRAS, 505, 4935

Hall, A., & Taylor, A. 2022, Phys. Rev. D, 105, 123527

Hamadouche, M. L., Carnall, A. C., McLure, R. J., et al. 2022, MNRAS, 512, 1262

Hamaus, N., Aubert, M., Pisani, A., et al. 2022, A&A, 658, A20

Hamaus, N., Sutter, P. M., & Wandelt, B. D. 2012, Phys. Rev. Lett., 112, 251302

Hambly, N. C., MacGillivray, H. T., Read, M. A., et al. 2001, MNRAS, 326, 1279

Hamilton, A. J. S. 1993, ApJ, 417, 19

Hamilton, A. J. S. 1998, in The Evolving Universe, ed. D. Hamilton, Astrophysics and Space Science Library, 231, 185

Hand, N., Addison, G. E., Aubourg, E., et al. 2012, Phys. Rev. Lett., 109, 041101

Handley, W. J., Hobson, M. P., & Lasenby, A. N. 2015a, MNRAS, 450, L61

Handley, W. J., Hobson, M. P., & Lasenby, A. N. 2015b, MNRAS, 453, 4384

Hanser, F. A., & Sellers, F. B. 1996, SPIE Conf. Ser., 2812, 344

Harikane, Y., Ono, Y., Ouchi, M., et al. 2022, ApJS, 259, 20

Harnois-Déraps, J., Amon, A., Choi, A., et al. 2018, MNRAS, 481, 1337

Harnois-Déraps, J., Giblin, B., & Joachimi, B. 2019, A&A, 631, A160

Harnois-Déraps, J., Martinet, N., Castro, T., et al. 2021, MNRAS, 506, 1623

Harrison, C. M., Costa, T., Tadhunter, C. N., et al. 2018, Nat. Astron., 2, 198

Hasinger, G., Capak, P., Salvato, M., et al. 2018, ApJ, 858, 77

Hazumi, M., Ade, P. A. R., Adler, A., et al. 2020, SPIE Conf. Ser., 11443, 114432F

Heavens, A., Refregier, A., & Heymans, C. 2000, MNRAS, 319, 649

Helgason, K., Cappelluti, N., Hasinger, G., Kashlinsky, A., & Ricotti, M. 2014, ApJ, 785, 38

Helmi, A., Babusiaux, C., Koppelman, H. H., et al. 2018, Nature, 563, 85

Hernández-Monteagudo, C., Chaves-Montero, J., & Angulo, R. E. 2021, MNRAS, 503, L56

Heydenreich, S., Brück, B., Burger, P., et al. 2022, A&A, 667, A125

Heydenreich, S., Linke, L., Burger, P., & Schneider, P. 2023, A&A, 672, A44

Heymans, C., Van Waerbeke, L., Bacon, D., et al. 2006, MNRAS, 368, 1323

Hezaveh, Y. D., Dalal, N., Marrone, D. P., et al. 2016, ApJ, 823, 37

Hickox, R. C., Jones, C., Forman, W. R., et al. 2009, ApJ, 696, 891

Hilbert, S., Barreira, A., Fabbian, G., et al. 2020, MNRAS, 493, 305

Hildebrandt, H., Viola, M., Heymans, C., et al. 2017, MNRAS, 465, 1454

Hildebrandt, H., van den Busch, J. L., Wright, A. H., et al. 2021, A&A, 647, A124

Hill, J. C., Ferraro, S., Battaglia, N., Liu, J., & Spergel, D. N. 2016, Phys. Rev. Lett., 117, 051301

Hilton, M., Sifón, C., Naess, S., et al. 2021, ApJS, 253, 3

Hinshaw, G., Larson, D., Komatsu, E., et al. 2013, ApJS, 208, 19

Hirata, C. M., & Seljak, U. 2004, Phys. Rev. D, 70, 063526

Hirata, C. M., & Choi, A. 2019, PASP, 132

Hirayama, K. 1918, AJ, 31, 185

Hoekstra, H. 2004, MNRAS, 347, 1337

Hoekstra, H. 2021, A&A, 656, A135

Hoekstra, H., Herbonnet, R., Muzzin, A., et al. 2015, MNRAS, 449, 685

Hoekstra, H., Viola, M., & Herbonnet, R. 2017, MNRAS, 468, 3295

Hoekstra, H., Kannawadi, A., & Kitching, T. D. 2021, A&A, 646, A124

Hopkins, H. H., & Yzuel, M. J. 1970, Optica Acta, 17, 157

Hopkins, P. F., Hernquist, L., Cox, T. J., & Kereš, D. 2008, ApJS, 175, 356

Horne, K. 1986, PASP, 98, 609

Hu, W., & Jain, B. 2004, Phys. Rev. D, 70, 043009

Huertas-Company, M., Bernardi, M., Pérez-González, P. G., et al. 2016, MNRAS, 462, 4495

Huertas-Company, M., & Lanusse, F. 2023, PASA, 40, e001

Huertas-Company, M., Iyer, K. G., Angeloudi, E., et al. 2024, A&A, 685, A48

Huff, E., & Mandelbaum, R. 2017, arXiv e-prints [arXiv:1702.02600]

Hunt, L., Annibali, F., Cuillardre, J.-C., et al. 2025, A&A, 697, A9 (Euclid on Sky SI)

Huterer, D., Takada, M., Bernstein, G., & Jain, B. 2006, MNRAS, 366, 101

Ibata, R. A., Malhan, K., & Martin, N. F. 2019, ApJ, 872, 152

Ilbert, O., Capak, P., Salvato, M., et al. 2009, ApJ, 690, 1236

Ilbert, O., Salvato, M., Le Floc'h, E., et al. 2010, ApJ, 709, 644

Ilbert, O., McCracken, H. J., Le Fèvre, O., et al. 2013, A&A, 556, A55

Ingoglia, L., Covone, G., Sereno, M., et al. 2022, MNRAS, 511, 1484

Inserra, C., Nichol, R. C., Scovacricchi, D., et al. 2018, A&A, 609, A83

Israel, H., Massey, R., Prod'homme, T., et al. 2015, MNRAS, 453, 561

Ivanov, M. M., Simonović, M., & Zaldarriaga, M. 2020, J. Cosmology Astropart. Phys., 05, 042

Ivezić, Ž., Kahn, S. M., Tyson, J. A., et al. 2019, ApJ, 873, 111

Jansen, H., Tewes, M., Schrabback, T., et al. 2024, A&A, 683, A240

Jarvis, M., Bernstein, G., & Jain, B. 2004, MNRAS, 352, 338

Jee, M. J., Mahdavi, A., Hoekstra, H., et al. 2012, ApJ, 747, 96

Jeffrey, N., Abdalla, F. B., Lahav, O., et al. 2018, MNRAS, 479, 2871

Jego, B., Alonso, D., García-García, C., & Ruiz-Zapatero, J. 2023a, MNRAS, 520, 583

Jego, B., Ruiz-Zapatero, J., García-García, C., Koukoufiliippas, N., & Alonso, D. 2023b, MNRAS, 520, 1895

Jian, H.-Y., Lin, L., Koyama, Y., et al. 2020, ApJ, 894, 125

Jiang, L., McGreer, I. D., Fan, X., et al. 2016, AJ, 833, 222

Joachimi, B., & Bridle, S. L. 2010, A&A, 523, A1

Joachimi, B., Cacciato, M., Kitching, T. D., et al. 2015, Space Sci. Rev., 193, 1

Joachimi, B., Lin, C. A., Asgari, M., et al. 2021, A&A, 646, A129

Johnston, K. V., Bullock, J. S., Sharma, S., et al. 2008, ApJ, 689, 936

Johnston, H., Wright, A. H., Joachimi, B., et al. 2021, A&A, 648, A98

Joudaki, S., Blake, C., Johnson, A., et al. 2018, MNRAS, 474, 4894

Jullo, E., Kneib, J.-P., Limousin, M., et al. 2007, New J. Phys., 9, 447

Jullo, E., Natarajan, P., Kneib, J. P., et al. 2010, Science, 329, 924

Kaasalainen, M. 2004, A&A, 422, L39

Kaiser, N. 1984, ApJ, 284, L9

Kaiser, N. 1987, MNRAS, 227, 1

Kaiser, N. 1998, ApJ, 498, 26

Kaiser, N. 1992, ApJ, 388, 272

Kaiser, N., & Squires, G. 1993, ApJ, 404, 441

Kaiser, N., Wilson, G., & Luppino, G. A. 2000, arXiv e-print [arXiv:astro-ph/0003338]

Kannawadi, A., Hoekstra, H., Miller, L., et al. 2019, A&A, 624, A92

Kannawadi, A., Rosenberg, E., & Hoekstra, H. 2021, MNRAS, 502, 4048

Kansal, V. 2023, A&A, 670, A34

Kashlinsky, A., Arendt, R. G., Mather, J., & Moseley, S. H. 2005, Nature, 438, 45

Kashlinsky, A., Arendt, R. G., Ashby, M. L. N., et al. 2012, ApJ, 753, 63
Kashlinsky, A., Arendt, R. G., Atrio-Barandela, F., et al. 2018, Rev. Mod. Phys., 90, 025006

Kashlinsky, A., Arendt, R. G., Cappelluti, N., et al. 2019, ApJ, 871, L6

Kasliwal, M. M., Bally, J., Masci, F., et al. 2017, ApJ, 839, 88

Kauffmann, G., White, S. D. M., Heckman, T. M., et al. 2004, MNRAS, 353, 713

Kayo, I., & Takada, M. 2013, arXiv e-prints [arXiv:1306.4684]

Keihänen, E., Kurki-Suonio, H., Lindholm, V., et al. 2019, A&A, 631, A73

Kelly, P. L., Rodney, S. A., Treu, T., et al. 2015, Science, 347, 1123

Kennicutt, Robert C., J. 1998a, ARA&A, 36, 189

Kennicutt, Robert C., J. 1998b, ApJ, 498, 541

Kerins, E., Bachelet, E., Beaulieu, J.-P., et al. 2023, arXiv e-prints
[arXiv:2306.10210]

Kilbinger, M. 2015, Rep. Progr. Phys., 78, 086901

Kilbinger, M., Heymans, C., Asgari, M., et al. 2017, MNRAS, 472, 2126

Kirk, D., Brown, M. L., Hoekstra, H., et al. 2015, Space Sci. Rev., 193, 139

Kirkpatrick, J. D. 2005, ARA&A, 43, 195

Kitching, T. D., & Deshpande, A. C. 2022, Open J. Astrophys., 5, 6

Kitching, T. D., Miller, L., Heymans, C. E., van Waerbeke, L., & Heavens, A. F. 2008a, MNRAS, 390, 149

Kitching, T. D., Taylor, A. N., & Heavens, A. F. 2008b, MNRAS, 389, 173

Kitching, T. D., Balan, S. T., Bridle, S., et al. 2012a, MNRAS, 423, 3163

Kitching, T. D., Rhodes, J., Heymans, C., et al. 2012b, arXiv e-prints
[arXiv:1204.4096]

Kitching, T. D., Rowe, B., Gill, M., et al. 2013, ApJS, 205, 12

Kitching, T. D., Alsing, J., Heavens, A. F., et al. 2017, MNRAS, 469, 2737

Kitching, T. D., Taylor, P. L., Capak, P., Masters, D., & Hoekstra, H. 2019, Phys. Rev. D 99, 063536

Kitching, T. D., Deshpande, A. C., & Taylor, P. L. 2020, Open J. Astrophys., 3, 14

Kitching, T., Deshpande, A., & Taylor, P. 2021, Open J. Astrophys., 4, 17

Kluge, M., Hatch, N., Montes, M., et al. 2025, A&A, 697, A13 (Euclid on Sky SI)

Kneib, J., Mellier, Y., Fort, B., & Mathez, G. 1993, A&A, 273, 367

Knobel, C., Lilly, S. J., Iovino, A., et al. 2012, ApJ, 753, 121

Köhlinger, F., Hoekstra, H., & Eriksen, M. 2015, MNRAS, 453, 3107

Kohonen, T., & Honkela, T. 2007, Scholarpedia, 2, 1568

Koo, D. C. 1985, AJ, 90, 418

Kool, E. C., Ryder, S., Kankare, E., et al. 2018, MNRAS, 473, 5641

Koopmans, L. V. E. 2005, MNRAS, 363, 1136

Korsch, D. 1977, Appl. Opt., 16, 2074

Kou, R., & Bartlett, J. G. 2023, A&A, 675, A149

Koukoufilippas, N., Alonso, D., Bilicki, M., & Peacock, J. A. 2020, MNRAS, 491, 5464

Kraljic, K., Arnouts, S., Pichon, C., et al. 2018, MNRAS, 474, 547

Kraljic, K., Pichon, C., Codis, S., et al. 2020, MNRAS, 491, 4294

Kravtsov, A. V., & Borgani, S. 2012, ARA&A, 50, 353

Kriek, M., Shapley, A. E., Reddy, N. A., et al. 2015, ApJS, 218, 15

Krolewski, A., Percival, W. J., Ferraro, S., et al. 2024, J. Cosmology Astropart. Phys., 2024, 021

Kubik, B., Barbier, R., Chabanat, E., et al. 2016, PASP, 128, 104504

Kuijken, K., Heymans, C., Hildebrandt, H., et al. 2015, MNRAS, 454, 3500

Kümmel, M., Walsh, J. R., Pirzkal, N., Kuntschner, H., & Pasquali, A. 2009, PASP, 121, 59

Kümmel, M., Vassallo, T., Dabin, C., & Gracia Carpio, J. 2022, in ASP Conf. Ser., 532, ASP Conf. Ser., eds. J. E. Ruiz, F. Pierfedereci, & P. Teuben, 329

Kurk, J. D., Röttgering, H. J. A., Pentericci, L., et al. 2000, A&A, 358, L1

Lacasa, F., & Grain, J. 2019, A&A, 624, A61

Lagarde, N., Reylé, C., Chiappini, C., et al. 2021, A&A, 654, A13

Lahav, O., Lilje, P. B., Primack, J. R., & Rees, M. J. 1991, MNRAS, 251, 128

Laigle, C., Pichon, C., Arnouts, S., et al. 2018, MNRAS, 474, 5437

Lam, D., Broadhurst, T., Diego, J. M., et al. 2014, ApJ, 797, 98

Landy, S. D., & Szalay, A. S. 1993, ApJ, 412, 64

Lange, J. U. 2023, MNRAS, 525, 3181

Laureijs, R., Amiaux, J., Arduini, S., et al. 2011, ESA/SRE(2011)12
[arXiv:1110.3193]

Le Brun, A. M. C., McCarthy, I. G., Schaye, J., & Ponman, T. J. 2014, MNRAS, 441, 1270

Le Fèvre, O., Vettolani, G., Garilli, B., et al. 2005, A&A, 439, 845

Le Fèvre, O., Cassata, P., Cucciati, O., et al. 2013, A&A, 559, A14

Le Graët, J., Secroun, A., Barbier, R., et al. 2022, SPIE Conf. Ser., 12191, 121911M

Lee, H. M., Kim, S. J., Im, M., et al. 2009, PASJ, 61, 375

Legrand, L., Hernández-Monteagudo, C., Douspis, M., Aghanim, N., & Angulo, R. E. 2021, A&A, 646, A109

Lemos, P., Challinor, A., & Efstathiou, G. 2017, J. Cosmology Astropart. Phys., 05, 014

Lesci, G. F., Marulli, F., Moscardini, L., et al. 2022, A&A, 659, A88

Lesgourgues, J. 2011, arXiv e-prints [arXiv:1104.2932]

Lesgourgues, J., & Pastor, S. 2006, Phys. Rep., 429, 307

Lewis, A., & Challinor, A. 2006, Phys. Rep., 429, 1

Lewis, A., Challinor, A., & Lasenby, A. 2000, ApJ, 538, 473

Lezmy, J., Copin, Y., Rigault, M., Smith, M., & Neill, J. D. 2022, A&A, 668, A43

Li, Y., Cappelluti, N., Arendt, R. G., et al. 2018, ApJ, 864, 141

Li, S.-S., Kuijken, K., Hoekstra, H., et al. 2023a, A&A, 670, A100

Li, X., Zhang, T., Sugiyama, S., et al. 2023b, Phys. Rev. D, 108, 123518

Liesenborgs, J., De Rijcke, S., & Dejonghe, H. 2006, MNRAS, 367, 1209

Lilly, S. J., Le Fèvre, O., Renzini, A., et al. 2007, ApJS, 172, 70

Lim, S., Peng, E. W., Côté, P., et al. 2018, ApJ, 862, 82

Lim, S., Hill, R., Scott, D., et al. 2023, MNRAS, 525, 1443

Limber, D. N. 1953, ApJ, 117, 134

Linder, E. V. 2005, Phys. Rev. D, 72, 043529

Linke, L., Simon, P., Schneider, P., et al. 2020, A&A, 640, A59

Linke, L., Simon, P., Schneider, P., et al. 2022, A&A, 665, A38

Lintott, C. J., Schawinski, K., Slosar, A., et al. 2008, MNRAS, 389, 1179

Liu, M. C., Magnier, E. A., Deacon, N. R., et al. 2013, ApJ, 777, L20

Liu, A., Bulbul, E., Ghirardini, V., et al. 2022, A&A, 661, A2

Loh, E. D., & Spillar, E. J. 1986, ApJ, 303, 154

Lotz, J. M., Primack, J., & Madau, P. 2004, AJ, 128, 163

Lotz, J. M., Koekemoer, A., Coe, D., et al. 2017, ApJ, 837, 97

LSST Science Collaboration (Abell, P. A., et al.) 2009, arXiv e-prints
[arXiv:0912.0201]

Ludlow, A. D., Navarro, J. F., Boylan-Kolchin, M., et al. 2013, MNRAS, 432, 1103

Lusso, E., & Risaliti, G. 2016, ApJ, 819, 154

Lusso, E., Risaliti, G., Nardini, E., et al. 2020, A&A, 642, A150

Ma, Z., Hu, W., & Huterer, D. 2006, ApJ, 636, 21

Ma, Z., Bernstein, G., Weinstein, A., & Sholl, M. 2008, PASP, 120, 1307

MacCrann, N., Becker, M. R., McCullough, J., et al. 2022, MNRAS, 509, 3371

Maciaszek, T., Ealet, A., Gillard, W., et al. 2022, in SPIE Conf. Ser., 12180, Space Telescopes and Instrumentation 2022: Optical, Infrared, and Millimeter Wave, eds. L. E. Coyle, S. Matsuura, & M. D. Perrin, 121801K

Mackey, A. D., Beasley, M. A., & Leaman, R. 2016, MNRAS, 460, L114

Mackey, D., Lewis, G. F., Brewer, B. J., et al. 2019, Nature, 574, 69

Madau, P., & Dickinson, M. 2014, ARA&A, 52, 415

Magliocchetti, M. 2022, A&Rev, 30, 6

Magnier, E. A., Chambers, K. C., Flewelling, H. A., et al. 2020, ApJS, 251, 3

Mahlke, M., Bouy, H., Altieri, B., et al. 2018, A&A, 610, A21

Mahlke, M., Carry, B., & Denneau, L. 2021, Icarus, 354, 114094

Mahlke, M., Carry, B., & Mattei, P. A. 2022, A&A, 665, A26

Mahony, C., Fortuna, M. C., Joachimi, B., et al. 2022, MNRAS, 513, 1210

Mainieri, V., Hasinger, G., Cappelluti, N., et al. 2007, ApJS, 172, 368

Maiolino, R., & Mannucci, F. 2019, A&A Rev., 27, 3

Maiolino, R., Scholtz, J., Witstok, J., et al. 2024, Nature, 627, 59

Malavasi, N., Pozzetti, L., Cucciati, O., et al. 2017, MNRAS, 470, 1274

Mamon, G. A., Cava, A., Biviano, A., et al. 2019, A&A, 631, A131

Mandelbaum, R. 2018, ARA&A, 56, 393

Mandelbaum, R., Rowe, B., Armstrong, R., et al. 2015, MNRAS, 450, 2963

Maniyar, A., Lagache, G., Béthermin, M., & Ilić, S. 2019, A&A, 621, A32

Mantz, A. B., von der Linden, A., Allen, S. W., et al. 2015, MNRAS, 446, 2205

Mao, S., & Schneider, P. 1998, MNRAS, 295, 587

Marleau, F., Habas, R., Poulain, M., et al. 2021, A&A, 654, A105

Marleau, F., Guillardre, J.-C., Cantiello, M., et al. 2025, A&A, 697, A12 (Euclid on Sky SI)

Marques, G. A., Liu, J., Huffenberger, K. M., & Colin Hill, J. 2020, ApJ, 904, 182

Martignac, J., Carty, M., Tourette, T., et al. 2014, SPIE Conf. Ser., 9143, 91432Y

Martín, E. L., Zhang, J. Y., Esparza, P., et al. 2021, A&A, 655, L3

Martin, G., Bazkiaei, A. E., Spavone, M., et al. 2022, MNRAS, 513, 1459

Martín, E., Žerjal, M., Bouy, H., et al. 2025, A&A, 697, A7 (Euclid on Sky SI)

Martinelli, M., Tutusaus, I., Archidiacono, M., et al. 2021, A&A, 649, A100

Martinelli, M., Dalal, R., Majidi, F., et al. 2022, MNRAS, 510, 1964

Martinet, F., R., Habas, R., Poulain, M., et al. 2021, A&A, 654, A105

Marleau, F., V. R., Habas, R., Poulain, M., et al. 2021, A&A, 654, A105

Marulli, F., Veropalumbo, A., & Moresco, M. 2016, Astron. Comput., 14, 35

Mason, C. A., Trenti, M., & Treu, T. 2015, ApJ, 813, 21

Massari, D., Fiorentino, G., McConnachie, A., et al. 2016, A&A, 586, A51

Massari, D., Dalessandro, E., Erkal, D., et al. 2025, A&A, 697, A8 (Euclid on Sky SI)

Massey, R., Rhodes, J., Ellis, R., et al. 2007, Nature, 445, 286

Massey, R., Hoekstra, H., Kitching, T., et al. 2013, MNRAS, 429, 661

Massey, R., Schrabback, T., Cordes, O., et al. 2014, MNRAS, 439, 887

Masters, D., Capak, P., Stern, D., et al. 2015, ApJ, 813, 53

Masters, D. C., Stern, D. K., Cohen, J. G., et al. 2017, ApJ, 841, 111
Masters, D. C., Stern, D. K., Cohen, J. G., et al. 2019, ApJ, 877, 81

Matarrese, S., Verde, L., & Jimenez, R. 2000, ApJ, 541, 10

Maturi, M., Meneghetti, M., Bartelmann, M., Dolag, K., & Moscardini, L. 2005, A&A, 442, 851

Maturi, M., Bellagamba, F., Radovich, M., et al. 2019, MNRAS, 485, 498

Maturi, M., Finoguenov, A., Lopes, P. A. A., et al. 2023, A&A, 678, A145

McCarthy, I. G., Schaye, J., Bird, S., & Le Brun, A. M. C. 2017, MNRAS, 465, 2936

McCarthy, F., Madhavacheril, M. S., & Maniyar, A. S. 2023, Phys. Rev. D, 108, 083522

McEwen, J. E., Fang, X., Hirata, C. M., & Blazek, J. A. 2016, J. Cosmology Astropart. Phys., 09, 015

McGee, S. L., Balogh, M. L., Bower, R. G., Font, A. S., & McCarthy, I. G. 2009, MNRAS, 400, 937

McLure, R. J., Pentericci, L., Cimatti, A., et al. 2018, MNRAS, 479, 25

McMahon, R. G., Banerji, M., Gonzalez, E., et al. 2021, VizieR Online Data Catalog: II/367

Mead, A. J., Heymans, C., Lombriser, L., et al. 2016, MNRAS, 459, 1468

Mead, A. J., Brieden, S., Tröster, T., & Heymans, C. 2021, MNRAS, 502, 1401

Mei, S., Blakeslee, J. P., Côté, P., et al. 2007, ApJ, 655, 144

Meiksin, A. 2005, MNRAS, 356, 596

Meiksin, A., White, M., & Peacock, J. A. 1999, MNRAS, 304, 851

Mellier, Y. 1999, ARA&A, 37, 127

Meneghetti, M., Yoshida, N., Bartelmann, M., et al. 2001, MNRAS, 325, 435

Meneghetti, M., Fedeli, C., Zitrin, A., et al. 2011, A&A, 530, A17

Meneghetti, M., Rasia, E., Vega, J., et al. 2014, ApJ, 797, 34

Meneghetti, M., Davoli, G., Bergamini, P., et al. 2020, Science, 369, 1347

Meneghetti, M., Ragagnin, A., Borgani, S., et al. 2019, A&A, 668, A188

Meneghetti, M., Cui, W., Rasia, E., et al. 2023, A&A, 678, L2

Merlin, E., Fontana, A., Ferguson, H. C., et al. 2015, A&A, 582, A15

Merlin, E., Pilo, S., Fontana, A., et al. 2019, A&A, 622, A169

Merloni, A., Bongiorno, A., Brusa, M., et al. 2014, MNRAS, 437, 3550

Merten, J., Meneghetti, M., Postman, M., et al. 2015, ApJ, 806, 4

Metcalf, R. B., Meneghetti, M., Avestruz, C., et al. 2019, A&A, 625, A119

Mignoli, M., Vignali, C., Gilli, R., et al. 2013, A&A, 556, A29

Mignoli, M., Feltre, A., Bongiorno, A., et al. 2019, A&A, 626, A9

Miller, L., Kitching, T. D., Heymans, C., Heavens, A. F., & van Waerbeke, L. 2007, MNRAS, 382, 315

Miller, L., Heymans, C., Kitching, T. D., et al. 2013, MNRAS, 429, 2858

Miralda-Escude, J. 1991, ApJ, 380, 1

Miralda-Escudé, J. 2002, ApJ, 564, 60

Mitchell-Wynne, K., Cooray, A., Xue, Y., et al. 2016, ApJ, 832, 104

Miyazaki, S., Komiyama, Y., Kawanomoto, S., et al. 2018, PASJ, 70, S1

Mo, H. J., & White, S. D. M. 1996, MNRAS, 282, 347

Mohr, J. J., Adams, D., Barkhouse, W., et al. 2008, SPIE Conf. Ser., 7016, 70160L

Mohr, J. J., Armstrong, R., Bertin, E., et al. 2012, SPIE Conf. Ser., 8451, 84510D

Montes, M. 2022, Nat. Astron., 6, 308

Montes, M., & Trujillo, I. 2019, MNRAS, 482, 2838

More, S., Sugiyama, S., Miyatake, H., et al. 2023, Phys. Rev. D, 108, 123520

Moresco, M. 2015, MNRAS, 450, L16

Moresco, M., Amati, L., Amendola, L., et al. 2022, Liv. Rev. Relativ., 25, 6

Moretti, C., Tsedrik, M., Carrilho, P., & Pourtsidou, A. 2023, J. Cosmology Astropart. Phys., 12, 025

Moriya, T. J., Inserra, C., Tanaka, M., et al. 2022, A&A, 666, A157

Moustakas, L. A., & Metcalf, R. B. 2003, MNRAS, 339, 607

Muñoz, R. P., Puzia, T. H., Lançon, A., et al. 2014, ApJS, 210, 4

Müller, E.-M., Rezaie, M., Percival, W. J., et al. 2022, MNRAS, 514, 3396

Muir, J., Bernstein, G. M., Huterer, D., et al. 2020, MNRAS, 494, 4454

Müller, O., Durrell, P. R., Marleau, F. R., et al. 2021, ApJ, 923, 9

Myles, J., Alarcon, A., Amon, A., et al. 2021, MNRAS, 505, 4249

Naidu, R. P., Oesch, P. A., van Dokkum, P., et al. 2022, ApJ, 940, L14

Naidoo, K., Johnston, H., Joachimi, B., et al. 2023, A&A, 670, A149

Navarro, J. F., Frenk, C. S., & White, S. D. M. 1997, ApJ, 490, 493

Navarro, V., del Rio, S., Diego, M. A., et al. 2024, Space Data Manag., 1

Netzer, H. 2015, ARA&A, 53, 365

Newman, J. A. 2008, ApJ, 684, 88

Newman, J. A., & Gruen, D. 2022, ARA&A, 60, 363

Nickerson, R. S. 1998, Rev. Gen. Psychol., 2, 175

Niemi, S.-M., Cropper, M., Szafraniec, M., & Kitching, T. 2015, Exp. Astron., 39, 207

Nierenberg, A. M., Treu, T., Brammer, G., et al. 2017, MNRAS, 471, 2224

Novaković, B., Cellino, A., & Knežević, Z. 2011, Icarus, 216, 69

Oddo, A., Rizzo, F., Sefusatti, E., Porciani, C., & Monaco, P. 2021, J. Cosmology Astropart. Phys., 11, 038

Oesch, P. A., Brammer, G., van Dokkum, P. G., et al. 2016, ApJ, 819, 129

Oguri, M. 2010, PASJ, 62, 1017

Oguri, M., & Marshall, P. J. 2010, MNRAS, 405, 2579

Oguri, M., Miyazaki, S., Hikage, C., et al. 2018, PASJ, 70, S26

Osato, K., Shirasaki, M., Miyatake, H., et al. 2020, MNRAS, 492, 4780

Overzier, R. A. 2016, A&A Rev., 24, 14

Padmanabhan, N., Xu, X., Eisenstein, D. J., et al. 2012, MNRAS, 427, 2132

Palanque-Delabrouille, N., Yèche, C., Schöneberg, N., et al. 2020, J. Cosmology Astropart. Phys., 04, 038

Panagiotou, C., De, K., Masterson, M., et al. 2023, ApJ, 948, L5

Pandey, S., Krause, E., Jain, B., et al. 2020, Phys. Rev. D, 102, 123522

Pandey, S., Gatti, M., Baxter, E., et al. 2022, Phys. Rev. D, 105, 123526

Parroni, C., Cardone, V. F., Maoli, R., & Scaramella, R. 2020, A&A, 633, A71

Pascale, M., Frye, B. L., Pierel, J. D. R., et al. 2025, ApJ, 979, 13

Paulin-Henriksson, S., Refregier, A., & Amara, A. 2009, A&A, 500, 647

Peacock, J. A., Schneider, P., Efstathiou, G., et al. 2006, ESA-ESO Working Group on “Fundamental Cosmology”

Pearson, C., Cheale, R., Serjeant, S., et al. 2017, Publ. Korean Astron. Soc., 32, 219

Pearson, J., Serjeant, S., Wang, W.-H., et al. 2024, MNRAS, 527, 12044

Peebles, P. J. E. 1980, The Large-scale Structure of the Universe (Princeton University Press)

Pellejero-Ibanez, M., Stuecker, J., Angulo, R. E., et al. 2022, MNRAS, 514, 3993

Peng, Y.-j., Lilly, S. J., Kovač, K., et al. 2010, ApJ, 721, 193

Penny, M. T., Gaudi, B. S., Kerins, E., et al. 2019, ApJS, 241, 3

Pentericci, L., Kurk, J. D., Röttgering, H. J. A., et al. 2000, A&A, 361, L25

Percival, W. J., & White, M. 2009, MNRAS, 393, 297

Percival, W. J., Baugh, C. M., Bland-Hawthorn, J., et al. 2001, MNRAS, 327, 1297

Percival, W. J., Friedrich, O., Sellentin, E., & Heavens, A. 2022, MNRAS, 510, 3207

Pérez-Montaño, L. E., Rodriguez-Gomez, V., Cervantes Sodi, B., et al. 2022, MNRAS, 514, 5840

Perlmutter, S., Aldering, G., Goldhaber, G., et al. 1999, ApJ, 517, 565

Peter, A. H. G., Rocha, M., Bullock, J. S., & Kaplinghat, M. 2013, MNRAS, 430, 105

Petrillo, C. E., Tortora, C., Chatterjee, S., et al. 2019, MNRAS, 482, 807

Petrosian, V. 1976, ApJ, 210, L53

Pickles, A. J. 1998, PASP, 110, 863

Piga, L., Marinucci, M., D'Amico, G., et al. 2023, J. Cosmology Astropart. Phys., 04, 038

Pires, S., Vandenbussche, V., Kansal, V., et al. 2020, A&A, 638, A141

Pisani, A., Massara, E., Spergel, D. N., et al. 2019, BAAS, 51, 40

Planck Collaboration XI. 2014, A&A, 571, A11

Planck Collaboration XVI. 2014, A&A, 571, A16

Planck Collaboration XVIII. 2014, A&A, 571, A18

Planck Collaboration XIII. 2016, A&A, 594, A13

Planck Collaboration XXIV. 2016, A&A, 594, A24

Planck Collaboration XXVII. 2016, A&A, 594, A27

Planck Collaboration I. 2020, A&A, 641, A1

Planck Collaboration VI. 2020, A&A, 641, A6

Planck Collaboration VIII. 2020, A&A, 641, A8

Planck Collaboration IX. 2020, A&A, 641, A9

Planck Collaboration X. 2020, A&A, 641, A10

Planck Collaboration Int. XXVII. 2015, A&A, 582, A30

Planck Collaboration Int. XXXVII. 2016, A&A, 586, A140

Planck Collaboration Int. XXXIX. 2016, A&A, 596, A100

Plazas, A. A., Shapiro, C., Smith, R., Huff, E., & Rhodes, J. 2018, PASP, 130, 065004

Pogosian, L., Silvestri, A., Koyama, K., & Zhao, G.-B. 2010, Phys. Rev. D, 81, 104023

Pöntinen, M., Granvik, M., Nucita, A. A., et al. 2020, A&A, 644, A35

Pöntinen, M., Granvik, M., Nucita, A. A., et al. 2023, A&A, 679, A135

Popescu, M., Licandro, J., Morate, D., et al. 2016, A&A, 591, A115

Popesso, P., & Biviano, A. 2006, A&A, 460, L23

Popesso, P., Concas, A., Cresci, G., et al. 2023, MNRAS, 519, 1526

Porredon, A., Crocce, M., Elvin-Poole, J., et al. 2022, Phys. Rev. D, 106, 103530

Porth, L., & Smith, R. E. 2021, MNRAS, 508, 3474

Porth, L., Heydenreich, S., Burger, P., Linke, L., & Schneider, P. 2024, A&A, 689, A227

Potter, D., & Stadel, J. 2016, Astrophysics Source Code Library [record ascl:1609.016]

Powalka, M., Lançon, A., Puzia, T. H., et al. 2017, ApJ, 844, 104

Powell, D. M., Vegetti, S., McKean, J. P., et al. 2023, MNRAS, 524, L84

Pozzetti, L., Bolzonella, M., Zucca, E., et al. 2010, A&A, 523, A13

Pozzetti, L., Hirata, C. M., Geach, J. E., et al. 2016, A&A, 590, A3

Prat, J., Blazek, J., Sánchez, C., et al. 2022, Phys. Rev. D, 105, 083528
Prod'homme, T., Verhoeve, P., Kohley, R., Short, A., & Boudin, N. 2014, SPIE Conf. Ser., 9154, 915409

Pyne, S., & Joachimi, B. 2021, MNRAS, 503, 2300

Qu, F. J., Sherwin, B. D., Madhavacheril, M. S., et al. 2024, ApJ, 962, 112

Racca, G. D., Laureijs, R., Stagnaro, L., et al. 2016, SPIE Conf. Ser., 9904, 990400

Radinović, S., Nadathur, S., Winther, H. A., et al. 2023, A&A, 677, A78

Raj, M. A., Iodice, E., Napolitano, N. R., et al. 2020, A&A, 640, A137

Rau, M. M., Dalal, R., Zhang, T., et al. 2023, MNRAS, 524, 5109

Raymond, S. N., & Izidoro, A. 2017, Sci. Adv., 3, e1701138

Raymond, S. N., Izidoro, A., & Morbidelli, A. 2020, in Planetary Astrobiology, eds. V. S. Meadows, G. N. Arney, B. E. Schmidt, & D. J. Des Marais (University of Arizona Press), 287

Refregier, A. 2009, Exp. Astron., 23, 17

Refsdal, S. 1964, MNRAS, 128, 307

Reiprich, T. H., & Böhringer, H. 2002, ApJ, 567, 716

Renaud, D., Cara, C., Berthé, M., et al. 2018, SPIE Conf. Ser., 10705, 107051F

Rezaie, M., Ross, A. J., Seo, H.-J., et al. 2024, MNRAS, 532, 1902

Rhodes, J., Nichol, R., Peclet, R., Aubourg, S., & Picaud, S. 2003, A&A, 409, 523

Rieke, M. J., Kelly, D. M., & Horner, S. D. 2005, in Cryogenic Optical Systems and Instruments XI, 5904, eds. J. B. Heaney, & L. G. Burriesci, International Society for Optics and Photonics (SPIE), 590401

Riess, A. G., Filippenko, A. V., Challis, P., et al. 1998, AJ, 116, 1009

Riess, A. G., Casertano, S., Yuan, W., et al. 2021, ApJ, 908, L6

Risaliti, G., & Lusso, E. 2015, ApJ, 815, 33

Robberto, M. 2007, UVIS CCD EPER CTE measurements performed during the April 2007 Ambient Calibration campaign (SMS UV02S01), Instrument Science Report WFC3 2007-13, 9

Robertson, J. G. 1986, PASP, 98, 1220

Robertson, N. C., Alonso, D., Harnois-Déraps, J., et al. 2021, A&A, 649, A146

Robin, A. C., Reylé, C., Derrière, S., & Picaud, S. 2003, A&A, 409, 523

Rocha, M., Peter, A. H. G., Bullock, J. S., et al. 2013, MNRAS, 430, 81

Roche, N., Franzetti, P., Garilli, B., et al. 2012, MNRAS, 420, 1764

Rodríguez-Monroy, M., Weaverdyck, N., Elvin-Poole, J., et al. 2022, MNRAS, 511, 2665

Rood, H. J. 1988, ARA&A, 26, 245

Ross, A. J., Ho, S., Cuesta, A. J., et al. 2011, MNRAS, 417, 1350

Ross, A. J., Percival, W. J., Sánchez, A. G., et al. 2012, MNRAS, 424, 564

Ross, A. J., Beutler, F., Chuang, C.-H., et al. 2017, MNRAS, 464, 1168

Rothman, L., Gordon, I., Babikov, Y., et al. 2013, JQSRT, 130, 4

Sabater, J., Best, P. N., Tasse, C., et al. 2021, A&A, 648, A2

Sachs, R. K., & Wolfe, A. M. 1967, ApJ, 147, 73

Saifollahi, T., Janz, J., Peclet, R. F., et al. 2021, MNRAS, 504, 3580

Saifollahi, T., Verdoes Kleijn, G., Williams, R., et al. 2023, A&A, 673, A93

Saifollahi, T., Voggel, K., Lançon, A., et al. 2025, A&A, 697, A10 (Euclid on Sky SI)

Saifollahi, T., Zaritsky, D., Trujillo, I., et al. 2022, MNRAS, 511, 4633

Sailer, N., Castorina, E., Ferraro, S., & White, M. 2021, J. Cosmology Astropart. Phys., 12, 049

Sandage, A. 1975, in Galaxies and the Universe, eds. A. Sandage, M. Sandage, & J. Kristian (University of Chicago Press), 761

Sarpa, E., Veropalumbo, A., Schimd, C., Branchini, E., & Matarrese, S. 2021, MNRAS, 503, 540

Sarron, F., Adami, C., Durret, F., & Laigle, C. 2019, A&A, 632, A49

Sartoris, B., Borgani, S., Rosati, P., & Weller, J. 2012, MNRAS, 423, 2503

Sartoris, B., Biviano, A., Fedeli, C., et al. 2016, MNRAS, 459, 1764

Schaan, E., Ferraro, S., Vargas-Magaña, M., et al. 2016, Phys. Rev. D, 93, 082002

Schaan, E., Krause, E., Eifler, T., et al. 2017, Phys. Rev. D, 95, 123512

Schaan, E., Ferraro, S., Amodeo, S., et al. 2021, Phys. Rev. D, 103, 063513

Schaye, J., Dalla Vecchia, C., Booth, C. M., et al. 2010, MNRAS, 402, 1536

Schirmer, M., Erben, T., Hетterscheidt, M., & Schneider, P. 2007, A&A, 462, 875

Schneider, A., & Teyssier, R. 2015, J. Cosmology Astropart. Phys., 12, 049

Schneider, A., Teyssier, R., Stadel, J., et al. 2019, J. Cosmology Astropart. Phys., 03, 020

Schneider, P. 1996, MNRAS, 283, 837

Schneider, P. 2014, A&A, 568, L2

Schneider, P., Eifler, T., & Krause, E. 2010, A&A, 520, A116

Schneider, P. & Seitz, C. 1995, A&A, 294, 411

Schneider, P., van Waerbeke, L., Kilbinger, M., & Mellier, Y. 2002a, A&A, 396, 1

Schneider, P., van Waerbeke, L., & Mellier, Y. 2002b, A&A, 389, 729

Schneider, P., & Watts, P. 2005, A&A, 432, 783

Schulze, A., Bongiorno, A., Gavignaud, I., et al. 2015, MNRAS, 447, 2085

Scoccimarro, R. 2015, Phys. Rev. D, 92, 083532

Scoccimarro, R., Sheth, R. K., Hui, L., & Jain, B. 2001, ApJ, 546, 20

Scodeggio, M., Guzzo, L., Garilli, B., et al. 2007, A&A, 609, A84

Scoville, N., Aussel, H., Brusa, M., et al. 2007, ApJS, 172, 1

Secco, L. F., Jarvis, M., Jain, B., et al. 2022, Phys. Rev. D, 105, 103537

Sellentin, E. 2020, MNRAS, 492, 3396

Sellentin, E., & Heavens, A. F. 2016, MNRAS, 456, L132

Semboloni, E., Hoekstra, H., Schaye, J., van Daalen, M. P., & McCarthy, I. G. 2011, MNRAS, 417, 2020

Semboloni, E., Hoekstra, H., Huang, Z., et al. 2013a, MNRAS, 432, 2385

Semboloni, E., Hoekstra, H., & Schaye, J. 2013b, MNRAS, 434, 148

Sereno, M., Fedeli, C., & Moscardini, L. 2016, J. Cosmology Astropart. Phys., 1, 042

Sereno, M., Giocoli, C., Izzo, L., et al. 2018, Nat. Astron., 2, 744

Sérsic, J. L. 1963, Bol. Asoc. Argentina Astron. Plata Argentina, 6, 41

Shan, H. Y., Kneib, J.-P., Comparat, J., et al. 2014, MNRAS, 442, 2534

Shankar, F., Weinberg, D. H., & Miralda-Escudé, J. 2013, MNRAS, 428, 421

Sharma, D., Collett, T. E., & Linder, E. V. 2023, J. Cosmology Astropart. Phys., 04, 001

Shectman, S. A., Landy, S. D., Oemler, A., et al. 1996, ApJ, 470, 172

Sheldon, E. S., & Huff, E. M. 2017, ApJ, 841, 24

Shirasaki, M., & Yoshida, N. 2018, MNRAS, 475, 1665

Short, A. D., Barry, D., Berthe, M., et al. 2014, SPIE Conf. Ser., 9154, 91540R

Sifón, C., Herbonnet, R., Hoekstra, H., van der Burg, R. F. J., & Viola, M. 2018, MNRAS, 478, 1244

Simon, P., Watts, P., Schneider, P., et al. 2008, A&A, 479, 655

Simon, P., Schneider, P., & Kübler, D. 2012, A&A, 548, A102

Simon, P., Erben, T., Schneider, P., et al. 2013, MNRAS, 430, 2476

Skottfelt, J., Hall, D. J., Dryer, B., et al. 2017a, J. Instrum., 12, C12033

Skottfelt, J., Hall, D. J., Gow, J. P. D., et al. 2017b, J. Astron. Telesc. Instrum. Syst., 3, 028001

Skrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ, 131, 1163

Slepian, Z., & Eisenstein, D. J. 2015, MNRAS, 454, 4142

Smith, R. E., Peacock, J. A., Jenkins, A., et al. 2003, MNRAS, 311, 1311

Snodgrass, C., Carry, B., Berthier, J., et al. 2018, arXiv e-prints [arXiv:1812.00607]

Solano, E., Gálvez-Ortiz, M. C., Martín, E. L., et al. 2021, MNRAS, 501, 281

Sonnenfeld, A., Leauthaud, A., Auger, M. W., et al. 2018, MNRAS, 481, 164

Sorce, J. G., Creasey, P., & Libeskind, N. I. 2016, MNRAS, 455, 2644

Sousbie, T. 2011, MNRAS, 414, 350

Spavone, M., Capaccioli, M., Napolitano, N. R., et al. 2017, A&A, 603, A38

Spavone, M., Iodice, E., van de Ven, G., et al. 2020, A&A, 639, A14

Stanford, S. A., Masters, D., Darvish, B., et al. 2021, ApJS, 256, 9

Stark, D. P. 2016, ARA&A, 54, 761

Steinborn, L. K., Dolag, K., Hirschmann, M., Prieto, M. A., & Remus, R.-S. 2015, MNRAS, 448, 1504

Storey-Fisher, K., Hogg, D. W., Rix, H.-W., et al. 2024, ApJ, 964, 69

Taylor, P. L., & Markovič, K. 2022, Phys. Rev. D, 106, 063536

Sutter, P. M., Lavaux, G., Hamaus, N., et al. 2015, Astron. Comput., 9, 1

Szafraniec, M., Azzollini, R., Cropper, M., et al. 2016, SPIE Conf. Ser., 9915, 991510

Szalay, A. S., Matsubara, T., & Landy, S. D. 1998, ApJ, 498, L1

Takahashi, R., Sato, M., Nishimichi, T., Taruya, A., & Oguri, M. 2012, ApJ, 761, 152

Tananbaum, H., Avni, Y., Branduardi, G., et al. 1979, ApJ, 234, L9

Tanga, P., Pauwels, T., Mignard, F., et al. 2023, A&A, 674, A12

Tanikawa, A., Moriya, T. J., Tominaga, N., & Yoshida, N. 2023, MNRAS, 519, L32

Tasca, L. A. M., Le Fèvre, O., Ribeiro, B., et al. 2017, A&A, 600, A110

Taylor, P. L., & Markovič, K. 2022, Phys. Rev. D, 106, 063536

Taylor, P. L., Bernardeau, F., & Kitching, T. D. 2018a, Phys. Rev. D, 98, 083514

Taylor, P. L., Kitching, T. D., McEwen, J. D., & Tram, T. 2018b, Phys. Rev. D, 98, 023522

Taylor, P. L., Kitching, T., Cardone, V. F., et al. 2021, Open J. Astrophys., 4, 6

Terai, T., & Itoh, Y. 2011, PASJ, 63, 335

Tewes, M., Kuntzer, T., Nakajima, R., et al. 2019, A&A, 621, A36

Tinker, J., Kravtsov, A. V., Klypin, A., et al. 2008, ApJ, 688, 709

To, C., Krause, E., Rozo, E., et al. 2021, Phys. Rev. Lett., 126, 141301

Tohill, C., Ferreira, L., Conselice, C. J., Bamford, S. P., & Ferrari, F. 2021, ApJ, 916, 4

Tonry, J. L., Blakeslee, J. P., Ajhar, E. A., & Dressler, A. 2000, ApJ, 530, 625

Tonry, J. L., Denneau, L., Flewelling, H., et al. 2018, ApJ, 867, 105

Torrado, J., & Lewis, A. 2021, J. Cosmology Astropart. Phys., 05, 057

Tramacere, A., Paraficz, D., Dubath, P., Kneib, J. P., & Courbin, F. 2016, MNRAS, 463, 2939

Treu, T., Suyu, S. H., & Marshall, P. J. 2022, A&A Rev., 30, 8

Tröster, T., Mead, A. J., Heymans, C., et al. 2022, A&A, 660, A27

Troxel, M. A., & Ishak, M. 2015, Phys. Rep., 558, 1

Troxel, M. A., MacCrann, N., Zuntz, J., et al. 2018, Phys. Rev. D, 98, 043528

Trujillo, I., & Fliri, J. 2016, ApJ, 823, 123

Tsedrik, M., Moretti, C., Carrilho, P., Rizzo, F., & Pourtsidou, A. 2023, MNRAS, 520, 2611

Tutusaus, I., Martinelli, M., Cardone, V. F., et al. 2020, A&A, 643, A70
Tyson, J. A., Valdes, F., & Wenk, R. A. 1990, ApJ, 349, L1

Umetsu, K., & Diemer, B. 2017, ApJ, 836, 231

Umetsu, K., Zitrin, A., Gruen, D., et al. 2016, ApJ, 821, 116

Upham, R. E., Brown, M. L., & Whittaker, L. 2021, MNRAS, 503, 1999

Upham, R. E., Brown, M. L., Whittaker, L., et al. 2022, A&A, 660, A114

Urry, C. M., & Padovani, P. 1995, PASP, 107, 803

Valdes, F., Tyson, J. A., & Jarvis, J. F. 1983, ApJ, 271, 431

Vallinotto, A. 2012, ApJ, 759, 32

van Daalen, M. P., Schaye, J., Booth, C. M., & Dalla Vecchia, C. 2011, MNRAS, 415, 3649

van Daalen, M. P., McCarthy, I. G., & Schaye, J. 2020, MNRAS, 491, 2424

van der Burg, R. F. J., Muzzin, A., & Hoekstra, H. 2016, A&A, 590, A20

van Dokkum, P. G., Abraham, R., Merritt, A., et al. 2015, ApJ, 798, L45

van Uitert, E., Joachimi, B., Joudaki, S., et al. 2018, MNRAS, 476, 4662

Van Waerbeke, L., Mellier, Y., Erben, T., et al. 2000, A&A, 358, 30

Van Waerbeke, L., Benjamin, J., Erben, T., et al. 2013, MNRAS, 433, 3373

Vanzella, E., Calura, F., Meneghetti, M., et al. 2017a, MNRAS, 467, 4304

Vanzella, E., Castellano, M., Meneghetti, M., et al. 2017b, ApJ, 842, 47

Vega-Ferrero, J., Huertas-Company, M., Costantin, L., et al. 2024, ApJ, 961, 51

Vegetti, S., & Koopmans, L. V. E. 2009, MNRAS, 400, 1583

Vegetti, S., Lagattuta, D. J., McKean, J. P., et al. 2012, Nature, 481, 341

Venhola, A., Peletier, R. F., Salo, H., et al. 2022, A&A, 662, A43

Verdugo, M., Lerchster, M., Böhringer, H., et al. 2012, MNRAS, 421, 1949

Verza, G., Pisani, A., Carbone, C., Hamaus, N., & Guzzo, L. 2019, J. Cosmology Astropart. Phys., 12, 040

Vikhlinin, A., Kravtsov, A. V., Burenin, R. A., et al. 2009, ApJ, 692, 1060

Voggel, K., Hilker, M., & Richtler, T. 2016, A&A, 586, A102

Voggel, K. T., Seth, A. C., Sand, D. J., et al. 2020, ApJ, 899, 140

Voit, G. M. 2005, Rev. Mod. Phys., 77, 207

Voigt, L. M., Bridle, S. L., Amara, A., et al. 2012, MNRAS, 421, 1385

Wadekar, D., & Scoccimarro, R. 2020, Phys. Rev. D, 102, 123517

Wadekar, D., Ivanov, M. M., & Scoccimarro, R. 2020, Phys. Rev. D, 102, 123521

Wagner-Carena, S., Aalbers, J., Birrer, S., et al. 2023, ApJ, 942, 75

Walsh, K. J., Morbidelli, A., Raymond, S. N., O'Brien, D. P., & Mandell, A. M. 2011, Nature, 475, 206

Wang, Y. 2008a, J. Cosmology Astropart. Phys., 2008, 021

Wang, Y. 2008b, Phys. Rev. D, 77, 123525

Wang, Y., Percival, W., Cimatti, A., et al. 2010, MNRAS, 409, 737

Wang, F., Yang, J., Fan, X., et al. 2021, ApJ, 907, L1

Wang, K., Peng, E. W., Liu, C., et al. 2023, Nature, 623, 296

Waters, C. Z., Magnier, E. A., Price, P. A., et al. 2020, ApJS, 251, 4

Weaver, J. R., Kauffmann, O. B., Ilbert, O., et al. 2022, ApJS, 258, 11

Weaver, J. R., Davidzon, I., Toft, S., et al. 2023, A&A, 677, A184

Weaver, J., Taamoli, S., McPartland, C., et al. 2025, A&A, 697, A16 (Euclid on Sky SI)

Weinberg, D. H., Mortonson, M. J., Eisenstein, D. J., et al. 2013, Phys. Rep., 530, 87

Weller, J., Battye, R. A., & Kneissl, R. 2002, Phys. Rev. Lett., 88, 231301

Werner, S. V., Cypriano, E. S., Gonzalez, A. H., et al. 2023, MNRAS, 519, 2630

Winkel, N., Pasquali, A., Kraljic, K., et al. 2021, MNRAS, 505, 4920

Wittman, D. M., Tyson, J. A., Kirkman, D., Dell'Antonio, I., & Bernstein, G. 2000, Nature, 405, 143

Wittman, D., Tyson, J. A., Margoniner, V. E., Cohen, J. G., & Dell'Antonio, I. P. 2001, ApJ, 557, L89

Wong, K. C., Suyu, S. H., Chen, G. C. F., et al. 2020, MNRAS, 498, 1420

Wong, A., Pope, B., Desdoigts, L., et al. 2021, J. Opt. Soc. Am. B Opt. Phys., 38, 2465

Woodfinden, A., Percival, W. J., Nadathur, S., et al. 2023, MNRAS, 523, 6360

Wu, W. L. K., Mocanu, L. M., Ade, P. A. R., et al. 2019, ApJ, 884, 70

Wu, H.-Y., Costanzi, M., To, C.-H., et al. 2022, MNRAS, 515, 4471

Yamamoto, K., Nakamichi, M., Kamino, A., Bassett, B. A., & Nishioka, H. 2006, PASJ, 58, 93

Yang, Q., & Shen, Y. 2023, ApJS, 264, 9

Yang, J., Wang, F., Fan, X., et al. 2020, ApJ, 897, L14

Yankelevich, V., & Porciani, C. 2019, MNRAS, 483, 2078

Yoo, J., & Seljak, U. 2015, MNRAS, 447, 1789

York, D. G., Adelman, J., Anderson, John E., J., et al. 2000, AJ, 120, 1579

Zamorani, G., Henry, J. P., Maccacaro, T., et al. 1981, ApJ, 245, 357

Zaritsky, D. 2022, MNRAS, 513, 2609

Zehavi, I., Zheng, Z., Weinberg, D. H., et al. 2011, ApJ, 736, 59

Žemaitis, R., Ferguson, A. M. N., Okamoto, S., et al. 2023, MNRAS, 518, 2497

Zennaro, M., Angulo, R. E., Pellejero-Ibáñez, M., et al. 2023, MNRAS, 524, 2407

Zhang, J. Y., Lodieu, N., & Martín, E. L. 2024, A&A, 686, A171

Zitrin, A., & Broadhurst, T. 2009, ApJ, 703, L132

Zitrin, A., Meneghetti, M., Umetsu, K., et al. 2013, ApJ, 762, L30

Zuntz, J., Paterno, M., Jennings, E., et al. 2015, Astron. Comput., 12, 45

Zuntz, J., Sheldon, E., Samuroff, S., et al. 2018, MNRAS, 481, 1149

Zuntz, J., Lanusse, F., Malz, A. I., et al. 2021, Open J. Astrophys., 4, 13

1 Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France

2 Institut d'Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France

3 Johns Hopkins University 3400 North Charles Street Baltimore, MD 21218, USA

4 Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland

5 Institute Lorentz, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands

6 Departamento de Física, Universidad del País Vasco UPV-EHU, 48940 Leioa, Spain

7 Department of Astrophysics, University of Zurich, Winterthur-erstrasse 190, 8057 Zurich, Switzerland

8 Université Côte d'Azur, Observatoire de la Côte d'Azur, CNRS, Laboratoire Lagrange, Bd de l'Observatoire, CS 34229, 06304 Nice Cedex 4, France

9 Université Paris-Saclay, CNRS, Institut d'astrophysique spatiale, 91405 Orsay, France

10 Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France

11 Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France

12 Institute for Particle Physics and Astrophysics, Dept. of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland

13 INFN-Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy

14 Institut de Física Teòrica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain

15 CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA

16 Mullard Space Science Laboratory, University College London, Holmbury St Mary, Dorking, Surrey RH5 6NT, UK

17 Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA

18 Institut de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal

19 Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53, Avenue des Martyrs, 38000 Grenoble, France

20 Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France

21 Kavli Institute for Particle Astrophysics & Cosmology (KIPAC), Stanford University, Stanford, CA 94305, USA

22 Department of Physics, Stanford University, 382 Via Pueblo Mall, Stanford, CA 94305, USA

23 SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA

24 INAF – Osservatorio Astronomico di Capodimonte, Via Moariello 16, 80131 Napoli, Italy

25 Department of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK

26 ESAC/ESA, Camino Bajo del Castillo, s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain

27 Instituto de Astrofísica de Andalucía, CSIC, Glorieta de la Astronomía, 18080 Granada, Spain

28 Instituto de Física Aplicada a las Ciencias y las Tecnologías, Universidad de Alicante, San Vicent del Raspeig, 03080 Alicante, Spain

29 Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy

30 School of Mathematics and Physics, University of Surrey, Guildford, Surrey GU2 7XH, UK

31 Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
32 Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85748 Garching, Germany

33 Technical University of Munich, TUM School of Natural Sciences, Physics Department, James-Franck-Str. 1, 85748 Garching, Germany

34 INAF – Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy

35 INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy

36 Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal, 4, 20018, Donostia-San Sebastián, Guipuzkoa, Spain

37 IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain

38 Thales Alenia Space – *Euclid* satellite Prime contractor, Strada Antica di Collegno 253, 10146 Torino, Italy

39 INFN-Padova, Via Marzolo 8, 35131 Padova, Italy

40 Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy

41 Laboratoire Univers et Théorie, Observatoire de Paris, Université PSL, Université Paris Cité, CNRS, 92190 Meudon, France

42 Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy

43 Dipartimento di Fisica “Aldo Pontremoli”, Università degli Studi di Milano, Via Celoria 16, 20133 Milano, Italy

44 INFN-Sezione di Milano, Via Celoria 16, 20133 Milano, Italy

45 IRFU, CEA, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France

46 Université Paris Diderot, AIM, Sorbonne Paris Cité, CEA, CNRS, 91191 Gif-sur-Yvette Cedex, France

47 School of Mathematics, Statistics and Physics, Newcastle University, Herschel Building, Newcastle-upon-Tyne NE1 7RU, UK

48 Departamento de Física Teórica and Instituto de Física de Partículas y del Cosmos (IPARCOS-UCM), Universidad Complutense de Madrid, 28040 Madrid, Spain

49 Departamento de Física Fundamental. Universidad de Salamanca. Plaza de la Merced s/n, 37008 Salamanca, Spain

50 Université Clermont Auvergne, CNRS/IN2P3, LPC, 63000 Clermont-Ferrand, France

51 Université Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, Villeurbanne, 69100, France

52 Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France

53 Institut für Planetologie, Universität Münster, Wilhelm-Klemm-Str. 10, 48149 Münster, Germany

54 Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

55 Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal

56 School of Physics and Astronomy, University of Nottingham, University Park, Nottingham NG7 2RD, UK

57 Institut de Física d'Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra (Barcelona), Spain

58 IFPU, Institute for Fundamental Physics of the Universe, via Beirut 2, 34151 Trieste, Italy

59 INAF-Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy

60 INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste TS, Italy

61 SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste TS, Italy

62 Caltech/IPAC, 1200 E. California Blvd., Pasadena, CA 91125, USA

63 Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK

64 Sterrenkundig Observatorium, Universiteit Gent, Krijgslaan 281 S9, 9000 Gent, Belgium

65 The University of Texas at Austin, Austin, TX 78712, USA

66 UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France

67 Instituto de Astrofísica de Canarias, Calle Vía Láctea s/n, 38204 San Cristóbal de La Laguna, Tenerife, Spain

68 Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain

69 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands

70 Leiden Observatory, Leiden University, Einsteinweg 55, 2333 CC Leiden, The Netherlands

71 Isaac Newton Group of Telescopes, Apartado 321, 38700 Santa Cruz de La Palma, Spain

72 Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy

73 INFN-Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

74 Astrophysics Research Institute, Liverpool John Moores University, 146 Brownlow Hill, Liverpool L3 5RF, UK

75 INAF-Osservatorio Astronomico di Padova, Via dell'Osservatorio 5, 35122 Padova, Italy

76 Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

77 Waterloo Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

78 Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany

79 ECEO, Universidade Lusófona, Campo Grande 376, 1749-024 Lisboa, Portugal

80 Instituto de Astrofísica de Canarias, c/ Via Lactea s/n, La Laguna 38200, Spain; Departamento de Astrofísica de la Universidad de La Laguna, Avda. Francisco Sanchez, La Laguna, 38200, Spain

81 CEA-Saclay, DRF/IRFU, departement d'ingenierie des systemes, bat472, 91191 Gif sur Yvette Cedex, France

82 Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany

83 Centre National d'Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France

84 Research School of Astronomy and Astrophysics, Australian National University, Cotter Road, Weston Creek, ACT 2611, Australia

85 ARC Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia

86 Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA

87 Department of Physics, Institute for Computational Cosmology, Durham University, South Road DH1 3LE, UK

88 School of Natural Sciences, University of Tasmania, Private Bag 37 Hobart, Tasmania 7001, Australia

89 Institut national de physique nucléaire et de physique des particules, 3 rue Michel-Ange, 75794 Paris Cedex 16, France

90 ATG Europe BV, Huygensstraat 34, 2201 DK Noordwijk, The Netherlands

91 Aix-Marseille Université, Université de Toulon, CNRS, CPT, Marseille, France

92 Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France

93 Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany

94 INFN, Sezione di Roma 2, Via della Ricerca Scientifica 1, Roma, Italy

95 Institut de Physique Théorique, CEA, CNRS, Université Paris-Saclay 91191 Gif-sur-Yvette Cedex, France

96 IMCCE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Univ. Lille, 77 av. Denfert-Rochereau, 75014 Paris, France

97 Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, 67000 Strasbourg, France

98 Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK

99 Airbus Defence & Space SAS, Toulouse, France
100 OCA, P.H.C. Boulevard de l'Observatoire CS 34229, 06304 Nice Cedex 4, France

101 INAF, Istituto di Radioastronomia, Via Piero Gobetti 101, 40129 Bologna, Italy

102 Department of Physics, Northeastern University, Boston, MA 02115, USA

103 Kavli Institute for the Physics and Mathematics of the Universe (WPI), University of Tokyo, Kashiwa, Chiba 277-8583, Japan

104 European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands

105 Ludwig-Maximilians-University, Schellingstrasse 4, 80799 Munich, Germany

106 Max-Planck-Institut für Physik, Boltzmannstr. 8, 85748 Garching, Germany

107 Space Science Data Center, Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy

108 INAF-IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy

109 Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

110 INAF-Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese (TO), Italy

111 Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland

112 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

113 Dipartimento di Fisica – Sezione di Astronomia, Università di Trieste, Via Tiepolo 11, 34131 Trieste, Italy

114 NASA Ames Research Center, Moffett Field, CA 94035, USA

115 Bay Area Environmental Research Institute, Moffett Field, CA 94035, USA

116 Scuola Superiore Meridionale, Via Mezzocannone 4, 80138 Napoli, Italy

117 INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy

118 Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, LAPP, 74000 Annecy, France

119 Thales Services S.A.S., 290 Allée du Lac, 31670 Labège, France

120 Laboratoire d'Astrophysique de Bordeaux, CNRS and Université de Bordeaux, Allée Geoffroy St. Hilaire, 33165 Pessac, France

121 Institut universitaire de France (IUF), 1 rue Descartes, 75231 Paris Cedex 05, France

122 Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK

123 Universita di Salerno, Dipartimento di Fisica “E.R. Caianiello”, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy

124 INFN – Gruppo Collegato di Salerno – Sezione di Napoli, Dipartimento di Fisica “E.R. Caianiello”, Universita di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy

125 Department of Astronomy, University of Geneva, ch. d'Ecogia 16, 1290 Versoix, Switzerland

126 Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy

127 INFN-Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy

128 Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muhlenberg 1, 14476 Potsdam-Golm, Germany

129 Norwegian Space Agency, Drammensveien 165, 0277 Oslo, Norway

130 School of Physics, HH Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK

131 Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy

132 Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain

133 Institut de Ciencies de l'Espai (IEEC-CSIC), Campus UAB, Carrer de Can Magrans, s/n Cerdanyola del Vallés, 08193 Barcelona, Spain

134 Department of Physics and Astronomy, University of Missouri, 5110 Rockhill Road, Kansas City, MO 64110, USA

135 Minnesota Institute for Astrophysics, University of Minnesota, 116 Church St SE, Minneapolis, MN 55455, USA

136 Departamento de Física Teórica, Atómica y Óptica, Universidad de Valladolid, 47011 Valladolid, Spain

137 Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal

138 Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany

139 INFN-Bologna, Via Irnerio 46, 40126 Bologna, Italy

140 Port d'Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra (Barcelona), Spain

141 Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA), Loc. Lignan 39, 11020 Nus (Aosta Valley), Italy

142 INAF – Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy

143 Institut d'Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels, Barcelona, Spain

144 Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy

145 INAF – Osservatorio Astronomico d’Abruzzo, Via Maggini, 64100 Teramo, Italy

146 Department of Physics, University of Miami, Coral Gables, FL 33124, USA

147 Cosmic Dawn Center (DAWN)

148 INFN-Sezione di Roma, Piazzale Aldo Moro 2, c/o Dipartimento di Fisica, Edificio G. Marconi, 00185 Roma, Italy

149 David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto, 50 St George Street, Toronto, Ontario M5S 3H4, Canada

150 Institut de Ciències del Cosmos (ICCCUB), Universitat de Barcelona (IEEC-UB), Martí i Franquès 1, 08028 Barcelona, Spain

151 Departament de Física Quàntica i Astrofísica (FQA), Universitat de Barcelona (UB), Martí i Franquès 1, 08028 Barcelona, Spain

152 Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain

153 Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal

154 Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany

155 Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

156 ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data e Quantum Computing, Via Magnanelli 2, Bologna, Italy

157 Institute for Astronomy, University of Hawaii, 2680 Woodlawn Drive, Honolulu, HI 96822, USA

158 Carnegie Observatories, Pasadena, CA 91101, USA

159 Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy

160 Leibniz-Institut für Astrophysik (AIP), An der Sternwarte 16, 14482 Potsdam, Germany

161 SCITAS, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland

162 Astrophysics Group, Blackett Laboratory, Imperial College London, London SW7 2AZ, UK

163 Université Libre de Bruxelles (ULB), Service de Physique Théorique CP225, Boulevard du Triophe, 1050 Bruxelles, Belgium

164 Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy

165 Department of Theoretical Physics, Maynooth University, Maynooth, Co. Kildare, Ireland

166 Collège de France, 11 Place Marcelin Berthelot, 75231 Paris, France

167 Sorbonne Université, Observatoire de Paris, Université PSL, CNRS, LERMA, 75014 Paris, France
168 European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy

169 Department of Physics & Astronomy, University of California Irvine, Irvine CA 92697, USA

170 European Space Agency/ESOC, Robert-Bosch-Str. 5, 64293 Darmstadt, Germany

171 Department of Physics, Oxford University, Keble Road, Oxford OX1 3RH, UK

172 INAF-Osservatorio Astrofisico di Arcetri, Largo E. Fermi 5, 50125 Firenze, Italy

173 Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria

174 Canada-France-Hawaii Telescope, 65-1238 Mamahoa Hwy, Kamuela, HI 96743, USA

175 Faculdade de Ciências da Universidade do Porto, Rua do Campo de Alegre, 4150-007 Porto, Portugal

176 Dipartimento di Fisica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, Roma, Italy

177 CIGUS CITIC, Centre for Information and Communications Technologies Research, Universidade da Coruña, Campus de Elviña s/n, 15071 A Coruña, Spain

178 Université Paris-Saclay, CEA, Département d'Électronique des Détecteurs et d'Informatique pour la Physique, 91191 Gif-sur-Yvette, France

179 Dipartimento di Scienze Matematiche, Fisiche e Informatiche, Università di Parma, Viale delle Scienze 7/A, 43124 Parma, Italy

180 INFN Gruppo Collegato di Parma, Viale delle Scienze 7/A, 43124 Parma, Italy

181 Instituto de Astrofísica de Canarias (IAC); Departamento de Astrofísica, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain

182 Department of Mathematics and Physics, Roma Tre University, Via della Vasca Navale 84, 00146 Rome, Italy

183 INFN-Sezione di Roma Tre, Via della Vasca Navale 84, 00146, Roma, Italy

184 Department of Mathematics and Physics E. De Giorgi, University of Salento, Via per Arnesano, CP-193, 73100 Lecce, Italy

185 INFN, Sezione di Lecce, Via per Arnesano, CP-193, 73100 Lecce, Italy

186 INAF-Sezione di Lecce, c/o Dipartimento Matematica e Fisica, Via per Arnesano, 73100 Lecce, Italy

187 Dipartimento di Fisica, Sapienza Università di Roma, Piazzale Aldo Moro 2, 00185 Roma, Italy

188 Dept. of Physics, IIT Hyderabad, Kandi, Telangana 502285, India

189 Technion Israel Institute of Technology, Israel

190 Department of Astronomy & Physics and Institute for Computational Astrophysics, Saint Mary's University, 923 Robie Street, Halifax, Nova Scotia B3H 3C3, Canada

191 Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal

192 Departamento Física Aplicada, Universidad Politécnica de Cartagena, Campus Muralla del Mar, 30202 Cartagena, Murcia, Spain

193 Instituto de Física de Cantabria, Edificio Juan Jordá, Avenida de los Castros, 39005 Santander, Spain

194 INAF - Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy

195 Observatorio Nacional, Rua General José Cristino, 77-Bairro Imperial de São Cristóvao, Rio de Janeiro 20921-400, Brazil

196 Centro de Estudios de Física del Cosmos de Aragón (CEFCA), Plaza San Juan, 1, planta 2, 44001 Teruel, Spain

197 California institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA

198 Centre for Information Technology, University of Groningen, PO Box 11044, 9700 CA Groningen, The Netherlands

199 School of Physical Sciences, The Open University, Milton Keynes MK7 6AA, UK

200 Department of Physics, Lancaster University, Lancaster LA1 4YB, UK

201 XCAM Limited, 2 Stone Circle Road, Northampton NN3 8RF, UK

202 School of Physics and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, UK

203 Center for Computational Astrophysics, Flatiron Institute, 162 5th Avenue, New York, NY 10010, USA

204 Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

205 Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway

206 Department of Physics, PO Box 64, 00014 University of Helsinki, Finland

207 School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK

208 Dipartimento di Fisica "G. Occhialini", Università degli Studi di Milano Bicocca, Piazza della Scienza 3, 20126 Milano, Italy

209 Univ. Grenoble Alpes, CNRS, IPAG, Grenoble, France

210 Department of Astronomy, University of Florida, Bryant Space Science Center, Gainesville, FL 32611, USA

211 Code 665, NASA/GSFC, 8800 Greenbelt Road, Greenbelt, MD 20771, USA

212 CEA Saclay, DFR/IRFU, Service d'Astrophysique, Bât. 709, 91191 Gif-sur-Yvette, France

213 Dipartimento di Fisica e Astronomia, Università di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy

214 Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Via Irnerio 46, 40126 Bologna, Italy

215 Nordita, KTH Royal Institute of Technology and Stockholm 1859 University, Hannes Alfvén's väg 12, Stockholm 106 91, Sweden

216 FRACTAL S.L.N.E., calle Tulipán 2, Portal 13 1A, 28231 Las Rozas de Madrid, Spain

217 Departamento de Física Teórica, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Cantoblanco, Madrid, Spain

218 Instituto de Astronomia Teórica y Experimental (IATE-CONICET), Laprida 854, X5000BGR Córdoba, Argentina

219 ASDEX Upgrade Team, Max-Planck-Institut für Plasmaphysik, Garching, Germany

220 Department of Computer Science, Aalto University, PO Box 15400, Espoo 00 076, Finland

221 Asteroid Engineering Laboratory, Luleå University of Technology, Box 848, 98128 Kiruna, Sweden

222 Université Paris Cité, Université Paris-Saclay, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France

223 NRC Herzberg, 5071 West Saanich Rd, Victoria BC V9E 2E7, Canada

224 Department of Physics and Helsinki Institute of Physics, Gustaf Hällströminkatu 2, 00014 University of Helsinki, Finland

225 Centre for Electronic Imaging, Open University, Walton Hall, Milton Keynes MK7 6AA, UK

226 Excellence Cluster ORIGINS, Boltzmannstrasse 2, 85748 Garching, Germany

227 UK Space Agency, Swindon SN2 1SZ, UK

228 Technische Universität Dresden, Institut für Kern- und Teilchenphysik, Zellescher Weg 19, 01069 Dresden, Germany

229 Deutsches Elektronen-Synchrotron DESY, Platanenallee 6, 15738 Zeuthen, Germany

230 European Southern Observatory, Alonso de Cordova 3107, Casilla 19001, Santiago, Chile

231 University of Applied Sciences and Arts of Northwestern Switzerland, School of Engineering, 5210 Windisch, Switzerland

232 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

233 Department of Astronomy and Astrophysics, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064, USA

234 Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing (GCCL), 44780 Bochum, Germany

235 Institute of Physics, Laboratory for Galaxy Evolution, Ecole Polytechnique Fédérale de Lausanne, Observatoire de Sauverny, 1290 Versoix, Switzerland
236 DARK, Niels Bohr Institute, University of Copenhagen, Jagtvej 155, 2200 Copenhagen, Denmark

237 Felix Hormuth Engineering, Goethestr. 17, 69181 Leimen, Germany

238 Technical University of Denmark, Elektrovej 327, 2800 Kgs. Lyngby, Denmark

239 Université PSL, Observatoire de Paris, Sorbonne Université, CNRS, LERMA, 75014 Paris, France

240 Université Paris-Cité, 5 Rue Thomas Mann, 75013 Paris, France

241 DTx - Digital Transformation CoLAB, Building 1, Azurém Campus, University of Minho, 4800-058 Guimarães, Portugal

242 Department of Physics, School of Advanced Science and Engineering, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku, 169-8555 Tokyo, Japan

243 Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405 Orsay, France

244 Ernst-Reuter-Str. 4e, 31224 Peine, Germany

245 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19146, USA

246 Department of Astronomy, Stockholm University, Albanova, 10691 Stockholm, Sweden

247 Department of Physics, Centre for Extragalactic Astronomy, Durham University, South Road DH1 3LE, UK

248 Astrophysics Research Centre, University of KwaZulu-Natal, Westville Campus, Durban 4041, South Africa

249 School of Mathematics, Statistics & Computer Science, University of KwaZulu-Natal, Westville Campus, Durban 4041, South Africa

250 NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

251 Department of Physics and Astronomy, Vesiilinnantie 5, 20014 University of Turku, Finland

252 Serco for European Space Agency (ESA), Camino bajo del Castillo s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

253 Department of Physics, Duke University, Box 90305, Durham, NC 27708, USA

254 ARC Centre of Excellence for Dark Matter Particle Physics, Melbourne, Australia

255 Centre for Astrophysics & Supercomputing, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia

256 Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town, 7535, South Africa

257 SSAI, Lanham, MD 20706, USA

258 Department of Astronomy, University of Maryland, College Park, MD 20742, USA

259 Center For Advanced Mathematical Sciences, American University of Beirut PO Box 11-0236, Riad El-Solh, Beirut 11097 2020, Lebanon

260 Centro de Investigación Avanzada en Física Fundamental (CIAFF), Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain

261 International Centre for Radio Astronomy Research, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia

262 Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, 15236 Penteli, Greece

263 Department of Physics & Astronomy, University of Sussex, Brighton BN1 9QH, UK

264 MTA-CSFK Lendület Large-Scale Structure Research Group, Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary

265 Konkoly Observatory, HUN-REN CSFK, MTA Centre of Excellence, Budapest, Konkoly Thege Miklós út 15-17, 1121, Hungary

266 University of Nottingham, University Park, Nottingham NG7 2RD, UK

267 Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland

268 SRON Netherlands Institute for Space Research, Landleven 12, 9747 AD, Groningen, The Netherlands

269 APCO Technologies, Chemin de Champex 10, 1860 Aigle, Switzerland

270 Department of Astrophysics/IMAPP, Radboud University, PO Box 9010, 6500 GL Nijmegen, The Netherlands

271 Surrey Satellite Technology Limited, Tycho House, 20 Stephenson Road, Surrey Research Park, Guildford, GU2 7YE, UK

272 Centre de Calcul de l'IN2P3/CNRS, 21 avenue Pierre de Coubertin 69627 Villeurbanne Cedex, France

273 ICTP South American Institute for Fundamental Research, Instituto de Física Teórica, Universidade Estadual Paulista, São Paulo, Brazil

274 Lawrence Berkeley National Laboratory, One Cyclotron Road, Berkeley, CA 94720, USA

275 University of California, Berkeley, Berkeley, CA 94720, USA

276 NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991PD Dwingeloo, The Netherlands

277 Aurora Technology for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

278 Universidad Europea de Madrid, 28670 Madrid, Spain

279 INAF-IASF Bologna, Via Piero Gobetti 101, 40129 Bologna, Italy

280 Oskar Klein Centre for Cosmoparticle Physics, Department of Physics, Stockholm University, Stockholm, 106 91, Sweden

281 Institute of Space Sciences and Astronomy (ISSA), University of Malta, Msida, MSD 2080, Malta

282 STAR Institute, Quartier Agora - Allée du six Août 19c, 4000 Liège, Belgium

283 McWilliams Center for Cosmology, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA

284 Serra Húnter Fellow, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain

285 HE Space for European Space Agency (ESA), Camino bajo del Castillo, s/n, Urbanizacion Villafranca del Castillo, Villanueva de la Cañada, 28692 Madrid, Spain

286 Gran Sasso Science Institute (GSSI), Viale F. Crispi 7, L'Aquila (AQ) 67100, Italy

287 Research Center for Space and Cosmic Evolution, Ehime University, 2-5 Bunkyo-cho, Matsuyama, Ehime 790-8577, Japan

288 Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 Copenhagen, Denmark

289 Université Paris-Saclay, CEA, Département de Physique des Particules, 91191 Gif-sur-Yvette, France

290 Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig de Lluís Companys 23, 08010 Barcelona, Spain

291 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan

292 Institute for Advanced Research, Nagoya University, Chikusa-ku, Nagoya, 464-8601, Japan

293 Physics and Astronomy Department, University of California, 900 University Ave., Riverside, CA 92521, USA

294 Dribia Data Research S.L., Pg. de Grácia, 55, 3r 4a, 08007 Barcelona, Spain

295 Laboratoire d'Annecy-le-Vieux de Physique Theorique, CNRS & Universite Savoie Mont Blanc, 9 Chemin de Bellevue, BP 110, Annecy-le-Vieux, 74941 Annecy Cedex, France

296 National Astronomical Observatory of Japan, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

297 School of Physics and Astronomy, Faculty of Science, Monash University, Clayton, Victoria 3800, Australia

298 Department of Mathematics, Imperial College London, London SW7 2AZ, UK

299 Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Turku, Finland

300 Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

301 Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-Cho, Inage-Ku, Chiba 263-8522, Japan

302 Dipartimento di Fisica “E. Pancini”, Universita degli Studi di Napoli Federico II, Via Cinthia 6, 80126, Napoli, Italy

303 Dipartimento di Fisica, Università degli studi di Genova, and INFN-Sezione di Genova, via Dodecaneso 33, 16146 Genova, Italy
304 Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, 8000 Aarhus C, Denmark

305 Department of Physics & Astronomy, Louisiana State University, 202 Nicholson Hall, Baton Rouge, LA 70803, USA

306 Dipartimento di Scienze Fisiche e Chimiche, University of L'Aquila, Italy

307 Department of Astrophysical Sciences, Peyton Hall, Princeton University, Princeton, NJ 08544, USA

308 The Cooper Union for the Advancement of Science and Art, 41 Cooper Square, New York, NY 10003, USA

309 Teledyne E2V, 106, Waterhouse Lane, Chelmsford CM1 2QU, UK

310 Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania

311 Space physics and astronomy research unit, University of Oulu, Pentti Kaiteran katu 1, 90014 Oulu, Finland

312 Higgs Centre for Theoretical Physics, School of Physics and Astronomy, The University of Edinburgh, Edinburgh EH9 3FD, UK

313 Centre de Recherche Astrophysique de Lyon, UMR5574, CNRS, Université Claude Bernard Lyon 1, ENS de Lyon, 69230 Saint-Genis-Laval, France

314 CERN, Theoretical Physics Department, Geneva, Switzerland

315 Université de Franche-Comté, Institut UTINAM, CNRS UMR6213, OSU THETA Franche-Comté-Bourgogne, Observatoire de Besançon, BP 1615, 25010 Besançon Cedex, France

316 NOVA, Netherlands Research School For Astronomy, Einsteinweg 55, 2333CC Leiden, The Netherlands

317 Theoretical astrophysics, Department of Physics and Astronomy, Uppsala University, Box 515, 751 20 Uppsala, Sweden

318 Université St Joseph; Faculty of Sciences, Beirut, Lebanon

319 Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile

320 Institut de Recherche en Informatique de Toulouse (IRIT) et Centre de Biologie Intégrative (CBI), Laboratoire MCD, CNRS, Université de Toulouse, 31062 Toulouse, France

321 Hamburger Sternwarte, University of Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany

322 Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada

323 Junia, EPA department, 41 Bd Vauban, 59800 Lille, France

324 Mathematical Institute, University of Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands

325 Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain

326 School of Physics & Astronomy, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK

327 ASTRON, the Netherlands Institute for Radio Astronomy, Postbus 2, 7990 AA Dwingeloo, The Netherlands

328 Anton Pannekoek Institute for Astronomy, University of Amsterdam, Postbus 94249, 1090 GE Amsterdam, The Netherlands

329 School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT, UK

330 Clara Venture Labs AS, Fantoftvegen 38, 5072 Bergen, Norway

331 Univ. Lille, CNRS, Centrale Lille, UMR 9189 CRISTAL, 59000 Lille, France

332 Department of Physics, Royal Holloway, University of London TW20 0EX, UK

333 Department of Physics and Astronomy, University of California, Davis, CA 95616, USA

334 Department of Physics, Université de Montréal, 2900 Edouard Montpetit Blvd, Montréal, Québec H3T 1J4, Canada

335 Academia Sinica Institute of Astronomy and Astrophysics (ASIAA), 11F of ASMAB, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan

336 Observatorio Astronómico Nacional, IGN, Calle Alfonso XII 3, 28014 Madrid, Spain

337 Center for Cosmology and AstroParticle Physics, The Ohio State University, 191 West Woodruff Avenue, Columbus, OH 43210, USA

338 Department of Physics, The Ohio State University, Columbus, OH 43210, USA

339 Laboratoire univers et particules de Montpellier, Université de Montpellier, CNRS, 34090 Montpellier, France

340 Centre Spatial de Liege, Universite de Liege, Avenue du Pre Aily, 4031 Angleur, Belgium

341 National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

342 Universidad Politécnica de Cartagena, Departamento de Elétrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain

343 Italian Space Agency, via del Politecnico snc, 00133 Roma, Italy

344 University of Trento, Via Sommarive 14, 38123 Trento, Italy

345 Telespazio Germany GmbH, Europapl. 5, 64293 Darmstadt, Germany

346 Center for Cosmology and Particle Physics, Department of Physics, New York University, New York, NY 10003, USA

347 RAL Space, Rutherford Appleton Laboratory, STFC, UKRI, Harwell Campus, Oxfordshire OX11 0QX, UK

348 Space Telescope Science Institute, 3700 San Martin Dr, Baltimore, MD 21218, USA
# Appendix A: List of acronyms

## Acronyms

zPDF redshift probability density function

2PCF two-point correlation function

2dFGRS 2-degree Field Galaxy Redshift Survey

3PCF three-point correlation function

AA alpha angle

ACT Atacama Cosmology Telescope

ADS Airbus Defence and Space

AGN active galactic nucleus

ALMA Atacama Large Millimeter/Sub-millimetre Array

AM abundance matching

AOCS attitude and orbit-control system

AP Alcock-Paczynski

APE absolute pointing error

BAO baryon acoustic oscillation

BBN big bang nucleosynthesis

BFE brighter-fatter effect

BG blue grism

BNT Bernardeau–Nishimichi–Taruya

BOSS Baryon Oscillation Spectroscopic Survey

BPT Baldwin–Phillips–Terlevich

CAS concentration, asymmetry and smoothness

CCD charge-coupled device

CDPU Control and Data Processing Unit

CFHT Canada-France-Hawaii Telescope

CIB cosmic infrared background

CLOE Cosmology Likelihood for Observables in Euclid

CMB cosmic microwave background

CMD colour-magnitude diagram

COSEBIs Complete Orthogonal Sets of E/B-Integrals

CPC completeness and purity calibration

CPU central processing unit

CTI charge-transfer inefficiency

CU calibration unit

CXB cosmic X-ray background

DECam Dark Energy Camera

DES Dark Energy Survey

DESI Dark Energy Spectroscopic Instrument experiment

DI direct integration

DPU data-processing unit

DR data release

DR1 first data release

DTCP daily telemetry communication period

DUNE Dark Universe Explorer

EAF Euclid Auxiliary Field

EC Euclid Consortium

EDF Euclid Deep Field

EDF-F Euclid Deep Field Fornax

EDF-N Euclid Deep Field North

EDF-S Euclid Deep Field South

EDS Euclid Deep Survey

EFS Euclid Flagship Simulation

EFT effective field theory

EGC extragalactic globular cluster

EoR epoch of reionisation

ERO Early Release Observations

eROSITA extended ROentgen Survey with and Imaging Telescope Array

ESA European Space Agency

ESAC European Space Astronomy Centre

ESOC European Science Operations Centre

ESOP early science operations

EUDF Euclid Ultra-Deep Field

EW equivalent width

EWS Euclid Wide Survey

FFT fast Fourier transform

FGS fine-guidance sensor

FITS flexible image transport system

FKP Feldman–Kaiser–Peacock

FoM figure of merit

FoV field of view

FPA focal-plane array

FWHM full width at half maximum

G3L galaxy-galaxy-galaxy lensing

GBTDS Galactic Bulge Time Domain Survey

GC globular cluster

GF Gaussian fit

GGL galaxy-galaxy lensing

GP Gaussian process

GR general relativity

HGA high-gain antenna

HOD halo-occupation distribution

HOS higher-order statistics

HSC Hyper Suprime-Cam

HST Hubble Space Telescope

IA intrinsic alignment

ICRS International Celestial Reference System

IGM intergalactic medium

ISCS IRAC Shallow Cluster Survey

ISW integrated Sachs–Wolfe

JWST James Webb Space Telescope

KiDS Kilo-Degree Survey

KS Kaiser–Squires

kSZ kinetic Sunyaev–Zeldovich

LED light-emitting diode

LF luminosity function

LoS line of sight

LRG luminous red galaxy

LSB low-surface brightness

LSS large-scale structure

LSST Legacy Survey of Space and Time

M2M M2 mechanism

MACC multi-accumulate

MAMBO Mocks with Abundance Matching in BOlogna

MCMC Markov chain Monte Carlo

MLI multi-layer thermal insulation

MOC mission operation centre

MS main sequence

NEP north ecliptic pole

NFW Navarro–Frenk–White