$10^9 M_{\odot}$ (Atek et al. 2022; Finkelstein et al. 2022a; Harikane et al. 2023; Naidu et al. 2022; Yan et al. 2023). A note of caution here is in order, as spectroscopic follow-up will be necessary to confirm current observation only based on photometry. However, if confirmed, such early formation of massive galaxies reported by the JWST is hardly reconcilable with the standard ΛCDM expectations. Recently, Labbé et al. (2023) derived the cumulative stellar mass density at $z = 8$ and 10 for $M_{\star} \gtrsim 10^{10} M_{\odot}$ based on 14 galaxy candidates with masses in the range $\sim 10^9 \div 10^{11} M_{\odot}$ at $7 < z < 11$ observed by the CEERS program. They found

$$ \rho_{*} (> 10^{10} M_{\odot}) \approx 1.3^{+1.1}_{-0.6} \cdot 10^{6} M_{\odot} \text{ Mpc}^{-3}, \quad (162) $$

at $z \simeq 10$. These values are larger than the ΛCDM predictions, even allowing maximum Star Formation Efficiency (SFE) $\epsilon = 1$, or invoking extreme value statistics (Lovell et al. 2022).

Recently, Liu and Bromm (2022), Hütsi et al. (2023) investigated the hypothesis that early structure formation was induced by the seeding effect of PBH induced Poisson isocurvature perturbations.<fnref n="16" /> Their result shows that such early formation of massive galaxies is possible if the PBH abundance is such that $m_{\text{PBH}}/m_{\text{PBH}} \gtrsim 6 \times 10^6 (2 \times 10^5) M_{\odot}$ for SFE $\epsilon < 0.1$ (1). Such abundance for massive PBHs are ruled out by observations of the CMB $\mu$-distortion, although this conclusion relies on the assumptions that primordial density fluctuations are sufficiently Gaussian and that PBHs formed in the standard scenario of primordial density fluctuations not growing during the radiation-dominated era. However, strong isocurvature perturbations of PBHs with $m_{\text{PBH}}/m_{\text{PBH}} \gtrsim 170 M_{\odot}$ are ruled out by high-$z$ Lyman-$\alpha$ forest data (Murgia et al. 2019).

### 7.5.5 Ultra-compact mini haloes

It has been claimed in Adamek et al. (2019), Bertone et al. (2019) that a small fraction of dark matter made of PBHs is not compatible with the rest of the dark matter being made of weakly interacting massive particles (WIMPs) because PBHs should seed the formation of ultra-compact mini-halos with steep density profiles (DM overdensities formed around PBHs are also referred as DM spikes or mini-spikes; Boudaud et al. 2021). Then, the WIMPs in the dense innermost part of these halos would annihilate, which produces a detectable gamma-ray signal. The absence of detection allows to set limits on the PBH fraction in presence of WIMPs, of at most one billionth of the dark matter for PBH masses larger than $10^{-6} M_{\odot}$. An interesting corollary is that any firm detection of PBHs implies that the remaining dark matter cannot be constituted by WIMPs. Similar analysis, e.g. including the effect of primordial non-Gaussianity or the mass dependence of this limit in the case of light PBHs, have been performed in Nakama et al. (2019), Carr et al. (2021d), Kadota and Silk (2021). The s-wave and p-wave annihilation scenarios have been compared in Kadota and Tashiro (2022) where a stringent limit has been obtained for

<footnote n="16">¹⁶ See also Biagetti et al. (2023), Menci et al. (2022), Gong et al. (2023) for different potential explanations.</footnote>
the thermal relic p-wave with a WIMP mass of 100 GeV (see also Chanda et al. 2024). It has been also shown in Tashiro and Kadota (2021b) that WIMPs around PBHs enhance the heating and ionization in the intergalactic medium, due to WIMP annihilations, leading to comparable or even tighter bounds of the possible DM fraction made of PBHs, for instance $f_{\text{PBH}} \lesssim O(10^{-10} - 10^{-8})$ for a WIMP mass of order $10-10^3$ GeV with a conventional annihilation cross section $\langle \sigma v \rangle = 3 \times 10^{-26} \text{cm}^3/\text{s}$. Some of those limits were recently reanalyzed in Ginés et al. (2022). WIMP annihilation in ultra-compact mini-halos around PBHs can also lead to a potentially detectable neutrino signal (Freese et al. 2022) and the limits can be competitive with respect to gamma-ray searches (Boucenna et al. 2018) if PBHs are heavy. Another proposed way to probe DM dresses around PBHs is by observing the gravitational strong lensing of sources like fast radio bursts in the PBH mass range from $10 M_{\odot}$ to $10^3 M_{\odot}$ (Oguri et al. 2023).

The specific case of SU(2)L triplet fermion “winos,” has been studied in Hertzberg et al. (2021). In this case as well, after the wino kinetic decoupling, DM particles are captured by PBHs leading to dark mini-halos, constrained by the production of narrow line gamma rays from wino annihilation in the Galactic Center. Another very specific scenario of parsec-size ultra-compact mini-halos around PBHs, in the context of the QCD axion dark matter, encountering neutron stars and leading to transient radio emissions due to resonant axion-photon conversion in the neutron star magnetosphere, has been explored in Nurmi et al. (2021).

Finally, it has recently been argued in Sten Delos and Silk (2023) that the large density fluctuations required for PBH formation should also lead to ultradense DM halos (see also Ricotti and Gould 2009; Kohri et al. 2014; Gosenca et al. 2017; Delos et al. 2018a, b; Nakama et al. 2019; Hertzberg et al. 2020; Ando et al. 2022) that would actually host a large fraction of the DM (in much greater abundance than PBHs), enabling a variety of new observational tests. This conclusion is viable as long as clustering of the dark matter is possible on the relevant scales (e.g. Bringmann 2009). The formation of such halos can already take place before matter-radiation equality (Kolb and Tkachev 1994; Berezinsky et al. 2010, 2013; Delos 2019; Sten Delos and Silk 2023), which occurred at redshift $z \simeq 3400$ (Aghanim et al. 2020) Due to their early formation, ultradense DM halos could be compact enough to produce detectable microlensing signatures. If a dark matter spike forms around a PBH binary, it would induce a dephasing that could be measured with future detectors (Cole et al. 2023a).

In Delos and Franciolini (2023) it is investigated whether the EROS, OGLE, and HSC surveys can probe these halos by fully accounting for finite source size and extended lens effects. Interestingly, current data by the EROS-2 (Tisserand et al. 2007), OGLE-IV (Niikura et al. 2019a) and Subaru-HSC (Niikura et al. 2019b) surveys may already constrain the amplitudes of primordial curvature perturbations in a new region of parameter space, even though this conclusion is sensitive to details about the internal structures of these ultradense halos. Adopting optimistic assumptions, HSC data would constrain a power spectrum that features an enhancement at scales $k \sim 10^7$/Mpc, and an amplitude as low as $P_{\zeta} \simeq 10^{-4}$ may be accessible. This range of scale is particularly interesting as it connects to
primordial black hole formation in a portion of the LVK mass range and the production of scalar induced gravitational waves in the nanohertz frequency range reachable by pulsar timing arrays. Further dedicated numerical simulations are required to investigate in details the central density reached by such DM halos, to which lensing constraints are particularly sensitive.

In summary, the study of dark matter halos, seeded or induced by the existence of PBHs, brings support for the incompatibility of the coexistence of PBHs and WIMPs and all-or-nothing scenarios.

### 7.5.6 Discussion and limitations

The primordial fluctuations at the origin of the formation of PBHs with masses above $60 M_{\odot}$ can have left detectable signatures in the form of spectral distortions of the CMB black-body spectrum, which have been constrained by FIRAS, in high-redshift Lyman-$\alpha$ forest observations, which can typically probe smaller length scales than large scale structure surveys or CMB anisotropies, and in a GW background sourced at second order in perturbation theory that was discussed in a dedicated section. Those indirect probes are therefore independent of the details of the PBH formation and their subsequent complex evolution. They also depend on the statistical properties of primordial fluctuations, e.g. they can be suppressed in the presence of large non-Gaussianities. These indirect probes are therefore very interesting to discriminate between the possible PBH formation models in a way that is independent of the complex physical processes that could have impacted the PBH properties. This is of particular interest to constrain models with broad PBH distributions aiming at explaining LVK observations and SMBH seeds in a unified way. The absence of any detection of CMB distortions would bring support to non-Gaussian models or to scenarios where PBHs are not formed by primordial density fluctuations.

## 7.6 Gravitational waves

### 7.6.1 LVK GW mergers

The LVK collaboration has been searching for compact binary coalescences. By the end of the O3 run, 90 binary black hole (BBH) candidates have been found (Abbott et al. 2023a), providing rich information on the BH population (Abbott et al. 2023b). The latest catalog GWTC-3 indicates that the BBH merger rate is between $17.3 \text{ Gpc}^{-3}\text{yr}^{-1}$ and $45 \text{ Gpc}^{-3}\text{yr}^{-1}$ at a fiducial redshift ($z = 0.2$).

Soon after the first discovery of the BBH event GW150914, it has been pointed out that the observed BBH could be of primordial origin (Bird et al. 2016; Sasaki et al. 2016; Clesse and García-Bellido 2017b). More detection of BBH events provided information on the merger rate and the chirp mass distribution, and Clesse and García-Bellido (2018) made the first MCMC analysis to infer the PBH mass function. Statistical tests have been performed with the GWTC-1 catalog to test the hypothesis that all or part of observed BBHs is primordial (Hall et al. 2020). The use of the effective spin parameter has also been discussed (Fernandez and Profumo
2019; García-Bellido et al. 2021c). With more events from GWTC-2, the combination of an astrophysical and a primordial BH population have been tested, both using phenomenological models to describe the ABH population (De Luca et al. 2021c; Hütsi et al. 2021c) as well as state-of-the-art astrophysical population synthesis results (Franciolini et al. 2022a). These analyses confirm it is difficult to explain all the features observed in the GWTC-3 catalog of events by means of a single binary population, while showing shortcomings of both astrophysical and primordial scenarios, but still allows for PBH to contribute to a fraction of the observed BBHs.

Indication of particular events has been also discussed. GW190521 has attracted attention because at least the primary component mass lies in the so-called pair-instability mass gap, where there should not be direct formation of stellar black holes, and the possibility of a primordial origin has been discussed in De Luca et al. (2021a). The events GW190425 and GW190814 have both companions with masses [1.6–2.5]M☉ and [2.5–2.7]M☉, which is unexpected if they originated from a neutron star or a stellar black hole. Vattis et al. (2020) discussed the possibility of PBH pairing with an astrophysical BH, and concluded that it is unlikely that such binaries form and merge within a Hubble time (see also Kritos et al. 2021; Sasaki et al. 2022). Jedamzik (2021, 2020), Carr et al. (2021b), Clesse and García-Bellido (2022) investigated the possibility that both the primary and secondary BHs are primordial considering the thermal history mass function, which indeed has a bump at a few M☉ and around 30–50M☉ and explains the events very well, together with GW190521.

Recently, Franciolini et al. (2022e) performed the most comprehensive Bayesian population analysis of LVK data, that includes both BH and NS merger events, while testing the hypothesis that a fraction of events may come from the primordial scenario, where the latter is derived from first principles with the inclusion of QCD effects on the mass distribution. The results of such an analysis can currently only set an upper bound on the PBH fraction, showing the still limited constraining power of available data, but interestingly peaked up some aforementioned special events with high probability of being primordial (i.e. GW190924_021846, GW190814, GW190412, and GW190521). One peculiar property of the PBH channel, is that if it produced mergers in the NS mass range, due to the QCD enhancement and the critical collapse, it would necessarily produce a mass distribution which is wider the one expected for astrophysical NS mergers (Franciolini et al. 2022e). This would inevitably predicts subsolar, as well as lower mass gap event mergers.

Due to the much improved sensitivity of future observation runs, we notice that O4 and O5 may have more chances to detect many PBH events. However, unless some of these events have smoking-gun features (Franciolini et al. 2022b), it would be hard to distinguish them from ordinary astrophysical channels. Therefore, an interesting prediction, reported in Table 5, is the number of subsolar and mass-gap events detectable in O4 and O5, assuming GW190814 is primordial. Such numbers can be considered conservative upper bounds, as well as complementary tests of the primordial origin of the aforementioned events. In particular, in O5 there could be as many as ≈ 8 subsolar events per year (but the 90% confidence interval is also compatible with zero events). Then O5 should detect one to a few dozen events per
<table><caption>**Table 5** Assuming GW190814 had primordial origin, this table reports the 90% C.I. for the number of detected PBH events within GWTC-3, and predicted events (per year) with LVK O4 and O5 sensitivity</caption><thead><tr><th>LVK observing run</th><th>N<sup>det</sup><sub>PBH</sub></th><th>N<sup>det</sup><sub>PBH</sub>(SS)</th><th>N<sup>det</sup><sub>PBH</sub>(LMG)</th><th>N<sup>det</sup><sub>PBH</sub>(UMG)</th></tr></thead><tbody><tr><td>O1-O3</td><td>[0.8, 22.4]</td><td>[0.0, 0.6]</td><td>[0.1, 2.3]</td><td>[0.0, 6.1]</td></tr><tr><td>O4</td><td>[1.9, 43.7]</td><td>[0.0, 1.3]</td><td>[0.3, 13.0]</td><td>[0.0, 13.1]</td></tr><tr><td>O5</td><td>[10.3, 216.7]</td><td>[0.0, 8.6]</td><td>[0.8, 25.2]</td><td>[0.0, 47.3]</td></tr></tbody></table>

We also indicate forecasted detections (within the 90% C.I.) that would fall in the subsolar ($m_1 < M_\odot$, SS), lower mass gap ($m_1 \in [2.5, 5] M_\odot$ and/or $m_2 \in [2.5, 5] M_\odot$, LMG) and upper mass gap ($m_1 > 50 M_\odot$, UMG) ranges. Table adapted from Franciolini et al. (2022e)

<figure><img src="image_46.png" /><figcaption>**Fig. 41** Projected upper limit on $f_{\text{PBH}}$ as a function of central PBH mass scale $M_c$ (assuming a narrow log-normal mass distribution) obtained from null high redshift merger detections with one year of observations at a CE-ET network. See the main text for a discussion of the other (non-GW constraints). In yellow, we show forecasts for the limits that will be set by microlensing searches with the Rubin observatory (Drlica-Wagner et al. 2019; Bird et al. 2023). Image reproduced with permission from Ng et al. (2022b), copyright by the author(s). Image reproduced with permission</figcaption></figure>

year in the lower mass-gap (and up to ≈ 50 upper mass-gap events), which might be more difficult to interpret in astrophysical scenarios.

Future observations at third generation experiments will be able to further constrain the abundance of PBHs in the LVK mass range by searching for high redshift PBH mergers, where the possible astrophysical contamination from Pop III mergers fades out (Ng et al. 2022b) (see also Nakamura et al. 2016; Koushiappas and Loeb 2017b; De Luca et al. 2021d; Pujolas et al. 2021; Ng et al. 2022a; Franciolini
et al. 2022b; Martinelli et al. 2022). This technique would allow to constrain the PBH abundance down to values as small as $f_{\text{PBH}} \lesssim \mathcal{O}(10^{-5})$ in the standard scenario, see Fig. 41 (Ng et al. 2022b).<fnref n="17" />

### 7.6.2 LVK sub-solar searches

In addition to the standard compact binary coalescence search, the LVK has been updating the constraint on sub-solar mass binaries, where at least one binary component has a mass between [0.2–1] $M_\odot$ (Abbott et al. 2018, 2019c, 2022) (see also Nitz and Wang 2021a, b; Phukon et al. 2021; Nitz and Wang 2022). So far, no firm detection of such GWs has been reported, but four subsolar black hole candidates with false alarm rate smaller than $2\ \text{yr}^{-1}$ and signal-to-noise ratio SNR > 8 were reported in Phukon et al. (2021) after re-analysing the data from the second observing run within an extended mass range. If such a binary system were to be found with a clear statistical significance, it could be strong support for the existence of PBHs, since neither black holes nor neutron stars are expected to form below $\sim 1 M_\odot$ through conventional stellar evolution. The recent analysis with the data from the first half of the LVK O3 run has provided a bound on the merger rate of subsolar binaries in the range [220–24200] $\text{Gpc}^{-3}\text{yr}^{-1}$. Assuming an isotropic distribution of equal-mass primordial black holes, the bound on the merger rate translates to the bound on the fraction of PBHs as $f_{\text{PBH}} \equiv \Omega_{\text{PBH}}/\Omega_{\text{DM}} \lesssim 6\%$. Although the LVK collaboration papers have placed stringent constraints on the PBH abundance, they can be relaxed by two orders of magnitude if we take into account merger rate suppression due to binary disruption by early forming clusters, matter inhomogeneities and nearby PBHs (Phukon et al. 2021).

### 7.6.3 LVK SGWB

As mentioned in Sect. 5.6, overlapped GWs from binary PBHs form a SGWB. The most updated bound on the SGWB by the LVK O3 run is $\Omega_{\text{GW}} < 5.8 \times 10^{-9}$ at the 95% credible level for a flat (frequency-independent) SGWB (Abbott et al. 2021b). The first constraints on PBH abundance were argued in Wang et al. (2018) using the O1 data. The updated constraints by O2 and O3 data can be found in Raidal et al. (2017), Hütsi et al. (2021c). In addition, parameter estimation has been attempted by Mukherjee and Silk (2021) using the O3 data by considering both astrophysical and primordial components. The analysis provided weak constraints on the PBH merger rate and time delay parameter, while it indicated the difficulty of separating astrophysical and primordial BBH contributions with the current sensitivity of the detectors (see also Bavera et al. 2022). We may be able to obtain meaningful constraints on the PBH merger rate with the increased sensitivity of upcoming runs and future detectors.

<footnote n="17">¹⁷ Such constraint becomes much more stringent if one assumes clustered PBH initial conditions, boosting the PBH merger rate (De Luca et al. 2021d). However, further work on understanding the merger rate of initially clustered scenarios is needed.</footnote>
It is worth mentioning that the upper bound on the SGWB can provide constraints also on the ultralight PBHs in the mass range of $[10^{-20} - 10^{-19}]M_{\odot}$ through the scalar induced GWs. Those PBHs are strongly constrained by the Hawking radiation, but with the upgraded sensitivity, the ground-based interferometers could provide constraints that are several orders of magnitude stronger than existing constraints (Kapadia et al. 2020). The first constraint was demonstrated by (Kapadia et al. 2021) with the O2 data. See (Romero-Rodriguez et al. 2022) for the updated constraint by the O3 data.

### 7.6.4 PTAs and NANOGgrav

As discussed in Sect. 5.1, enhanced density perturbations inevitably source stochastic GWs, dubbed as scalar induced GWs, or SIGW. The SIGW can be used to probe the small scale power spectrum (Nakama et al. 2017; Inomata and Nakama 2019; Byrnes et al. 2019; Cai et al. 2019b; Kalaja et al. 2019; Ünal et al. 2021; Papanikolaou 2022a). The amplitude of this signal can be estimated as $\Omega_{GW} \sim (\text{symmetry factors}) \cdot \Omega_{\text{rad}} \cdot P_{\zeta}^2$, where symmetry factors include possible contractions and different diagrams. Hence, it is seen that current PTA experiments can probe $P_{\zeta} > 10^{-2.5}$ at the nano-Hertz (nHz) scale.

In 2020, the NANOGgrav collaboration first reported evidence in their 12.5-year dataset (Arzoumanian et al. 2020) for a common spectrum of a stochastic nature, representing the first hint of the existence of a nHz SGWB (also later on confirmed in Goncharov et al. 2021; Chen et al. 2021b; Antoniadis et al. 2022). However, at the time, no evidence was found for a quadrupolar spatial correlation (i.e. Hellings-Down (HD) curve; Hellings and Downs 1983), necessary to interpret the signal as a GW background consistent with General Relativity. Interestingly, the more recent PTA data released in 2023 by the NANOGgrav (Agazie et al. 2023b, c), EPTA (in combination with InPTA) (Antoniadis et al. 2023b, a, 2024), PPTA (Reardon et al. 2023a; Zic et al. 2023; Reardon et al. 2023b) and CPTA (Xu et al. 2023) collaborations, gathered significant evidence for a HD angular correlation.

Focusing on the most stringent dataset, the latest NANOGgrav 15-yr, the reported observations can be fitted by a smooth power law with a scaling $\Omega_{GW} \propto f^{(1.6,2.3)}$ at $1\sigma$. It is known that supermassive black hole binaries produce a SGWB with a scaling $\Omega_{GW} \propto f^{2/3}$ (Phinney 2001) if binary evolution is GW driven, which is currently disfavoured at $2\sigma$ by the NANOGgrav 15-year data (Agazie et al. 2023a; Afzal et al. 2023). Nevertheless, environmental and statistical effects may play a relevant role, and lead to a steeper scaling (Sesana et al. 2008; Kocsis and Sesana 2011; Kelley et al. 2017; Perrodin and Sesana 2018; Ellis et al. 2023; Agazie et al. 2023a; Afzal et al. 2023; Ghoshal and Strumia 2024). At the present stage, current data does not allow to rule-out (or rule-in) a cosmological origin for the observed signal, which may also be due to first-order phase transitions (Arzoumanian et al. 2021; Xue et al. 2021; Nakai et al. 2021; Di Bari et al. 2021; Sakharov et al. 2021; Li et al. 2021; Ashoorioon et al. 2022; Benetti et al. 2022; Barir et al. 2023; Hindmarsh and Kume 2023; Gouttenoire and Volansky 2024; Baldes et al. 2023; Ghosh et al. 2024; Gouttenoire 2023), cosmic strings and domain walls (Ellis and Lewicki 2021;
Datta et al. 2021; Samanta and Datta 2021; Buchmüller et al. 2020, 2021; Blasi et al. 2021; Ramazanov et al. 2022; Babichev et al. 2022; Gorghetto et al. 2021; Blanco-Pillado et al. 2021b; Ferreira et al. 2023; An and Yang 2024; Qiu and Yu 2023; Zeng et al. 2023; King et al. 2024; Babichev et al. 2023; Kitajima et al. 2024; Barman et al. 2023; Blasi et al. 2023; Lazarides et al. 2023; Cai et al. 2023; Gouttenoire and Vitagliano 2024), and inflationary first order tensor perturbations (Vagnozzi 2023; García-Bellido et al. 2017; Ünal et al. 2024) (see also for other explanations Franciolini et al. 2024b; Madge et al. 2023; Figueroa et al. 2024; García-Bellido et al. 2024; Murai and Yin 2023).

Standard PBH formation scenarios generating a population of subsolar PBHs are related to the emission of an induced SGWB, which may explain current PTA detections (Vaskonen and Veermäe 2021; De Luca et al. 2021g; Bhaumik and Jain 2021; Inomata et al. 2021a; Kohri and Terada 2021; Domènech and Pi 2022; Vagnozzi 2021; Namba and Suzuki 2020; Sugiyama et al. 2021; Zhou et al. 2020; Lin et al. 2023; Rezazadeh et al. 2022; Kawasaki and Nakatsuka 2021; Ahmed et al. 2022; Yi and Fei 2023; Yi 2023; Zhao and Wang 2023; Dandoy et al. 2023; Zhao et al. 2023; Ferrante et al. 2023a; Cai et al. 2024; Franciolini et al. 2023; Balaji et al. 2023; Liu et al. 2024; You et al. 2023; Jin et al. 2023; Zhao et al. 2024; Wang et al. 2024a, b; Firouzjahi and Talebian 2023; Liu et al. 2024; Basilakos et al. 2024a, b; Abe and Tada 2023; Inomata et al. 2024). In Fig. 42 we show the parameter space that would be compatible with PTA signal and how this relates to PBH overproduction constraints (see also Sect. 3 for a discussion on the uncertainties affecting the computation of the PBH abundance).

<figure><img src="image_47.png" /><figcaption>**Fig. 42** The green and purple posterior indicate the 1, 2, 3σ contours obtained fitting to NANOGrav15 and EPTA dataset, respectively. This plot assumed a broken power law curvature spectrum with a fixed growth index $n = 4$ and varying decay power law index after the peak located at $k_*$. A indicates the power spectral peak amplitude and we indicate on top the corresponding peak SGWB frequency. We also show the corresponding PBH abundance for different models: Gaussian curvature perturbations including non-linear effects (black), quasi-inflection-point models with $\beta = 3$ (red), curvaton models with $r_{\text{dec}} = 0.9$ (blue) and negative $f_{\text{NL}}$ (cyan) (see Table 1 and references therein for more details). The colored bands cover values of PBH abundance in the range $f_{\text{PBH}} \in (1, 10^{-3})$ from top to bottom. The dashed line indicates an average PBH mass $\langle m \rangle = M_{\odot}$. We point the reader to Sect. 3 for a discussion on the uncertainties affecting the computation of the PBH abundance. Image reproduced with permission from Franciolini et al. (2023), copyright by APS Image reproduced with permission</figcaption></figure>
Due to the extreme sensitivity of PBHs to the statistics of the primordial perturbations, it is also possible to reduce or enhance the abundance of PBHs efficiently via non-Gaussian perturbations. This could result in a larger/smaller amplitude of curvature perturbations and of the associated SIGWs. On the one hand, assuming a fixed abundance of PBHs, negative non-Gaussianities would be able to enhance the associated amplitude of the GW signal, bringing it closer to the range preferred by PTA observations. On the other hand, positive non-Gaussianities could reduce ΩGW allowing this scenarios to escape the sensitivity level of current PTA experiments.

Future nHz frequency gravitational wave detectors will reach remarkable sensitivities, provided a potential astrophysical background can be tamed. Therefore, with future PTA-SKA experiments we will either detect or rule out conclusively the cosmological signals accompanying the formation of PBHs. PTA-SKA will robustly probe PBH mass formation in the range [0.1 – 10⁴]M⊙. This regime is extremely important for both astrophysical sources such as stellar mass BH binaries, intermediate BHs and SMBH seeds. In Fig. 43, from Ünal et al. (2021), we show the PTA-SKA detection capabilities of the stochastic GW background sourced by primordial scalar perturbations which obey different statistical distributions: Gaussian, chi-sqr (χ²) and cubic-Gaussian (G³) for the cases i) fPBH ~ 1 (i.e PBHs constituting all the DM) and ii) fPBH = 10⁻¹⁰.

One should point out here as well the possibility of future nHz PTA-SKA GW detectors to observe ultralight PBHs in the mass range 10⁷ – 10⁹ g given that the peak frequency associated to the scalar induced GWs sourced by Poisson PBH energy density fluctuations, related to the PBH spatial distribution, is well within the PTA-SKA frequency range (Papanikolaou et al. 2021). This potential detectability of such small mass PBHs is very important given the fact that these ultralight PBHs

<figure><img src="image_48.png" /><figcaption>**Fig. 43** PTA-SKA detection capabilities of the stochastic GW background sourced by scalar perturbations with distinct primordial statistical distributions: Gaussian (red), chi-sqr (χ², orange) and cubic-Gaussian (G³, blue) for i) *fPBH* ~ 1 (i.e. PBHs constituting all the DM) and ii) *fPBH* = 10⁻¹⁰. Image reproduced with permission from Ünal et al. (2021), copyright by APS Image reproduced with permission</figcaption></figure>
evaporate before BBN so they do not leave another direct observational imprint of their existence.

### 7.6.5 Continuous and high-frequency GWs from planetary-mass PBHs

PBH binary systems with a planetary chirp mass should emit very weak continuous GWs in the frequency range of ground-based interferometers, many years before they actually merge. It has been proposed to search for continuous waves from PBH binaries in our galaxy (Miller et al. 2021), either towards the galactic center or in the solar system vicinity. However, the current limits on continuous waves do not yet provide significant limits on the PBH abundance (Miller et al. 2022), even for the models with the highest merger rates. However, future instruments like Einstein Telescope should be able to probe $f_{PBH}$ between $10^{-2}$ and 1.

When they merge, these low-mass PBH binaries emit gravitational waves in the MHz or GHz range. These could be probed with high-frequency GW detectors like resonant microwave cavities, which could probe $f_{PBH}$ down to about $10^{-3}$ (Herman et al. 2021; Aggarwal et al. 2021). Additionally, one recent proposal involving resonant LC circuits may represent the best option in terms of individual merger detection prospects in the range (1 – 100) MHz. It was also shown in Franciolini et al. (2022d) that a detection of the stochastic gravitational wave background produced by unresolved light PBH binaries is possible only if the theoretical sensitivity of the proposed Gaussian beam detector is achieved. Such a detector, whose feasibility is subject to various caveats, may be able to rule-out some scenarios for asteroidal mass primordial black hole dark matter (see Franciolini et al. 2022d and references therein for more details).

### 7.6.6 Discussion and limitations

Gravitational wave observations already provide both limits on the PBH abundance and possible hints in favor of the PBH hypothesis. There is a rather general agreement that the observations of black hole mergers around $30 M_{\odot}$ do not allow for more than about a percent of the dark matter to be made of PBHs of this mass.

Exceptional GW events, e.g. including at least one black hole in the pair-instability mass gap (like GW190521), with one object in the low-mass gap or at least heavier than most of neutron stars (like GW190814 and GW190421) without electromagnetic counterparts, mergers with low mass ratios and small individual spins (like GW190814), with statistical evidence for a black hole spin not aligned or anti-aligned with orbital momentum, as well as the measured low effective spins, provide a series of indications that challenge most standard stellar-origin scenarios and suggest alternative formation mechanisms. Among these alternatives, the PBH hypothesis is a front-runner together with scenarios of stellar black hole binary formation in dense environments like globular clusters or nearby AGNs. All these observations are also pushing the odds in favor of PBHs when one performs model comparisons based on Bayesian statistics. But the statistical significance of these
observations, as well as the large theoretical uncertainties on both PBHs and stellar
black hole models, do not yet allow to draw a definitive conclusion.

If at least some of the detected black holes are primordial, this suggests a somehow extended mass function, which is also more realistic theoretically. This means that thermal effects induced by the QCD transition needs to be taken into account, as recently done in Franciolini et al. (2022e), Escrivà et al. (2023), which have important effects in the stellar mass range and can modify the merger rate distribution previously derived with phenomenological lognormal models.

Limits on GW backgrounds is another way to already probe the possible DM
fraction made of PBHs, but these limits highly depend on the model parameters and
are impacted by the merger rate uncertainties or by the possible non-Gaussian
statistics of scalar perturbations in the case of a SGWB from second order
perturbations. Nevertheless, it has been claimed that the possible signal from PTAs at
nHz frequencies could come from the scalar perturbations leading to stellar-mass or
planetary-mass PBHs.

Altogether, GWs appear to be a very novel and promising way to probe and set a
limit on the abundance of PBHs. Once again, one must be cautious because of the
large model uncertainties, but the intriguing LVK observations provide a very strong
motivation to investigate further the PBH hypothesis with improved models and
Bayesian statistical methods. Among the GW signatures of PBHs, signals from the
coalescence of subsolar black holes provide the most compelling way to distinguish
between stellar and primordial origin. A few candidates have been recently found but
whose statistical significance is too limited to claim a detection. Upcoming data will
have the ability to detect subsolar PBHs if they significantly contribute to the dark
matter.

7.7 Summary

There are dozens of ways to probe and constrain the abundance of PBHs, which have
been reviewed in this section. If one strictly follows the claimed limits and assume a
monochromatic distribution, it seems excluded that PBHs account for the entirety of
the dark matter below $10^{-16} M_{\odot}$ due to limits based on PBH evaporation through
Hawking radiation and above $10^{-10} M_{\odot}$ due to microlensing limits up to the solar
mass scale, and multiple other astrophysical and cosmological observations at masses
above a solar mass. This has fed the interest for the asteroid-mass region that until
know remains open, even if some limits have been claimed from the capture of PBHs
by stars, but still using quite specific assumptions.

It is however worth noticing that the situation is in reality much less simplistic,
and that all the limits rely on assumptions that can be debated and that very often are
also model dependent. The simplest example of the mitigation of these limits is
probably the fact that all the evaporation-based limits rely on a still unproven
physical phenomena mixing quantum theory and gravity. If for any reason our
current description of the Hawking radiation is incorrect or if it is less efficient than
expected, all the limits on the PBH abundance below $10^{-16} M_{\odot}$ disappear. Lots of
work have tried to examine the validity of the assumptions in different contexts and
these were also discussed in this section. It is also worth noticing that the strength of
the microlensing limits can vary depending on the PBH clustering, on the galactic
halo profiles, etc. Another example of how limits can change depending on
assumptions is provided by CMB limits, varying by many orders of magnitude
depending on the details of the accretion process onto PBHs or on the dark matter
content.

Besides asteroid-mass PBHs, one can also notice that in the solar-mass region, the number of probes is limited to microlensing and X-ray limits and are not extremely stringent, varying between 10⁻² and 10⁻¹. For quite extended PBH mass functions, it could remain a viable possibility that the main peak of PBHs arises within this range as one could expect from the QCD-transition. Scenarios combining a peak in the asteroid-mass range and a peak in the solar-mass range, possibly explaining GW observations, are also an interesting possibility.

Finally, one should note that limits on PBH abundances cohabit with possible positive evidence (Carr et al. 2024), e.g. from detected microlensing events, cosmic background properties supporting the high redshift existence of PBH clusters, and obviously GW observations and the intriguing properties of black hole binary mergers. Most of these evidences point to the stellar-mass region.

Taken all these considerations into account, it seems indeed difficultly plausible
that all the dark matter is made of planetary-mass or intermediate mass (above $10M_{\odot}$)
PBHs. But both the asteroid-mass region and the stellar-mass region remain of very
high interest, especially in the context of extended mass distributions. But strong
claims are probably premature given the remaining large level of uncertainties for all
the probes.

8 Detectability with LISA

In this section, we aim at summarizing the different ways with which the LISA
mission can probe PBHs, and the possible impact that LISA will have on our
understanding of the viable PBH models, in particular their mass function, merging
rates, and the underlying formation scenarios. Remarkably, we emphasize that not
only LISA will be able to probe intermediate-mass PBHs but also solar-mass and
subsolar mass PBHs, and even tiny PBHs formed at very high energies in the early
Universe that would have entirely evaporated, due to the Poisson fluctuations and the
resulting SGWB they would have left.

8.1 SGWB from second order curvature fluctuations

The generation of PBHs from the collapse of sizeable density perturbations is
unavoidably associated with the emission of a SGWB at second order in perturbation
theory, whose characteristic frequency can be related to the PBH mass (Yuan and
Huang 2021a; Domènech 2021). It has been found that the formation of PBHs with
masses around $O(10^{-15} - 10^{-8})M_{\odot}$, where they can comprise the dark matter in the
Universe, corresponds to the emission of a SGWB with frequency and abundance
well within the LISA sensitivity curve (Bartolo et al. 2019b).
The properties of such a SGWB can be summarised as follows:

* The shape of the signal depends on the power spectrum of the curvature perturbations and is model dependent. However, the behaviour at low frequencies is predicted to be scaling like ~$k^3$ due to causality arguments (Cai et al. 2020).<fnref n="18" />

* Even though GW signals have an intrinsic non-Gaussian nature at emission epoch, their coherence in phase correlations is washed out by their propagation in the perturbed Universe due to time delay effects generated by large scale variations of the gravitational potential, leading to a completely low-redshift Gaussian signal at the LISA detector (Bartolo et al. 2019c).

* The presence of local scale-invariant primordial non-Gaussianities in the scalar curvature perturbation would be responsible in modifying the shape and abundance of the GW spectrum (Ünal 2019), as well as inducing a large amount of anisotropies in the SGWB, potentially detectable by LISA (Bartolo et al. 2022), if PBHs comprise only a small fraction of the dark matter in the Universe (Bartolo et al. 2020a).

These predictions can be used to disentangle this signal from other SGWBs of different nature.

## 8.2 SGWB from ultralight evaporated PBHs

LISA will also probe the formation of PBHs of mass between 10 g and $10^9$ g that are too light to have survived until today, due to Hawking evaporation. In particular, a SGWB comes from the Poisson fluctuations in the spatial distribution of these PBHs at formation (Papanikolaou et al. 2021). These Poisson fluctuations correspond actually to scalar inhomogeneities, sourcing a SGWB at second order. This will be particularly interesting in the context of modified-gravity setups (Papanikolaou et al. 2022, 2023b) that could be constrained or even ruled out using the SGWB from ultralight PBHs.

Through this PBH-induced SGWB, LISA will indirectly probe the early Universe at energies up to the scale of grand-unified theory, including inflationary models, even if these PBHs have quickly evaporated.

## 8.3 SGWB from early binaries

As seen in Fig. 30, the SGWB amplitude for a log-normal mass function with central mass $\mu = 2.5M_\odot$ and width $\sigma = 1$ reaches its peak at around 100 Hz, and starts to be greatly suppressed below the LISA frequencies. For the thermal broad-mass function, one notices in Fig. 31 the important contribution to the SGWB from binaries composed of intermediate and solar-mass PBH (coming from the electron peak and the QCD peak in the PBH mass function respectively, see Fig. 13). These low-mass-ratio binaries start to boost the SGWB below 0.1 Hz by up to 3 orders of magnitude

<footnote n="18">¹⁸ See Domènech et al. (2020), Hook et al. (2021), Witkowski et al. (2022) where the impact of thermal history on the SGWB spectral shape was investigated.</footnote>
at most, compared to the log-normal case (Fig. 30). In particular, one can notice a bump in the SGWB around $10^{-3}$ Hz, originating from the bump around $10^6 M_{\odot}$ in the broad PBH mass function. The shape of the background could therefore give us important details about the PBH mass function and allow for precise reconstruction. The SGWB spectral index $(d\log\Omega_{\text{GW}}/d\log f)$ is overall positive for the early binaries contrary to the late-time PBH binaries (see next Subsection), thus probing the SGWB spectral index at the LISA frequencies could be a way to differentiate PBH binaries in clusters from early PBH binaries.

## 8.4 SGWB from late binaries

Similarly to the early binaries case, the SGWB amplitude for a log-normal mass function is much lower at the LISA frequencies, but we can still expect a detection if the GW amplitude is high enough to be detected by LVK. In the case of a thermal history mass function, the SGWB amplitude is enhanced at LISA frequencies because we have more massive PBHs paring with the $2M_{\odot}$ PBHs (see Figs. 32 and 33). The overall amplitude is determined by the merger rate, which still has a large uncertainty. As discussed in Sect. 4.2, it can be enhanced by increasing the PBH density in clusters and/or lowering the PBH velocity. Further observations by LVK would provide useful implications on the merger rate to refine the prediction on the SGWB amplitude at LISA frequency.

## 8.5 Intermediate-mass binary mergers

As shown in Fig. 21 for two typical models, intermediate-mass PBHs between $10^3$ and $10^5 M_{\odot}$ that are contributing to the dark matter at the sub-percent level at most, due to other limits in this range, could merge with rates above $10^{-3} \text{yr}^{-1} \text{Gpc}^{-3}$. Interestingly, this mass range corresponds to GW frequencies where LISA has the highest range, effectively probing any merger in the observable Universe up to redshifts of 100 to 1000. This means that even if the merger rate is lower than in the stellar-range, LISA could detect more than a few of these mergers every year. Determining the merger rate and redshift distribution of intermediate-mass BH mergers is therefore a promising way to constrain the PBH mass functions and clustering properties, possibly linking them to the seeds of supermassive black holes.

## 8.6 Extreme mass ratio inspirals

The capability of LISA of targeting low frequency regimes makes it an ideal experiment for the search of GW signals generated from the inspiral of a subsolar mass compact object that could have a primordial origin around a supermassive black hole (SMBH). GW constraints can be set on the PBH abundance from the expected PBH-SMBH merger rate (Guo et al. 2019a; Kuhnel et al. 2020). In particular, a null-detection during a 5-year operation of the experiment would constrain the PBH abundance to values smaller than $f_{\text{PBH}} \lesssim 3 \times 10^{-4}$ for PBHs masses in the range $(10^{-2} - 1) M_{\odot}$ (Guo et al. 2019a). Furthermore, the detection of these extreme mass-
ratio inspirals at LISA will be crucial in the search for subsolar-mass black holes, given the unparalleled precision in measuring the mass of the secondary object at subpercent level for PBHs as light as $O(0.01)M_\odot$ up to luminosity distances around hundred megaparsecs (Barsanti et al. 2022). This would allow the claim of detection of a subsolar-mass black hole with very high statistical confidence.

## 8.7 High-redshift binary mergers

It is challenging to explain how supermassive black holes can exist in only partially reionized environments at redshifts as high as $z \ge 7$ (Banados et al. 2018). If the seeds of these black holes come from the first population of stars, this typically needs super-Eddington accretion rate and large mass seeds. Another possible mechanism is the direct collapse of gas into BHs. Both models have their caveats. Even if one invokes super-Eddington accretion, it is very challenging for these seeds to reach sufficiently large masses to explain observations. PBHs are an alternative explanation to the existence of SMBHs since they can provide seeds of intermediate-mass BHs at higher redshift than for the other astrophysical mechanisms (Duechting 2004; Kawasaki et al. 2012; Clesse and García-Bellido 2015; Bernal et al. 2018; De Luca et al. 2023a). Therefore, the easiest way to distinguish PBH seeds from other candidates is to observe intermediate-mass or even supermassive black holes at $z \ge 20$, prior to star formation.

The astrophysical range of LISA will allow for the observation of IMBBH mergers at redshifts $z > 20$ with a SNR larger than five, for equal-mass mergers and progenitor masses between $10^3 M_\odot$ and $10^6 M_\odot$ (Colpi et al. 2024). The possible merger rates of PBHs for a broad mass function with the imprints of the thermal history, shown in Fig. 21, can be larger than $O(1)yr^{-1}$ for primordial IMBBHs that would be formed in PBH clusters at high redshift. The existence of these clusters is relevant since they would also form in the standard Press-Schechter theory. LISA observations will be complementary to those of Earth-based GW detectors, like CE and ET, which will probe mergers with lower masses, and to future PTA limits from SKA, which will probe eventual mergers of SMBHs.

## 8.8 Combination with LVK observations

Numerous compact binary coalescences with total mass between $10 M_\odot$ and $100 M_\odot$ and a merger frequency in the range probed by Earth-based interferometers will also be detected by LISA due to the GW emission in the inspiral phase, as illustrated in Fig. 44. This provides a unique way to determine months or even years in advance when and in which sky location these mergers are going to occur. It will be then easier to search for electromagnetic counterparts of mergers. Parameter reconstruction will also be improved, which could also help to better determine the source location, distance and redshift. According to Sesana (2016), up to hundreds of binary black hole mergers could be pre-determined with an accuracy of about 10 s and 1 deg$^2$, as well as a chirp mass reconstruction at the $10^{-6}$ level. The latest analysis (Klein et al. 2022) uses the state-of-art waveforms and Bayesian parameter
<figure><img src="image_49.png" /><figcaption>**Fig. 44** Illustration of the concept of multi-band GW astronomy, combining (e)LISA and aLIGO (LVK). Each blue line corresponds to a trajectory in the strain-frequency plane for black hole mergers. The horizontal time scale corresponds to the probed time before the merger. Image reproduced with permission from Sesana (2016), copyright by APS. Image reproduced with permission</figcaption></figure>

estimation for both frequency bands to assess the potential of multi-band GW observations of the stellar-mass BBHs starting from 3 years before the merger (LISA) up to the coalescence (ground-based detectors: upgraded LVK or 3 G – either ET or CE). Such observations will allow to determine all 17 parameters describing the binary with at least percent-level accuracy, possibly to identify a likely host galaxy and to alert about the expected merger days in advance significantly improving the chances of detection of any electromagnetic signature associated with it.

In Franciolini et al. (2022b) the measurement accuracy by LISA, ET and LVK has been quantified for such PBH binary discriminators as eccentricity, spin and mass-spin correlation, as well as the horizon redshift for subsolar-mass mergers with negligible spins and eccentricity has been determined.

A better reconstruction of the black hole mass, rate and redshift distribution will help to distinguish between primordial and stellar scenarios, as well as the black hole environment and binary formation channel (merger from a cluster, stellar binary origin, AGNs...). This could be particularly the case for mergers with black hole masses in the pair-instability mass gaps that would be seen as short bursts in LVK detectors, not allowing for a precise mass reconstruction. LISA will significantly help to determine their still enigmatic (possibly primordial) origin.

## 8.9 Quasi-monochromatic continuous waves from subsolar PBHs

It has been pointed out in Pujolas et al. (2021), Barsanti et al. (2022), Guo and Miller (2022) that LISA will probe the existence of galactic subsolar PBHs in binaries with very long coalescence times up to distances of tens of kiloparsecs, allowing to probe the galactic center or PBH clusters in the galactic dark matter halo. This range is
<figure><img src="image_50.png" /><figcaption>**Fig. 45** Distance for which a circular binary of total mass *m* and coalescence time τ leads to quasi-continuous gravitational waves detectable with a SNR = 8 in different detectors. The expectations for LISA are shown in the right panel. Image reproduced with permission from Pujolas et al. (2021), copyright by APS Image reproduced with permission</figcaption></figure>

shown in the right panel of Fig. 45 coming from Pujolas et al. (2021) as a function of
the binary mass and time before collapse. The most interesting region is probably for
$10^{-2} M_{\odot} < m < 1 M_{\odot}$ and collapse time $\tau$ up to $10^8$ years, for which the range is of
order of tens of parsecs.

Therefore, with the use of continuous-wave methods, LISA will be able to probe
different mass and collapse time scales than ground-based instruments like Einstein
telescope (De Luca et al. 2021d). It will therefore be complementary to probe the
existence of subsolar black holes or primordial origin in our galaxy, which if they are
found, would lead to groundbreaking implications in cosmology.

**8.10 Observing near-Earth asteroid-mass primordial black holes**

The LISA instrument will have the sensitivity to detect the gravitational influence of dark matter clumps or dark asteroid-mass compact objects like tiny primordial black holes passing nearby the detector. This possibility was recently studied in Baum et al. (2022) (see also the old work by Seto and Cooray 2004).

With typical galactic velocities of hundreds kilometers per second, the signal
duration is of order of hours or days, and would correspond to a burst at a frequency
of order 10<sup>-6</sup>–10<sup>-4</sup> Hz, within the LISA sensitivity band. Since the signal would
come from a transient change in the acceleration on the three mirrors resulting from
the gravitational force exerted by the compact object, the shape of the signal is
expected to be different than for a gravitational-wave tensor fluctuation. Therefore
specific analysis tools are probably needed to search for them, but those could be
used to detect near-Earth asteroids as well, which would be an interesting bi-product
of such an analysis. For instance, one expects one observable transit every 20
years (Baum et al. 2022) for PBHs with mass of order 10<sup>14</sup> kg, if they constitute all
the DM density. The expected LISA range to asteroid-mass PBHs and the
corresponding rate of expected events is shown in Fig. 46.
<figure><img src="image_51.png" /></figure>

**Fig. 46** Left: Expected mass of dark matter clumps or compact objects like PBHs $m_{\text{cl}}$ in the inner solar system that could be detected at a distance $d$ by LISA and other types of gravitational-wave detectors, due to the transient acceleration of test masses (which for LISA corresponds to the mirrors in the three space probes). Right: Corresponding rate of expected observable events as a function of the object mass, if they comprise all the dark matter and assuming galactic velocities. Image reproduced with permission from Baum et al. (2022), copyright by APS Image reproduced with permission

Observing tiny primordial black holes in the solar system would be clearly revolutionary and LISA will probably be the first instrument to reach the required sensitivity to make such a great achievement.

## 8.11 Summary

LISA will have the ability to probe primordial black holes of a very broad range of masses, based on different signals and GW production mechanisms:

* $10^3 - 10^9 M_{\odot}$: GWs from the merging of intermediate-mass and supermassive black holes, including at redshift $z \ge 20$, and their SGWB.

* $10 - 100 M_{\odot}$: GWs from the merging of binaries with extreme-mass ratios and their SGWB.

* $0.01 - 1 M_{\odot}$: Quasi-continuous GWs from sub-solar PBH in our galaxy.

* $10^{-15} - 10^{-8} M_{\odot}$: SGWB from second order perturbations.

* $10^{-19} - 10^{-16} M_{\odot}$: Newtonian gravitational force from PBHs in the inner solar system.

* $10^{-20} M_{\odot}$: SGWB induced by Poisson PBH energy density fluctuations.
This includes the two best ways to almost unambiguously prove the existence of PBHs, i.e. detecting subsolar black holes (in binaries with extreme mass ratios) and black holes at higher redshift than the stellar formation scenario can account for.

As a consequence, LISA will be an instrument of premiere importance in order to
probe the existence of PBHs, which will be complementary to other astrophysical
and cosmological signals, as well as other types of GW detectors.

**9 Conclusions**

Since the first detection of gravitational waves in 2015, primordial black holes (PBHs) have been the subject of an exponential growth of interest. Not only could PBHs explain some of the LVK black hole mergers but they could also have important cosmological consequences in cosmology: their existence would unveil new high-energy physics needed for their formation in the early Universe, they could significantly contribute to or even entirely constitute the dark matter, they may be related to baryogenesis, may have seeded supermassive black holes at the center of galaxies, and may as well have significantly modified the formation and growth of structures through the Universe's history.

With this work, we provide a review including the most recent scenarios of primordial black hole formation. The most up-to-date formalisms to be used for end-to-end calculations of their gravitational-wave signatures are also reviewed. A particular emphasis is placed on the observational perspectives in the context of the LISA mission. The present astrophysical and cosmological limits are also briefly reviewed and discussed, as well as the possible clues for their existence.

Among the plethora of formation mechanisms, we have discussed in particular the recent classes of models in which PBHs are formed from Gaussian or non-Gaussian inhomogeneities that could be produced from quantum fluctuations or quantum diffusion of one or more scalar fields during inflation. Wherever possible, we provided the concrete formula to be used to calculate the primordial power spectrum of curvature fluctuations in these models and their possible non-Gaussian statistics. We went beyond the standard formalism of PBH formation by reviewing recent progress on the relation between the curvature perturbation and the density contrast, the model-dependent computation of the overdensity threshold leading to PBH formation, including thermal effects at the QCD transition that provide a good theoretical motivation for a peak in the PBHs distribution at the stellar-mass scale (possibly associated with LVK observations). We also went beyond the standard computation of the present PBH mass function and spin distribution by including non-trivial effects related to accretion, which have been studied recently.

PBHs can lead to different types of signatures in gravitational-wave observations and we have reviewed their calculation in a model-dependent way. We provided the most recent prescriptions for the calculation of the PBH merging rates, for different binary formation mechanisms (early binaries, binaries formed in clusters, disrupted binaries). These mergers would leave distinct GW signatures that are searched for with GW template-based methods. The PBH mass function and the underlying formation model could be reconstructed from the rate, mass, spin and redshift
distribution of black hole mergers with present and future gravitational-wave interferometers. Recent analysis of LVK observations have revealed that there could be some statistical significance in favor of the PBHs hypothesis, depending on which astrophysical channels one compares them to. Another source of GWs comes from the transient bursts produced during close hyperbolic encounters, for which we also provide the expected rate and typical shape. Besides transient events, PBH binaries and hyperbolic encounters should also have produced a stochastic GW background covering the full frequency range accessible with observations of pulsar timing arrays, LISA and ground-based interferometers. The general formalism to compute this background has been reviewed and particular examples based on broad PBH mass functions including thermal effects have been given and discussed. At second order in perturbation theory, one gets another source of gravitational-waves associated with PBHs, coming from the large density fluctuations that are at the origin of their formation or, for lighter PBHs which have already evaporated today, that are produced by their Poisson distribution. We have reviewed the most recent prescriptions to calculate these SGWBs for any PBH model, and discussed their observability.

The future LISA space-based interferometer will probe PBHs in several ways. First, by searching for intermediate-mass PBH mergers. Based on the expected noise power spectral density, we estimated the number and distribution of PBH merger events in some models. LISA will also be able to detect mergers with very low mass ratios, for instance between an intermediate-mass PBH and a solar-mass PBH produced at the QCD transition. Also, it will probe the SGWB from PBH binaries, which could be strongly boosted for wide PBH mass functions, compared to a peaked PBH mass function. Therefore, LISA will be very useful to disentangle the different possible PBH mass functions and formation scenarios. Searching for high-redshift mergers is another way to distinguish astrophysical and primordial origins of black holes and test the hypothesis that supermassive black hole seeds are primordial. Finally, the broad gravitational-wave frequency range covered by LISA will allow to probe the stochastic GW background induced by scalar perturbations, corresponding to PBH scales ranging from $10^{-15} M_{\odot}$ to $10^{-8} M_{\odot}$, therefore covering the interesting asteroid-mass range where there is no significant limit on the PBH abundance. By probing a scalar-induced background from Poisson fluctuations in even lighter, evaporating PBHs, that would have totally disappeared from the Universe today due to Hawking evaporation. This would be another unique way to probe physics at much higher scales than can be done with particle accelerators.

Our work will soon be accompanied by a numerical code to compute all these gravitational-wave observations, for a wide variety of models. This code is currently under development and testing, but some of our key figures were already produced using it. This is a first promising perspective of this work. Then, our review also sheds light on the physical processes that are still subject of large uncertainties, like the role of PBH accretion and clustering, or the PBH binary disruption. We also discuss the fact that all signatures are highly model dependent.

One important conclusion of our analysis of the recent literature on PBHs is that strong claims, in one or another direction, are certainly premature and generally rely
on hypotheses that are very hard to test. Thus, there is still a huge amount of work to be done before making precise predictions. We therefore encourage others to pursue this direction and hope that our work will provide motivation and tools for researchers from other fields to join the growing PBH community.

**Acknowledgements** E.B. and S.C. acknowledge support from the Belgian Francqui Foundation through a start-up grant and to the Belgian Fund for Research FNRS-F.R.S. through the *Mandat d'impulsion scientifique* MIS/VA - F.4509.22 and an IISN grant. V.DL. is supported by funds provided by the Center for Particle Cosmology at the University of Pennsylvania. JME is supported by the European Union's Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 847523 INTERACTIONS, and by VILLUM FONDEN (grant no. 53101 and 37766). The work of G.F. partly received financial support provided under the European Union's H2020 ERC, Starting Grant agreement no. DarkGRA-757480 and under the MIUR PRIN programme, and support from the Amaldi Research Center funded by the MIUR program "Dipartimento di Eccellenza" (CUP: B81118001170001). J.G.B., E. R.M., and S.K.DeAr acknowledge support from the Spanish Research Project PID2021-123012NB-C43 [MICIN-FEDER], and the Centro de Excelencia Severo Ochoa Program CEX2020-001007-S at IFT, funded by MCIN/AEI/10.13039/501100011033. C.J. is supported in part by the National Key Research and Development Program of China Grant No. 2021YFC2203004, and by the FNRS-FRIA Grant No. 1. E.070.19F and the FNRS *Fonds de la Recherche Scientifique* Grant No. T.0198.19. R.K.J. acknowledges financial support from the new faculty seed start-up grant of IISc, the Core Research Grant CRG/2018/002200 from the Science and Engineering Research Board, Department of Science and Technology, Government of India and the Infosys Foundation, Bangalore through the Infosys Young Investigator award. S.K. is supported by the Spanish Atracción de Talento contract no. 2019-T1/TIC-13177 granted by Comunidad de Madrid, the I+D grant PID2020-118159GA-C42 funded by MCIN/AEI/10.13039/501100011033, the Consolidación Investigadora 2022 grant CNS2022-135211 and the i-LINK 2021 grant LINKA20416 of CSIC, and Japan Society for the Promotion of Science (JSPS) KAKENHI Grant no. 20H01899, 20H05853, and 23H00110. I.M. has received funding from the European Union's Horizon2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 754496. TP acknowledges financial support from the *Foundation for Education and European Culture in Greece* as well as from the *Fondation CFM pour la Recherche in France* and from the *Alexander S. Onassis Public Benefit Foundation* through the scholarship FZO 059-1/2018-2019. A.Ra. acknowledges funding from the Italian Ministry of University and Research (MUR) through the "Dipartimenti di eccellenza" project "Science of the Universe". A.R. is supported by the Boninchi Foundation. S.RP. is supported by the European Research Council under the European Union's Horizon 2020 research and innovation programme (Starting Grant agreement No 758792, project GEODESII). C.U. is supported by Ben Gurion University Kreitman Fellowship and the Israel Academy of Sciences and Humanities (IASH) & Council for Higher Education (CHE) Excellence Fellowship Program for International Postdoctoral Researchers, also European Structural and Investment Funds and the Czech Ministry of Education, Youth and Sports (Project CoGraDS - CZ.02.1.01/0.0/0.0/15 003/0000437). D.W. is supported by UK STFC grants ST/S000550/1 and ST/W001225/1. E.B. is supported by the FNRS-IISN (under grant number 4.4501.19).

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## References

Aad G et al (2019) Measurement of the top-quark mass in $t\bar{t}$ + 1-jet events collected with the ATLAS detector in $pp$ collisions at $\sqrt{s} = 8$ TeV. JHEP 11:150. https://doi.org/10.1007/JHEP11(2019)150. arXiv:1905.02302 [hep-ex]

Abbott B et al (2016) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116(6):061102. https://doi.org/10.1103/PhysRevLett.116.061102. arXiv:1602.03837 [gr-qc]

Abbott BP et al (2018b) Search for subsolar-mass ultracompact binaries in advanced LIGO's first observing run. Phys Rev Lett 121(23):231103. https://doi.org/10.1103/PhysRevLett.121.231103. arXiv:1808.04771 [astro-ph.CO]

Abbott B et al (2019a) Search for the isotropic stochastic background using data from Advanced LIGO's second observing run. Phys Rev D 100(6):061101. https://doi.org/10.1103/PhysRevD.100.061101. arXiv:1903.02886 [gr-qc]

Abbott BP et al (2019) GWTC-1: a gravitational-wave transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs. Phys Rev X 9(3):031040. https://doi.org/10.1103/PhysRevX.9.031040. arXiv:1811.12907 [astro-ph.HE]

Abbott BP et al (2019c) Search for subsolar mass ultracompact binaries in advanced LIGO's second observing run. Phys Rev Lett 123(16):161102. https://doi.org/10.1103/PhysRevLett.123.161102. arXiv:1904.08976 [astro-ph.CO]

Abbott R et al (2021a) GWTC-2: compact binary coalescences observed by LIGO and Virgo during the first half of the third observing run. Phys Rev X 11:021053. https://doi.org/10.1103/PhysRevX.11.021053. arXiv:2010.14527 [gr-qc]

Abbott R et al (2021b) Upper limits on the isotropic gravitational-wave background from Advanced LIGO and Advanced Virgo's third observing run. Phys Rev D 104(2):022004. https://doi.org/10.1103/PhysRevD.104.022004. arXiv:2101.12130 [gr-qc]

Abbott R et al (2022) Search for subsolar-mass binaries in the first half of advanced LIGO's and advanced Virgo's third observing run. Phys Rev Lett 129(6):061104. https://doi.org/10.1103/PhysRevLett.129.061104. arXiv:2109.12197 [astro-ph.CO]

Abbott R et al (2023a) GWTC-3: compact binary coalescences observed by LIGO and Virgo during the second part of the third observing run. Phys Rev X 13(4):041039. https://doi.org/10.1103/PhysRevX.13.041039. arXiv:2111.03606 [gr-qc]

Abbott R et al (2023b) Population of merging compact binaries inferred using gravitational waves through GWTC-3. Phys Rev X 13(1):011048. https://doi.org/10.1103/PhysRevX.13.011048. arXiv:2111.03634 [astro-ph.HE]

Abbott R et al (2023c) Search for subsolar-mass black hole binaries in the second part of Advanced LIGO's and Advanced Virgo's third observing run. Mon Not R Astron Soc 524(4):5984-5992. https://doi.org/10.1093/mnras/stad588. [Erratum: Mon. Not. R. Astron. Soc. 526, 6234 (2023)] arXiv:2212.01477 [astro-ph.HE]

Abdo A et al (2015) Milagro limits and HAWC sensitivity for the rate-density of evaporating primordial black holes. Astropart Phys 64:4-12. https://doi.org/10.1016/j.astropartphys.2014.10.007. arXiv:1407.1686 [astro-ph.HE]

Abe KT, Tada Y (2023) Translating nano-Hertz gravitational wave background into primordial perturbations taking account of the cosmological QCD phase transition. Phys Rev D 108(10): L101304. https://doi.org/10.1103/PhysRevD.108.L101304. arXiv:2307.01653 [astro-ph.CO]

Abe K, et al (2018) HyperKamiokande design report. arXiv e-prints arXiv:1805.04163 [physics.ins-det]

Acciarri R, et al (2016) Long-baseline neutrino facility (LBNF) and deep underground neutrino experiment (DUNE): conceptual design report, Volume 1: The LBNF and DUNE Projects. arXiv e-prints arXiv:1601.05471 [physics.ins-det]

Acharya SK, Khatri R (2020) CMB and BBN constraints on evaporating primordial black holes revisited. JCAP 06:018. https://doi.org/10.1088/1475-7516/2020/06/018. arXiv:2002.00898 [astro-ph.CO]

Ackermann M et al (2018) Search for gamma-ray emission from local primordial black holes with the Fermi Large Area Telescope. Astrophys J 857(1):49. https://doi.org/10.3847/1538-4357/aaac7b. arXiv:1802.00100 [astro-ph.HE]

Acquaviva V, Bartolo N, Matarrese S et al (2003) Second order cosmological perturbations from inflation. Nucl Phys B 667:119-148. https://doi.org/10.1016/S0550-3213(03)00550-9. arXiv:astro-ph/0209156
Adamek J, Byrnes CT, Gosenca M et al (2019) WIMPs and stellar-mass primordial black holes are incompatible. Phys Rev D 100(2):023506. https://doi.org/10.1103/PhysRevD.100.023506. arXiv: 1901.08528 [astro-ph.CO]

Adams FC, Bond J, Freese K et al (1993) Natural inflation: particle physics models, power law spectra for large scale structure, and constraints from COBE. Phys Rev D 47:426-455. https://doi.org/10.1103/PhysRevD.47.426. arXiv:hep-ph/9207245

Adshead P, Lozanov KD, Weiner ZJ (2021) Non-Gaussianity and the induced gravitational wave background. JCAP 10:080. https://doi.org/10.1088/1475-7516/2021/10/080. arXiv:2105.01659 [astro-ph.CO]

Afzal A et al (2023) The NANOGrav 15 yr data set: search for signals from new physics. Astrophys J Lett 951(1):L11. https://doi.org/10.3847/2041-8213/acdc91. arXiv:2306.16219 [astro-ph.HE]

Agazie G et al (2023a) The NANOGrav 15 yr data set: constraints on supermassive black hole binaries from the gravitational-wave background. Astrophys J Lett 952(2):L37. https://doi.org/10.3847/2041-8213/ace18b. arXiv:2306.16220 [astro-ph.HE]

Agazie G et al (2023b) The NANOGrav 15 yr data set: evidence for a gravitational-wave background. Astrophys J Lett 951(1):L8. https://doi.org/10.3847/2041-8213/acdac6. arXiv:2306.16213 [astro-ph.HE]

Agazie G et al (2023c) The NANOGrav 15 yr data set: observations and timing of 68 millisecond pulsars. Astrophys J Lett 951(1):L9. https://doi.org/10.3847/2041-8213/acda9a. arXiv:2306.16217 [astro-ph.HE]

Aggarwal N et al (2021) Challenges and opportunities of gravitational-wave searches at MHz to GHz frequencies. Living Rev Relativ 24:4. https://doi.org/10.1007/s41114-021-00032-5. arXiv:2011. 12414 [gr-qc]

Aghamousa A, et al (2016a) The DESI experiment part i: science, targeting, and survey design. arXiv e-prints arXiv:1611.00036 [astro-ph.IM]

Aghamousa A, et al (2016b) The DESI experiment part II: instrument design. arXiv e-prints arXiv:1611. 00037 [astro-ph.IM]

Aghanim N et al (2020) Planck 2018 results. VI. Cosmological parameters. Astron Astrophys 641:A6. https://doi.org/10.1051/0004-6361/201833910. [Erratum: Astron. Astrophys. 652, C4 (2021)] arXiv: 1807.06209 [astro-ph.CO]

Agius D, Essig R, Gaggero D et al (2024) Feedback in the dark: a critical examination of CMB bounds on primordial black holes. JCAP 07:003. https://doi.org/10.1088/1475-7516/2024/07/003. arXiv:2403. 18895 [hep-ph]

Aharonian F et al (2023) Search for the evaporation of primordial black holes with H.E.S.S. JCAP 04:040. https://doi.org/10.1088/1475-7516/2023/04/040. arXiv:2303.12855 [astro-ph.HE]

Ahmed W, Junaid M, Zubair U (2022) Primordial black holes and gravitational waves in hybrid inflation with chaotic potentials. Nucl Phys B 984:115968. https://doi.org/10.1016/j.nuclphysb.2022.115968. arXiv:2109.14838 [astro-ph.CO]

Ajith P et al (2011) Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins. Phys Rev Lett 106:241101. https://doi.org/10.1103/PhysRevLett.106.241101. arXiv:0909.2867 [gr-qc]

Akrami Y et al (2020a) Planck 2018 results. IX. Constraints on primordial non-Gaussianity. Astron Astrophys 641:A9. https://doi.org/10.1051/0004-6361/201935891. arXiv:1905.05697 [astro-ph.CO]

Akrami Y et al (2020b) Planck 2018 results. X. Constraints on inflation. Astron Astrophys 641:A10. https://doi.org/10.1051/0004-6361/201833887. arXiv:1807.06211 [astro-ph.CO]

Alba V, Maldacena J (2016) Primordial gravity wave background anisotropies. JHEP 03:115. https://doi. org/10.1007/JHEP03(2016)115. arXiv:1512.01531 [hep-th]

Albert A et al (2020) Constraining the local burst rate density of primordial black holes with HAWC. JCAP 04:026. https://doi.org/10.1088/1475-7516/2020/04/026. arXiv:1911.04356 [astro-ph.HE]

Alcock C et al (1997) The MACHO project LMC microlensing results from the first two years and the nature of the galactic dark halo. Astrophys J 486:697-726. https://doi.org/10.1086/304535. arXiv: astro-ph/9606165

Alcock C et al (2001) The MACHO project: microlensing detection efficiency. Astrophys J Suppl 136:439-462. https://doi.org/10.1086/322529. arXiv:astro-ph/0003392

Alexandre A, Dvali G, Koutsangelas E (2024) New mass window for primordial black holes as dark matter from the memory burden effect. Phys Rev D 110(3):036004. https://doi.org/10.1103/PhysRevD.110. 036004. arXiv:2402.14069 [hep-ph]
Ali-Haïmoud Y (2018) Correlation function of high-threshold regions and application to the initial small-scale clustering of primordial black holes. Phys Rev Lett 121(8):081304. https://doi.org/10.1103/PhysRevLett.121.081304. arXiv:1805.05912 [astro-ph.CO]

Ali-Haïmoud Y, Kamionkowski M (2017) Cosmic microwave background limits on accreting primordial black holes. Phys Rev D 95(4):043534. https://doi.org/10.1103/PhysRevD.95.043534. arXiv:1612.05644 [astro-ph.CO]

Ali-Haïmoud Y, Kovetz ED, Kamionkowski M (2017) Merger rate of primordial black-hole binaries. Phys Rev D 96(12):123523. https://doi.org/10.1103/PhysRevD.96.123523. arXiv:1709.06576 [astro-ph.CO]

Allahverdi R, Enqvist K, García-Bellido J et al (2006) Gauge invariant MSSM inflaton. Phys Rev Lett 97:191304. https://doi.org/10.1103/PhysRevLett.97.191304. arXiv:hep-ph/0605035

Allahverdi R, Enqvist K, García-Bellido J et al (2007) MSSM flat direction inflation: slow roll, stability, fine tuning and reheating. JCAP 06:019. https://doi.org/10.1088/1475-7516/2007/06/019. arXiv:hep-ph/0610134

Allsman R et al (2001) MACHO project limits on black hole dark matter in the 1-30 solar mass range. Astrophys J Lett 550:L169. https://doi.org/10.1086/319636. arXiv:astro-ph/0011506

Alonso D, Cusin G, Ferreira PG et al (2020) Detecting the anisotropic astrophysical gravitational wave background in the presence of shot noise through cross-correlations. Phys Rev D 102(2):023002. https://doi.org/10.1103/PhysRevD.102.023002. arXiv:2002.02888 [astro-ph.CO]

Amaro-Seoane P et al (2023) Astrophysics with the Laser Interferometer Space Antenna. Living Rev Relativ 26:2. https://doi.org/10.1007/s41114-022-00041-y. arXiv:2203.06016 [gr-qc]

Amaro-Seoane P, et al (2017) Laser Interferometer Space Antenna. arXiv e-prints arXiv:1702.00786 [astro-ph.IM]

Ambartsumian VA (1937) On the statistics of double stars. AZh 14:207–219

Amendola L et al (2018) Cosmology and fundamental physics with the Euclid satellite. Living Rev Relativ 21:2. https://doi.org/10.1007/s41114-017-0010-3. arXiv:1606.00180 [astro-ph.CO]

An F et al (2016) Neutrino physics with JUNO. J Phys G 43(3):030401. https://doi.org/10.1088/0954-3899/43/3/030401. arXiv:1507.05613 [physics.ins-det]

An H, Yang C (2024) Gravitational waves produced by domain walls during inflation. Phys Rev D 109 (12):123508. https://doi.org/10.1103/PhysRevD.109.123508. arXiv:2304.02361 [hep-ph]

Ananda KN, Clarkson C, Wands D (2007) The Cosmological gravitational wave background from primordial density perturbations. Phys Rev D 75:123518. https://doi.org/10.1103/PhysRevD.75.123518. arXiv:gr-qc/0612013

Anber MM, Sorbo L (2010) Naturally inflating on steep potentials through electromagnetic dissipation. Phys Rev D 81:043534. https://doi.org/10.1103/PhysRevD.81.043534. arXiv:0908.4089 [hep-th]

Anchordoqui LA, Antoniadis I, Lust D (2022) Dark dimension, the swampland, and the dark matter fraction composed of primordial black holes. Phys Rev D 106(8):086001. https://doi.org/10.1103/PhysRevD.106.086001. arXiv:2206.07071 [hep-th]

Anchordoqui LA, Antoniadis I, Lust D (2023) The dark universe: primordial black hole ⇌ dark graviton gas connection. Phys Lett B 840:137844. https://doi.org/10.1016/j.physletb.2023.137844. arXiv:2210.02475 [hep-th]

Ando S, Hiroshima N, Ishiwata K (2022) Constraining the primordial curvature perturbation using dark matter substructure. Phys Rev D 106(10):103014. https://doi.org/10.1103/PhysRevD.106.103014. arXiv:2207.05747 [astro-ph.CO]

Ando K, Inomata K, Kawasaki M et al (2018) Primordial black holes for the LIGO events in the axionlike curvaton model. Phys Rev D 97(12):123512. https://doi.org/10.1103/PhysRevD.97.123512. arXiv:1711.08956 [astro-ph.CO]

Ando K, Vennin V (2021) Power spectrum in stochastic inflation. JCAP 04:057. https://doi.org/10.1088/1475-7516/2021/04/057. arXiv:2012.02031 [astro-ph.CO]

Antoniadis J et al (2022) The international pulsar timing array second data release: search for an isotropic gravitational wave background. Mon Not R Astron Soc 510(4):4873–4887. https://doi.org/10.1093/mnras/stab3418. arXiv:2201.03980 [astro-ph.HE]

Antoniadis J et al (2023a) The second data release from the European Pulsar Timing Array - I. The dataset and timing analysis. Astron Astrophys 678:A48. https://doi.org/10.1051/0004-6361/202346841. arXiv:2306.16224 [astro-ph.HE]

Antoniadis J et al (2023b) The second data release from the European Pulsar Timing Array - III. Search for gravitational wave signals. Astron Astrophys 678:A50. https://doi.org/10.1051/0004-6361/202346844. arXiv:2306.16214 [astro-ph.HE]
Antoniadis J et al (2024) The second data release from the European Pulsar Timing Array - IV. Implications for massive black holes, dark matter, and the early Universe. Astron Astrophys 685:A94. https://doi.org/10.1051/0004-6361/202347433. arXiv:2306.16227 [astro-ph.CO]

Araya IJ, Rubio ME, San Martin M et al (2021) Magnetic field generation from PBH distributions. Mon Not R Astron Soc 503(3):4387-4399. https://doi.org/10.1093/mnras/stab729. arXiv:2012.09585 [astro-ph.CO]

Arbey A, Auffinger J (2019) BlackHawk: a public code for calculating the Hawking evaporation spectra of any black hole distribution. Eur Phys J C 79(8):693. https://doi.org/10.1140/epjc/s10052-019-7161-1. arXiv:1905.04268 [gr-qc]

Arbey A, Auffinger J, Silk J (2020) Constraining primordial black hole masses with the isotropic gamma ray background. Phys Rev D 101(2):023010. https://doi.org/10.1103/PhysRevD.101.023010. arXiv: 1906.04750 [astro-ph.CO]

Arbey A, Auffinger J (2020) Detecting Planet 9 via Hawking radiation. arXiv e-prints arXiv:2006.02944 [gr-qc]

Archambault S (2018) Search for Primordial Black Hole Evaporation with VERITAS. PoS ICRC2017:691. https://doi.org/10.22323/1.301.0691, arXiv:1709.00307 [astro-ph.HE]

Arun KG et al (2022) New horizons for fundamental physics with LISA. Living Rev Relativ 25:4. https:// doi.org/10.1007/s41114-022-00036-9. arXiv:2205.01597 [gr-qc]

Arya R, Jain RK, Mishra AK (2024) Primordial black holes dark matter and secondary gravitational waves from warm Higgs-G inflation. JCAP 02:034. https://doi.org/10.1088/1475-7516/2024/02/034. arXiv: 2302.08940 [astro-ph.CO]

Arzoumanian Z et al (2020) The NANOGrav 12.5 yr data set: search for an isotropic stochastic gravitational-wave background. Astrophys J Lett 905(2):L34. https://doi.org/10.3847/2041-8213/ abd401. arXiv:2009.04496 [astro-ph.HE]

Arzoumanian Z et al (2021) Searching for gravitational waves from cosmological phase transitions with the NANOGrav 12.5-year dataset. Phys Rev Lett 127(25):251302. https://doi.org/10.1103/PhysRevLett. 127.251302. arXiv:2104.13930 [astro-ph.CO]

Asencio E, Banik I, Kroupa P (2020) A massive blow for $\Lambda$CDM – the high redshift, mass, and collision velocity of the interacting galaxy cluster El Gordo contradicts concordance cosmology. Mon Not R Astron Soc 500(4):5249–5267. https://doi.org/10.1093/mnras/staa3441. arXiv:2012.03950 [astro-ph.CO]

Ashoorioon A, Rezazadeh K, Rostami A (2022) NANOGrav signal from the end of inflation and the LIGO mass and heavier primordial black holes. Phys Lett B 835:137542. https://doi.org/10.1016/j.physletb. 2022.137542. arXiv:2202.01131 [astro-ph.CO]

Askins M et al (2020) THEIA: an advanced optical neutrino detector. Eur Phys J C 80(5):416. https://doi. org/10.1140/epjc/s10052-020-7977-8. arXiv:1911.03501 [physics.ins-det]

Atal V, Domènech G (2021) Probing non-Gaussianities with the high frequency tail of induced gravitational waves. JCAP 06:001. https://doi.org/10.1088/1475-7516/2021/06/001. arXiv:2103. 01056 [astro-ph.CO]

Atal V, Garriga J, Marcos-Caballero A (2019) Primordial black hole formation with non-Gaussian curvature perturbations. JCAP 09:073. https://doi.org/10.1088/1475-7516/2019/09/073. arXiv:1905. 13202 [astro-ph.CO]

Atal V, Sanglas A, Triantafyllou N (2020) LIGO/Virgo black holes and dark matter: the effect of spatial clustering. JCAP 11:036. https://doi.org/10.1088/1475-7516/2020/11/036. arXiv:2007.07212 [astro-ph.CO]

Atek H, Shuntov M, Furtak LJ et al (2022) Revealing galaxy candidates out to $z \sim 16$ with jwst observations of the lensing cluster smacs0723. Mon Not R Astron Soc 519(1):1201–1220. https://doi. org/10.1093/mnras/stac3144. arXiv:2207.12338 [astro-ph.GA]

Aubourg E et al (1993) Evidence for gravitational microlensing by dark objects in the galactic halo. Nature 365:623–625. https://doi.org/10.1038/365623a0

Auclair P et al (2023) Cosmology with the Laser Interferometer Space Antenna. Living Rev Relativ 26:5. https://doi.org/10.1007/s41114-023-00045-2. arXiv:2204.05434 [astro-ph.CO]

Auclair P, Vennin V (2021) Primordial black holes from metric preheating: mass fraction in the excursion-set approach. JCAP 02:038. https://doi.org/10.1088/1475-7516/2021/02/038. arXiv:2011.05633 [astro-ph.CO]

Auffinger J (2022) Limits on primordial black holes detectability with Isatis: a BlackHawk tool. Eur Phys J C 82(4):384. https://doi.org/10.1140/epjc/s10052-022-10199-y. arXiv:2201.01265 [astro-ph.HE]
Babichev E, Gorbunov D, Ramazanov S et al (2022) Gravitational shine of dark domain walls. JCAP 04 (04):028. https://doi.org/10.1088/1475-7516/2022/04/028. arXiv:2112.12608 [hep-ph]

Babichev E, Gorbunov D, Ramazanov S et al (2023) NANOGrav spectral index $\gamma=3$ from melting domain walls. Phys Rev D 108(12):123529. https://doi.org/10.1103/PhysRevD.108.123529. arXiv:2307.04582 [hep-ph]

Bagui E, Clesse S (2022) A boosted gravitational wave background for primordial black holes with broad mass distributions and thermal features. Phys Dark Univ 38:101115. https://doi.org/10.1016/j.dark.2022.101115. arXiv:2110.07487 [astro-ph.CO]

Baibhav V et al (2021) Probing the nature of black holes: deep in the mHz gravitational-wave sky. Exper Astron 51(3):1385-1416. https://doi.org/10.1007/s10686-021-09741-9. arXiv:1908.11390 [astro-ph.HE]

Baker J et al (2021a) High angular resolution gravitational wave astronomy. Exper Astron 51(3):1441-1470. https://doi.org/10.1007/s10686-021-09712-0. arXiv:1908.11410 [astro-ph.HE]

Baker MJ, Breitbach M, Kopp J, et al (2021b) Detailed calculation of primordial black hole formation during first-order cosmological phase transitions. arXiv e-prints arXiv:2110.00005 [astro-ph.CO]

Baker MJ, Breitbach M, Kopp J, et al (2021c) Primordial black holes from first-order cosmological phase transitions. arXiv e-prints arXiv:2105.07481 [astro-ph.CO]

Balaji S, Domènech G, Franciolini G (2023) Scalar-induced gravitational wave interpretation of PTA data: the role of scalar fluctuation propagation speed. JCAP 10:041. https://doi.org/10.1088/1475-7516/2023/10/041. arXiv:2307.08552 [gr-qc]

Baldes I, Dichtl M, Gouttenoire Y, et al (2023) Bubbletrons. arXiv e-prints arXiv:2306.15555 [hep-ph]

Ballesteros G, Coronado-Blázquez J, Gaggero D (2020a) X-ray and gamma-ray limits on the primordial black hole abundance from Hawking radiation. Phys Lett B 808:135624. https://doi.org/10.1016/j.physletb.2020.135624. arXiv:1906.10113 [astro-ph.CO]

Ballesteros G, Rey J, Rompinéve F (2020b) Detuning primordial black hole dark matter with early matter domination and axion monodromy. JCAP 06:014. https://doi.org/10.1088/1475-7516/2020/06/014. arXiv:1912.01638 [astro-ph.CO]

Ballesteros G, Rey J, Taoso M et al (2020c) Primordial black holes as dark matter and gravitational waves from single-field polynomial inflation. JCAP 07:025. https://doi.org/10.1088/1475-7516/2020/07/025. arXiv:2001.08220 [astro-ph.CO]

Ballesteros G, Serpico PD, Taoso M (2018) On the merger rate of primordial black holes: effects of nearest neighbours distribution and clustering. JCAP 10:043. https://doi.org/10.1088/1475-7516/2018/10/043. arXiv:1807.02084 [astro-ph.CO]

Ballesteros G, Taoso M (2018) Primordial black hole dark matter from single field inflation. Phys Rev D 97 (2):023501. https://doi.org/10.1103/PhysRevD.97.023501. arXiv:1709.05565 [hep-ph]

Banados E et al (2018) An 800-million-solar-mass black hole in a significantly neutral Universe at redshift 7.5. Nature 553(7689):473-476. https://doi.org/10.1038/nature25180. arXiv:1712.01860 [astro-ph.GA]

Banerjee S, Papanikolaou T, Saridakis EN (2022) Constraining F(R) bouncing cosmologies through primordial black holes. Phys Rev D 106(12):124012. https://doi.org/10.1103/PhysRevD.106.124012. arXiv:2206.01150 [gr-qc]

Bardeen JM, Bond J, Kaiser N et al (1986) The statistics of peaks of gaussian random fields. Astrophys J 304:15-61. https://doi.org/10.1086/164143

Bardeen JM, Press WH, Teukolsky SA (1972) Rotating black holes: locally nonrotating frames, energy extraction, and scalar synchrotron radiation. Astrophys J 178:347. https://doi.org/10.1086/151796

Barír J, Geller M, Sun C et al (2023) Gravitational waves from incomplete inflationary phase transitions. Phys Rev D 108(11):115016. https://doi.org/10.1103/PhysRevD.108.115016. arXiv:2203.00693 [hep-ph]

Barman B, Borah D, Jyoti Das S et al (2023) Scale of Dirac leptogenesis and left-right symmetry in the light of recent PTA results. JCAP 10:053. https://doi.org/10.1088/1475-7516/2023/10/053. arXiv:2307.00656 [hep-ph]

Barnaby N, Namba R, Peloso M (2011) Phenomenology of a Pseudo-scalar inflaton: naturally large nongaussianity. JCAP 04:009. https://doi.org/10.1088/1475-7516/2011/04/009. arXiv:1102.4333 [astro-ph.CO]

Barnacka A, Glicenstein JF, Moderski R (2012) New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts. Phys Rev D 86:043001. https://doi.org/10.1103/PhysRevD.86.043001. arXiv:1204.2056 [astro-ph.CO]
Barrow JD, Carr BJ (1996) Formation and evaporation of primordial black holes in scalar - tensor gravity theories. Phys Rev D 54:3920-3931. https://doi.org/10.1103/PhysRevD.54.3920

Barsanti S, De Luca V, Maselli A et al (2022) Detecting subsolar-mass primordial black holes in extreme mass-ratio inspirals with LISA and einstein telescope. Phys Rev Lett 128(11):111104. https://doi.org/10.1103/PhysRevLett.128.111104. arXiv:2109.02170 [gr-qc]

Bartolo N et al (2016) Science with the space-based interferometer LISA. IV: probing inflation with gravitational waves. JCAP 12:026. https://doi.org/10.1088/1475-7516/2016/12/026. arXiv:1610.06481 [astro-ph.CO]

Bartolo N et al (2022) Probing anisotropies of the stochastic gravitational wave background with LISA. JCAP 11:009. https://doi.org/10.1088/1475-7516/2022/11/009. arXiv:2201.08782 [astro-ph.CO]

Bartolo N, Bertacca D, De Luca V et al (2020a) Gravitational wave anisotropies from primordial black holes. JCAP 02:028. https://doi.org/10.1088/1475-7516/2020/02/028. arXiv:1909.12619 [astro-ph.CO]

Bartolo N, Bertacca D, Matarrese S et al (2019a) Anisotropies and non-gaussianity of the cosmological gravitational wave background. Phys Rev D 100(12):121501. https://doi.org/10.1103/PhysRevD.100.121501. arXiv:1908.00527 [astro-ph.CO]

Bartolo N, Bertacca D, Matarrese S et al (2020b) Characterizing the cosmological gravitational wave background: anisotropies and non-gaussianity. Phys Rev D 102(2):023527. https://doi.org/10.1103/PhysRevD.102.023527. arXiv:1912.09433 [astro-ph.CO]

Bartolo N, Domcke V, Figueroa DG et al (2018) Probing non-gaussian stochastic gravitational wave backgrounds with LISA. JCAP 11:034. https://doi.org/10.1088/1475-7516/2018/11/034. arXiv:1806.02819 [astro-ph.CO]

Bartolo N, De Luca V, Franciolini G et al (2019b) Primordial black hole dark matter: LISA serendipity. Phys Rev Lett 122(21):211301. https://doi.org/10.1103/PhysRevLett.122.211301. arXiv:1810.12218 [astro-ph.CO]

Bartolo N, De Luca V, Franciolini G et al (2019c) Testing primordial black holes as dark matter with LISA. Phys Rev D 99(10):103521. https://doi.org/10.1103/PhysRevD.99.103521. arXiv:1810.12224 [astro-ph.CO]

Basilakos S, Nanopoulos DV, Papanikolaou T et al (2024a) Gravitational wave signatures of no-scale supergravity in NANOGrav and beyond. Phys Lett B 850:138507. https://doi.org/10.1016/j.physletb.2024.138507. arXiv:2307.08601 [hep-th]

Basilakos S, Nanopoulos DV, Papanikolaou T et al (2024b) Induced gravitational waves from flipped SU(5) superstring theory at nHz. Phys Lett B 849:138446. https://doi.org/10.1016/j.physletb.2024.138446. arXiv:2309.15820 [astro-ph.CO]

Bassett BA, Kaiser DI, Maartens R (1999a) General relativistic preheating after inflation. Phys Lett B 455:84-89. https://doi.org/10.1016/S0370-2693(99)00478-5. arXiv:hep-ph/9808404

Bassett BA, Tamburini F, Kaiser DI et al (1999b) Metric preheating and limitations of linearized gravity. 2. Nucl Phys B 561:188-240. https://doi.org/10.1016/S0550-3213(99)00495-2. arXiv:hep-ph/9901319

Bassett BA, Tsujikawa S (2001) Inflationary preheating and primordial black holes. Phys Rev D 63:123503. https://doi.org/10.1103/PhysRevD.63.123503. arXiv:hep-ph/0008328 [hep-ph]

Bassett BA, Viniegra F (2000) Massless metric preheating. Phys Rev D 62:043507. https://doi.org/10.1103/PhysRevD.62.043507. arXiv:hep-ph/9909353

Baum S, Fedderke MA, Graham PW (2022) Searching for dark clumps with gravitational-wave detectors. Phys Rev D 106(6):063015. https://doi.org/10.1103/PhysRevD.106.063015. arXiv:2206.14832 [astro-ph.CO]

Baumann D, Steinhardt PJ, Takahashi K et al (2007a) Gravitational wave spectrum induced by primordial scalar perturbations. Phys Rev D 76:084019. https://doi.org/10.1103/PhysRevD.76.084019. arXiv:hep-th/0703290

Baumann D, Steinhardt PJ, Turok N (2007b) Primordial Black Hole Baryogenesis. arXiv e-prints arXiv:hep-th/0703250

Bavera SS, Franciolini G, Cusin G et al (2022) Stochastic gravitational-wave background as a tool for investigating multi-channel astrophysical and primordial black-hole mergers. Astron Astrophys 660: A26. https://doi.org/10.1051/0004-6361/202142208. arXiv:2109.05836 [astro-ph.CO]

Belczynski K, Ryu T, Perna R et al (2017) On the likelihood of detecting gravitational waves from Population III compact object binaries. Mon Not R Astron Soc 471(4):4702-4721. https://doi.org/10.1093/mnras/stx1759. arXiv:1612.01524 [astro-ph.HE]
Bellomo N, Bernal JL, Scelfo G et al (2020) Beware of commonly used approximations. Part I. Errors in forecasts. JCAP 10:016. https://doi.org/10.1088/1475-7516/2020/10/016. arXiv:2005.10384 [astro-ph.CO]

Bellomo N, Bertacca D, Jenkins AC et al (2022) CLASS_GWB: robust modeling of the astrophysical gravitational wave background anisotropies. JCAP 06(06):030. https://doi.org/10.1088/1475-7516/2022/06/030. arXiv:2110.15059 [gr-qc]

Bellomo N, Bertacca D, Jenkins AC et al (2022) CLASS_GWB: robust modeling of the astrophysical gravitational wave background anisotropies. JCAP 6:030. https://doi.org/10.1088/1475-7516/2022/06/030. arXiv:2110.15059 [gr-qc]

Belotsky KM, Dmitriev AE, Esipova EA et al (2014) Signatures of primordial black hole dark matter. Modern Phys Lett A 29(37):1440005. https://doi.org/10.1142/S0217732314400057. arXiv:1410.0203 [astro-ph.CO]

Benetti M, Graef LL, Vagnozzi S (2022) Primordial gravitational waves from NANOGrav: a broken power-law approach. Phys Rev D 105(4):043520. https://doi.org/10.1103/PhysRevD.105.043520. arXiv:2111.04758 [astro-ph.CO]

Berezinsky V, Dokuchaev V, Eroshenko Y et al (2010) Superdense cosmological dark matter clumps. Physical Review D 81(10):103529. https://doi.org/10.1103/PhysRevD.81.103529. arXiv:1002.3444 [astro-ph.CO]

Berezinsky VS, Dokuchaev VI, Eroshenko YN (2013) Formation and internal structure of superdense dark matter clumps and ultracompact minihaloes. JCAP 11:059. https://doi.org/10.1088/1475-7516/2013/11/059. arXiv:1308.6742 [astro-ph.CO]

Berlin A, Blas D, Tito D'Agnolo R et al (2022a) Detecting high-frequency gravitational waves with microwave cavities. Phys Rev D 105(11):116011. https://doi.org/10.1103/PhysRevD.105.116011. arXiv:2112.11465 [hep-ph]

Berlin A, et al (2022b) Searches for new particles, dark matter, and gravitational waves with SRF cavities. arXiv e-prints arXiv:2203.12714 [hep-ph]

Bernal JL, Bellomo N, Raccanelli A et al (2020) Beware of commonly used approximations. Part II. Estimating systematic biases in the best-fit parameters. JCAP 10:017. https://doi.org/10.1088/1475-7516/2020/10/017. arXiv:2005.09666 [astro-ph.CO]

Bernal N, Muñoz Albornoz V, Palomares-Ruiz S et al (2022) Current and future neutrino limits on the abundance of primordial black holes. JCAP 10:068. https://doi.org/10.1088/1475-7516/2022/10/068. arXiv:2203.14979 [hep-ph]

Bernal JL, Raccanelli A, Verde L et al (2018) Signatures of primordial black holes as seeds of supermassive black holes. JCAP 05:017. https://doi.org/10.1088/1475-7516/2018/05/017. [Erratum: JCAP 01, E01 (2020)] arXiv:1712.01311 [astro-ph.CO]

Bertacca D, Ricciardone A, Bellomo N et al (2020) Projection effects on the observed angular spectrum of the astrophysical stochastic gravitational wave background. Phys Rev D 101(10):103513. https://doi.org/10.1103/PhysRevD.101.103513. arXiv:1909.11627 [astro-ph.CO]

Berteaud J, Calore F, Iguaz J et al (2022) Strong constraints on primordial black hole dark matter from 16 years of INTEGRAL/SPI observations. Phys Rev D 106(2):023030. https://doi.org/10.1103/PhysRevD.106.023030. arXiv:2202.07483 [astro-ph.HE]

Bertone G, Coogan AM, Gaggero D et al (2019) Primordial black holes as silver bullets for new physics at the weak scale. Phys Rev D 100(12):123013. https://doi.org/10.1103/PhysRevD.100.123013. arXiv:1905.01238 [hep-ph]

Bezrukov FL, Shaposhnikov M (2008) The standard model higgs boson as the inflaton. Phys Lett B 659:703-706. https://doi.org/10.1016/j.physletb.2007.11.072. arXiv:0710.3755 [hep-th]

Bhagwat S, De Luca V, Franciolini G et al (2021) The importance of priors on LIGO-Virgo parameter estimation: the case of primordial black holes. JCAP 01:037. https://doi.org/10.1088/1475-7516/2021/01/037. arXiv:2008.12320 [astro-ph.CO]

Bhattacharya T et al (2014) QCD phase transition with chiral quarks and physical quark masses. Phys Rev Lett 113(8):082001. https://doi.org/10.1103/PhysRevLett.113.082001. arXiv:1402.5175 [hep-lat]

Bhaumik N, Jain RK (2020) Primordial black holes dark matter from inflection point models of inflation and the effects of reheating. JCAP 01:037. https://doi.org/10.1088/1475-7516/2020/01/037. arXiv:1907.04125 [astro-ph.CO]

Bhaumik N, Jain RK (2021) Small scale induced gravitational waves from primordial black holes, a stringent lower mass bound, and the imprints of an early matter to radiation transition. Phys Rev D 104(2):023531. https://doi.org/10.1103/PhysRevD.104.023531. arXiv:2009.10424 [astro-ph.CO]
Biagetti M, Franciolini G, Kehagias A et al (2018) Primordial black holes from inflation and quantum diffusion. JCAP 07:032. https://doi.org/10.1088/1475-7516/2018/07/032. arXiv:1804.07124 [astro-ph.CO]

Biagetti M, Franciolini G, Riotto A (2023) High-redshift JWST observations and primordial non-gaussianity. Astrophys J 944(2):113. https://doi.org/10.3847/1538-4357/acb5ea. arXiv:2210.04812 [astro-ph.CO]

Biagetti M, De Luca V, Franciolini G et al (2021) The formation probability of primordial black holes. Phys Lett B 820:136602. https://doi.org/10.1016/j.physletb.2021.136602. arXiv:2105.07810 [astro-ph.CO]

Bicknell G, Henriksen RN (1979) Formation of primordial black holes. Astrophys J 232:670-682

Bird S et al (2023) Snowmass 2021 cosmic frontier white paper: primordial black hole dark matter. Phys Dark Univ 41:101231. https://doi.org/10.1016/j.dark.2023.101231. arXiv:2203.08967 [hep-ph]

Bird S, Cholis I, Muñoz JB et al (2016) Did LIGO detect dark matter? Phys Rev Lett 116(20):201301. https://doi.org/10.1103/PhysRevLett.116.201301. arXiv:1603.00464 [astro-ph.CO]

Bjorkmo T, Ferreira RZ, Marsh MCD (2019) Mild non-gaussianities under perturbative control from rapid-turn inflation models. JCAP 12:036. https://doi.org/10.1088/1475-7516/2019/12/036. arXiv:1908.11316 [hep-th]

Blanco-Pillado JJ, Olum KD, Wachter JM (2021b) Comparison of cosmic string and superstring models to NANOGrav 12.5-year results. Phys Rev D 103(10):103512. https://doi.org/10.1103/PhysRevD.103.103512. arXiv:2102.08194 [astro-ph.CO]

Blanco-Pillado JJ, Olum KD, Vilenkin A (2021a) No black holes from cosmic string cusps. arXiv e-prints arXiv:2101.05040 [astro-ph.CO]

Blasi S, Brdar V, Schmitz K (2021) Has NANOGrav found first evidence for cosmic strings? Phys Rev Lett 126(4):041305. https://doi.org/10.1103/PhysRevLett.126.041305. arXiv:2009.06607 [astro-ph.CO]

Blasi S, Mariotti A, Rase A et al (2023) Axionic domain walls at pulsar timing arrays: QCD bias and particle friction. JHEP 11:169. https://doi.org/10.1007/JHEP11(2023)169. arXiv:2306.17830 [hep-ph]

Blum B, et al (2022) Snowmass2021 cosmic frontier white paper: rubin observatory after LSST. In: 2022 Snowmass summer study, arXiv:2203.07220

Boehm C, Kobakhidze A, O'hare CAJ et al (2021) Eliminating the LIGO bounds on primordial black hole dark matter. JCAP 03:078. https://doi.org/10.1088/1475-7516/2021/03/078. arXiv:2008.10743 [astro-ph.CO]

Boldrini P, Miki Y, Wagner AY et al (2020) Cusp-to-core transition in low-mass dwarf galaxies induced by dynamical heating of cold dark matter by primordial black holes. Mon Not R Astron Soc 492 (4):5218-5225. https://doi.org/10.1093/mnras/staa150. arXiv:1909.07395 [astro-ph.CO]

Bondi H (1952) On spherically symmetrical accretion. Mon Not R Astron Soc 112:195. https://doi.org/10.1093/mnras/112.2.195

Bonvin C, Durrer R (2011) What galaxy surveys really measure. Phys Rev D 84:063505. https://doi.org/10.1103/PhysRevD.84.063505. arXiv:1105.5280 [astro-ph.CO]

Bosch-Ramon V, Bellomo N (2020) Mechanical feedback effects on primordial black hole accretion. Astron Astrophys 638:A132. https://doi.org/10.1051/0004-6361/202037537. arXiv:2004.11224 [astro-ph.CO]

Boscá V, Fleury P, García-Bellido J (2022) Accurate modelling of extragalactic microlensing by compact objects. JCAP 10:098. https://doi.org/10.1088/1475-7516/2022/10/098. arXiv:2205.00991 [astro-ph.CO]

Bosi M, Bellomo N, Raccanelli A (2023) Constraining extended cosmologies with GWxLSS cross-correlations. JCAP 11:086. https://doi.org/10.1088/1475-7516/2023/11/086. arXiv:2306.03031 [astro-ph.CO]

Boucenna SM, Kuhnel F, Ohlsson T et al (2018) Novel constraints on mixed dark-matter scenarios of primordial black holes and WIMPs. JCAP 07:003. https://doi.org/10.1088/1475-7516/2018/07/003. arXiv:1712.06383 [hep-ph]

Boudaud M, Cirelli M (2019) Voyager 1 $e^±$ further constrain primordial black holes as dark matter. Phys Rev Lett 122(4):041104. https://doi.org/10.1103/PhysRevLett.122.041104. arXiv:1807.03075 [astro-ph.HE]

Boudaud M, Lacroix T, Stref M et al (2021) In-depth analysis of the clustering of dark matter particles around primordial black holes. Part I. Density profiles. JCAP 08:053. https://doi.org/10.1088/1475-7516/2021/08/053. arXiv:2106.07480 [astro-ph.CO]
Bowman JD, Rogers AEE, Monsalve RA et al (2018) An absorption profile centred at 78 megahertz in the sky-averaged spectrum. Nature 555(7694):67–70. https://doi.org/10.1038/nature25792. arXiv:1810.05912 [astro-ph.CO]

Braglia M, Chen X, Hazra DK (2021a) Probing primordial features with the stochastic gravitational wave background. JCAP 03:005. https://doi.org/10.1088/1475-7516/2021/03/005. arXiv:2012.05821 [astro-ph.CO]

Braglia M, García-Bellido J, Kuroyanagi S (2021b) Testing primordial black holes with multi-band observations of the stochastic gravitational wave background. JCAP 12(12):012. https://doi.org/10.1088/1475-7516/2021/12/012. arXiv:2110.07488 [astro-ph.CO]

Braglia M, García-Bellido J, Kuroyanagi S (2023a) Tracking the origin of black holes with the stochastic gravitational wave background popcorn signal. Mon Not R Astron Soc 519(4):6008–6019. https://doi.org/10.1093/mnras/stad082. arXiv:2201.13414 [astro-ph.CO]

Braglia M, Hazra DK, Finelli F et al (2020) Generating PBHs and small-scale GWs in two-field models of inflation. JCAP 08:001. https://doi.org/10.1088/1475-7516/2020/08/001. arXiv:2005.02895 [astro-ph.CO]

Braglia M, Linde A, Kallosh R et al (2023b) Hybrid $\alpha$-attractors, primordial black holes and gravitational wave backgrounds. JCAP 04:033. https://doi.org/10.1088/1475-7516/2023/04/033. arXiv:2211.14262 [astro-ph.CO]

Brandt TD (2016) Constraints on MACHO dark matter from compact stellar systems in ultra-faint dwarf galaxies. Astrophys J Lett 824(2):L31. https://doi.org/10.3847/2041-8205/824/2/L31. arXiv:1605.03665 [astro-ph.GA]

Bringmann T (2009) Particle models and the small-scale structure of dark matter. New J Phys 11:105027. https://doi.org/10.1088/1367-2630/11/10/105027. arXiv:0903.0189 [astro-ph.CO]

Brito R, Cardoso V, Pani P (2015) Black holes as particle detectors: evolution of superradiant instabilities. Class Quant Grav 32(13):134001. https://doi.org/10.1088/0264-9381/32/13/134001. arXiv:1411.0686 [gr-qc]

Bromm V (2006) High-redshift gamma-ray bursts from population III progenitors. Astrophys J 642:382. https://doi.org/10.1086/500799. arXiv:astro-ph/0509303

Brown AR (2018) Hyperbolic inflation. Phys Rev Lett 121(25):251601. https://doi.org/10.1103/PhysRevLett.121.251601. arXiv:1705.03023 [hep-th]

Buchmüller W, Domcke V, Schmitz K (2020) From NANOGrav to LIGO with metastable cosmic strings. Phys Lett B 811:135914. https://doi.org/10.1016/j.physletb.2020.135914. arXiv:2009.10649 [astro-ph.CO]

Buchmüller W, Domcke V, Schmitz K (2021) Stochastic gravitational-wave background from metastable cosmic strings. JCAP 12(12):006. https://doi.org/10.1088/1475-7516/2021/12/006. arXiv:2107.04578 [hep-ph]

Bugaev E, Klimai P (2010) Induced gravitational wave background and primordial black holes. Phys Rev D 81:023517. https://doi.org/10.1103/PhysRevD.81.023517. arXiv:0908.0664 [astro-ph.CO]

Bugaev EV, Klimai PA (2013) Primordial black hole constraints for curvaton models with predicted large non-Gaussianity. Int J Mod Phys D 22:1350034. https://doi.org/10.1142/S021827181350034X. arXiv:1303.3146 [astro-ph.CO]

Bugaev E, Klimai P (2014) Axion inflation with gauge field production and primordial black holes. Phys Rev D 90(10):103501. https://doi.org/10.1103/PhysRevD.90.103501. arXiv:1312.7435 [astro-ph.CO]

Byrnes CT, Cole PS, Patil SP (2019) Steepest growth of the power spectrum and primordial black holes. JCAP 06:028. https://doi.org/10.1088/1475-7516/2019/06/028. arXiv:1811.11158 [astro-ph.CO]

Byrnes CT, Copeland EJ, Green AM (2012) Primordial black holes as a tool for constraining non-Gaussianity. Phys Rev D 86:043512. https://doi.org/10.1103/PhysRevD.86.043512. arXiv:1206.4188 [astro-ph.CO]

Byrnes CT, Hindmarsh M, Young S et al (2018) Primordial black holes with an accurate QCD equation of state. JCAP 08:041. https://doi.org/10.1088/1475-7516/2018/08/041. arXiv:1801.06138 [astro-ph.CO]

Bödeker D, Kühnel F, Oldengott IM et al (2021) Lepton flavor asymmetries and the mass spectrum of primordial black holes. Phys Rev D 103(6):063506. https://doi.org/10.1103/PhysRevD.103.063506. arXiv:2011.07283 [astro-ph.CO]

Cai YF, He XC, Ma XH et al (2023) Limits on scalar-induced gravitational waves from the stochastic background by pulsar timing array observations. Sci Bull 68:2929–2935. https://doi.org/10.1016/j.scib.2023.10.027. arXiv:2306.17822 [gr-qc]
Cai RG, Liu TB, Wang SJ (2018) Sensitivity of primordial black hole abundance on the reheating phase. Phys Rev D 98(4):043538. https://doi.org/10.1103/PhysRevD.98.043538. arXiv:1806.05390 [astro-ph.CO]

Cai YF, Ma XH, Sasaki M et al (2022a) Highly non-gaussian tails and primordial black holes from single-field inflation. JCAP 12:034. https://doi.org/10.1088/1475-7516/2022/12/034. arXiv:2207.11910 [astro-ph.CO]

Cai YF, Ma XH, Sasaki M et al (2022b) One small step for an inflaton, one giant leap for inflation: a novel non-gaussian tail and primordial black holes. Phys Lett B 834:137461. https://doi.org/10.1016/j.physletb.2022.137461. arXiv:2112.13836 [astro-ph.CO]

Cai Rg, Pi S, Sasaki M (2019a) Gravitational waves induced by non-gaussian scalar perturbations. Phys Rev Lett 122(20):201101. https://doi.org/10.1103/PhysRevLett.122.201101. arXiv:1810.11000 [astro-ph.CO]

Cai RG, Pi S, Sasaki M (2020) Universal infrared scaling of gravitational wave background spectra. Phys Rev D 102(8):083528. https://doi.org/10.1103/PhysRevD.102.083528. arXiv:1909.13728 [astro-ph.CO]

Cai RG, Pi S, Wang SJ et al (2019b) Pulsar timing array constraints on the induced gravitational waves. JCAP 10:059. https://doi.org/10.1088/1475-7516/2019/10/059. arXiv:1907.06372 [astro-ph.CO]

Cai Y, Zhu M, Piao YS (2024) Primordial black holes from null energy condition violation during inflation. Phys Rev Lett 133(2):021001. https://doi.org/10.1103/PhysRevLett.133.021001. arXiv:2305.10933 [gr-qc]

Calabrese R, Chianese M, Fiorillo DFG et al (2022a) Direct detection of light dark matter from evaporating primordial black holes. Phys Rev D 105(2):L021302. https://doi.org/10.1103/PhysRevD.105. L021302. arXiv:2107.13001 [hep-ph]

Calabrese R, Chianese M, Fiorillo DFG et al (2022b) Electron scattering of light new particles from evaporating primordial black holes. Phys Rev D 105(10):103024. https://doi.org/10.1103/PhysRevD. 105.103024. arXiv:2203.17093 [hep-ph]

Calabrese R, Fiorillo DFG, Miele G et al (2022c) Primordial black hole dark matter evaporating on the neutrino floor. Phys Lett B 829:137050. https://doi.org/10.1016/j.physletb.2022.137050. arXiv:2106. 02492 [hep-ph]

Calchi Novati S et al (2005) POINT-AGAPE pixel lensing survey of M31: evidence for a MACHO contribution to galactic halos. Astron Astrophys 443:911. https://doi.org/10.1051/0004-6361: 20053135. arXiv:astro-ph/0504188

Calchi Novati S, Mirzoyan S, Jetzer P et al (2013) Microlensing towards the SMC: a new analysis of OGLE and EROS results. Mon Not R Astron Soc 435:1582. https://doi.org/10.1093/mnras/stt1402. arXiv:1308.4281 [astro-ph.GA]

Calcino J, García-Bellido J, Davis TM (2018) Updating the MACHO fraction of the Milky Way dark halowith improved mass models. Mon Not R Astron Soc 479(3):2889-2905. https://doi.org/10.1093/ mnras/sty1368. arXiv:1803.09205 [astro-ph.CO]

Caldwell RR, Casper P (1996) Formation of black holes from collapsed cosmic string loops. Phys Rev D 53:3002-3010. https://doi.org/10.1103/PhysRevD.53.3002. arXiv:gr-qc/9509012

Caldwell RR, Gates E (1993) Constraints on cosmic strings due to black holes formed from collapsed cosmic string loops. Phys Rev D 48:2581-2586. https://doi.org/10.1103/PhysRevD.48.2581. arXiv: hep-ph/9306221

Calore F, Cuoco A, Regimbau T et al (2020) Cross-correlating galaxy catalogs and gravitational waves: a tomographic approach. Phys Rev Res 2:023314. https://doi.org/10.1103/PhysRevResearch.2.023314. arXiv:2002.02466 [astro-ph.CO]

Camera S, Nishizawa A (2013) Beyond concordance cosmology with magnification of gravitational-wave standard sirens. Phys Rev Lett 110(15):151103. https://doi.org/10.1103/PhysRevLett.110.151103. arXiv:1303.5446 [astro-ph.CO]

Capanema A, Esmaeili A, Esmaili A (2021) Evaporating primordial black holes in gamma ray and neutrino telescopes. JCAP 12:051. https://doi.org/10.1088/1475-7516/2021/12/051. arXiv:2110.05637 [hep-ph]

Capela F, Pshirkov M, Tinyakov P (2013a) Constraints on primordial black holes as dark matter candidates from capture by neutron stars. Phys Rev D 87(12):123524. https://doi.org/10.1103/PhysRevD.87. 123524. arXiv:1301.4984 [astro-ph.CO]

Capela F, Pshirkov M, Tinyakov P (2013b) Constraints on primordial black holes as dark matter candidates from star formation. Phys Rev D 87(2):023507. https://doi.org/10.1103/PhysRevD.87.023507. arXiv: 1209.6021 [astro-ph.CO]
Capozziello S, De Laurentis M, De Paolis F et al (2008) Gravitational waves from hyperbolic encounters. Mod Phys Lett A 23:99-107. https://doi.org/10.1142/S0217732308026236. arXiv:0801.0122 [gr-qc]

Cappelluti N, Hasinger G, Natarajan P (2022) Exploring the high-redshift PBH-ACDM universe: early black hole seeding, the first stars and cosmic radiation backgrounds. Astrophys J 926(2):205. https://doi.org/10.3847/1538-4357/ac332d. arXiv:2109.08701 [astro-ph.CO]

Caprini C, Figueroa DG (2018) Cosmological backgrounds of gravitational waves. Class Quant Grav 35 (16):163001. https://doi.org/10.1088/1361-6382/aac608. arXiv:1801.04268 [astro-ph.CO]

Cardoso V, Pani P (2019) Testing the nature of dark compact objects: a status report. Living Rev Relativ 22:4. https://doi.org/10.1007/s41114-019-0020-4. arXiv:1904.05363 [gr-qc]

Carr BJ (1975) The Primordial black hole mass spectrum. Astrophys J 201:1-19. https://doi.org/10.1086/153853

Carr B, Clesse S, García-Bellido J (2021a) Primordial black holes from the QCD epoch: linking dark matter, baryogenesis and anthropic selection. Mon Not R Astron Soc 501(1):1426-1439. https://doi.org/10.1093/mnras/staa3726. arXiv:1904.02129 [astro-ph.CO]

Carr B, Clesse S, García-Bellido J et al (2021b) Cosmic conundra explained by thermal history and primordial black holes. Phys Dark Univ 31:100755. https://doi.org/10.1016/j.dark.2020.100755. arXiv:1906.08217 [astro-ph.CO]

Carr B, Clesse S, García-Bellido J et al (2024) Observational evidence for primordial black holes: a positivist perspective. Phys Rept 1054:1-68. https://doi.org/10.1016/j.physrep.2023.11.005. arXiv:2306.03903 [astro-ph.CO]

Carr BJ, Coley AA (2011) Persistence of black holes through a cosmological bounce. Int J Mod Phys D 20:2733-2738. https://doi.org/10.1142/S0218271811020640. arXiv:1104.3796 [astro-ph.CO]

Carr B, Dimopoulos K, Owen C et al (2018) Primordial black hole formation during slow reheating after inflation. Phys Rev D 97(12):123535. https://doi.org/10.1103/PhysRevD.97.123535. arXiv:1804.08639 [astro-ph.CO]

Carr BJ, Gilbert JH, Lidsey JE (1994) Black hole relics and inflation: limits on blue perturbation spectra. Phys Rev D 50:4853-4867. https://doi.org/10.1103/PhysRevD.50.4853. arXiv:astro-ph/9405027

Carr BJ, Hawking SW (1974) Black holes in the early Universe. Mon Not R Astron Soc 168:399-415

Carr BJ, Kohri K, Sendouda Y et al (2010) New cosmological constraints on primordial black holes. Phys Rev D 81:104019. https://doi.org/10.1103/PhysRevD.81.104019. arXiv:0912.5297 [astro-ph.CO]

Carr B, Kohri K, Sendouda Y et al (2021c) Constraints on primordial black holes. Rept Prog Phys 84 (11):116902. https://doi.org/10.1088/1361-6633/ac1e31. arXiv:2002.12778 [astro-ph.CO]

Carr B, Kuhnel F (2019) Primordial black holes with multimodal mass spectra. Phys Rev D 99 (10):103535. https://doi.org/10.1103/PhysRevD.99.103535. arXiv:1811.06532 [astro-ph.CO]

Carr B, Kuhnel F (2020) Primordial black holes as dark matter: recent developments. Ann Rev Nucl Part Sci 70:355-394. https://doi.org/10.1146/annurev-nucl-050520-125911. arXiv:2006.02838 [astro-ph.CO]

Carr B, Kuhnel F, Visinelli L (2021d) Black holes and WIMPs: all or nothing or something else. Mon Not R Astron Soc 506(3):3648-3661. https://doi.org/10.1093/mnras/stab1930. arXiv:2011.01930 [astro-ph.CO]

Carr BJ, Lidsey JE (1993) Primordial black holes and generalized constraints on chaotic inflation. Phys Rev D 48:543-553. https://doi.org/10.1103/PhysRevD.48.543

Carr BJ, Sakellariadou M (1999) Dynamical constraints on dark matter in compact objects. Astrophys J 516(1):195-220. https://doi.org/10.1086/307071

Carr B, Silk J (2018) Primordial black holes as generators of cosmic structures. Mon Not R Astron Soc 478 (3):3756-3775. https://doi.org/10.1093/mnras/sty1204. arXiv:1801.00672 [astro-ph.CO]

Carr B, Tenkanen T, Vaskonen V (2017) Primordial black holes from inflaton and spectator field perturbations in a matter-dominated era. Phys Rev D 96(6):063507. https://doi.org/10.1103/PhysRevD.96.063507. arXiv:1706.03746 [astro-ph.CO]

Carrilho P, Malik KA, Mulryne DJ (2019) Dissecting the growth of the power spectrum for primordial black holes. Phys Rev D 100(10):103529. https://doi.org/10.1103/PhysRevD.100.103529. arXiv:1907.05237 [astro-ph.CO]

Cañas Herrera G, Contigiani O, Vardanyan V (2020) Cross-correlation of the astrophysical gravitational-wave background with galaxy clustering. Phys Rev D 102(4):043513. https://doi.org/10.1103/PhysRevD.102.043513. arXiv:1910.08353 [astro-ph.CO]

Challinor A, Lewis A (2011) The linear power spectrum of observed source number counts. Phys Rev D 84:043516. https://doi.org/10.1103/PhysRevD.84.043516. arXiv:1105.5292 [astro-ph.CO]
Chanda P, Scholtz J, Unwin J (2024) Improved constraints on dark matter annihilations around primordial black holes. JHEP 07:273. https://doi.org/10.1007/JHEP07(2024)273. arXiv:2209.07541 [hep-ph]

Chapline GF (1975) Cosmological effects of primordial black holes. Nature 253(5489):251–252. https://doi.org/10.1038/253251a0

Chen S et al (2021b) Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: inferences in the stochastic gravitational-wave background search. Mon Not R Astron Soc 508(4):4970–4993. https://doi.org/10.1093/mnras/stab2833. arXiv:2110.13184 [astro-ph.HE]

Chen ZC, Huang QG (2018) Merger rate distribution of primordial-black-hole binaries. Astrophys J 864 (1):61. https://doi.org/10.3847/1538-4357/aad6e2. arXiv:1801.10327 [astro-ph.CO]

Chen ZC, Huang F, Huang QG (2019) Stochastic gravitational-wave background from binary black holes and binary neutron stars and implications for LISA. Astrophys J 871(1):97. https://doi.org/10.3847/1538-4357/aaf581. arXiv:1809.10360 [gr-qc]

Chen JW, Liu J, Xu HL et al (2017) Tracing primordial black holes in nonsingular bouncing cosmology. Phys Lett B 769:561–568. https://doi.org/10.1016/j.physletb.2017.03.036. arXiv:1609.02571 [gr-qc]

Chen P, Koh S, Tumurtushaa G (2021a) Primordial black holes and induced gravitational waves from inflation in the Horndeski theory of gravity. arXiv e-prints arXiv:2107.08638 [gr-qc]

Cheng SL, Lee DS, Ng KW (2024) Primordial perturbations from ultra-slow-roll single-field inflation with quantum loop effects. JCAP 03:008. https://doi.org/10.1088/1475-7516/2024/03/008. arXiv:2305.16810 [astro-ph.CO]

Cheong DY, Kohri K, Park SC (2022) The inflaton that could: primordial black holes and second order gravitational waves from tachyonic instability induced in Higgs-R² inflation. JCAP 10:015. https://doi.org/10.1088/1475-7516/2022/10/015. arXiv:2205.14813 [hep-ph]

Cheong DY, Lee SM, Park SC (2021) Primordial black holes in Higgs-R² inflation as the whole of dark matter. JCAP 01:032. https://doi.org/10.1088/1475-7516/2021/01/032. arXiv:1912.12032 [hep-ph]

Chisholm JR (2006) Clustering of primordial black holes: basic results. Phys Rev D 73:083504. https://doi.org/10.1103/PhysRevD.73.083504. arXiv:astro-ph/0509141

Chisholm JR (2011) Clustering of Primordial Black Holes. II. Evolution of Bound Systems. Phys Rev D 84:124031. https://doi.org/10.1103/PhysRevD.84.124031. arXiv:1110.4402 [astro-ph.CO]

Cholis I, Kovetz ED, Ali-Haïmoud Y et al (2016) Orbital eccentricities in primordial black hole binaries. Phys Rev D 94(8):084013. https://doi.org/10.1103/PhysRevD.94.084013. arXiv:1606.07437 [astro-ph.HE]

Cicoli M, Diaz VA, Pedro FG (2018) Primordial black holes from string inflation. JCAP 06:034. https://doi.org/10.1088/1475-7516/2018/06/034. arXiv:1803.02837 [hep-th]

Clesse S (2011) Hybrid inflation along waterfall trajectories. Phys Rev D 83:063518. https://doi.org/10.1103/PhysRevD.83.063518. arXiv:1006.4522 [gr-qc]

Clesse S, Garbrecht B, Zhu Y (2014) Non-gaussianities and curvature perturbations from hybrid inflation. Phys Rev D 89(6):063519. https://doi.org/10.1103/PhysRevD.89.063519. arXiv:1304.7042 [astro-ph.CO]

Clesse S, García-Bellido J (2015) Massive primordial black holes from hybrid inflation as dark matter and the seeds of galaxies. Phys Rev D 92(2):023524. https://doi.org/10.1103/PhysRevD.92.023524. arXiv:1501.07565 [astro-ph.CO]

Clesse S, García-Bellido J (2015) Massive primordial black holes from hybrid inflation as dark matter and the seeds of galaxies. Phys Rev D 92(2):023524. https://doi.org/10.1103/PhysRevD.92.023524. arXiv:1501.07565 [astro-ph.CO]

Clesse S, García-Bellido J (2017a) Detecting the gravitational wave background from primordial black hole dark matter. Phys Dark Univ 18:105–114. https://doi.org/10.1016/j.dark.2017.10.001. arXiv:1610.08479 [astro-ph.CO]

Clesse S, García-Bellido J (2017b) The clustering of massive primordial black holes as dark matter: measuring their mass distribution with advanced LIGO. Phys Dark Univ 15:142–147. https://doi.org/10.1016/j.dark.2016.10.002. arXiv:1603.05234 [astro-ph.CO]

Clesse S, García-Bellido J (2018) Seven hints for primordial black hole dark matter. Phys Dark Univ 22:137–146. https://doi.org/10.1016/j.dark.2018.08.004. arXiv:1711.10458 [astro-ph.CO]

Clesse S, García-Bellido J (2022) GW190425, GW190521 and GW190814: three candidate mergers of primordial black holes from the QCD epoch. Phys Dark Univ 38:101111. https://doi.org/10.1016/j.dark.2022.101111. arXiv:2007.06481 [astro-ph.CO]

Clesse S, García-Bellido J, Orani S (2018) Detecting the stochastic gravitational wave background from primordial black hole formation. arXiv e-prints arXiv:1812.11011 [astro-ph.CO]
Cole PS, Coogan A, Kavanagh BJ et al (2023a) Measuring dark matter spikes around primordial black holes with einstein telescope and cosmic explorer. Phys Rev D 107(8):083006. https://doi.org/10.1103/PhysRevD.107.083006. arXiv:2207.07576 [astro-ph.CO]

Cole PS, Gow AD, Byrnes CT et al (2023b) Primordial black holes from single-field inflation: a fine-tuning audit. JCAP 08:031. https://doi.org/10.1088/1475-7516/2023/08/031. arXiv:2304.01997 [astro-ph.CO]

Cole PS, Gow AD, Byrnes CT et al (2024) Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes. JCAP 05:022. https://doi.org/10.1088/1475-7516/2024/05/022. arXiv:2204.07573 [astro-ph.CO]

Colpi M, et al (2024) LISA Definition Study Report. arXiv e-prints arXiv:2402.07571 [astro-ph.CO]

Contaldi CR (2017) Anisotropies of gravitational wave backgrounds: a line of sight approach. Phys Lett B 771:9-12. https://doi.org/10.1016/j.physletb.2017.05.020. arXiv:1609.08168 [astro-ph.CO]

Contaldi CR, Pieroni M, Renzini AI et al (2020) Maximum likelihood map-making with the Laser Interferometer Space Antenna. Phys Rev D 102(4):043502. https://doi.org/10.1103/PhysRevD.102.043502. arXiv:2006.03313 [astro-ph.CO]

Cook JL, Sorbo L (2012) Particle production during inflation and gravitational waves detectable by ground-based interferometers. Phys Rev D 85:023534. https://doi.org/10.1103/PhysRevD.85.023534. [Erratum: Phys. Rev. D 86, 069901 (2012)] arXiv:1109.0022 [astro-ph.CO]

Copeland EJ, Liddle AR, Lidsey JE et al (1998) Black holes and gravitational waves in string cosmology. Phys Rev D 58:063508. https://doi.org/10.1103/PhysRevD.58.063508. arXiv:gr-qc/9803070

Copeland EJ, Liddle AR, Lyth DH et al (1994) False vacuum inflation with Einstein gravity. Phys Rev D 49:6410-6433. https://doi.org/10.1103/PhysRevD.49.6410. arXiv:astro-ph/9401011

Cotner E, Kusenko A (2017) Primordial black holes from scalar field evolution in the early universe. Phys Rev D 96(10):103002. https://doi.org/10.1103/PhysRevD.96.103002. arXiv:1706.09003 [astro-ph.CO]

Cremonini S, Lalak Z, Turzynski K (2011) Strongly coupled perturbations in two-field inflationary models. JCAP 03:016. https://doi.org/10.1088/1475-7516/2011/03/016. arXiv:1010.3021 [hep-th]

Cruz-Osorio A, Lora-Clavijo FD, Herdeiro C (2021) GW190521 formation scenarios via relativistic accretion. JCAP 07:032. https://doi.org/10.1088/1475-7516/2021/07/032. arXiv:2101.01705 [astro-ph.HE]

Cruz-Osorio A, Rezzolla L (2020) Common-envelope dynamics of a stellar-mass black hole: general relativistic simulations. Astrophys J 894(2):147. https://doi.org/10.3847/1538-4357/ab89aa. arXiv:2004.13782 [gr-qc]

Cusin G, Durrer R, Ferreira PG (2019a) Polarization of a stochastic gravitational wave background through diffusion by massive structures. Phys Rev D 99(2):023534. https://doi.org/10.1103/PhysRevD.99.023534. arXiv:1807.10620 [astro-ph.CO]

Cusin G, Dvorkin I, Pitrou C et al (2018a) First predictions of the angular power spectrum of the astrophysical gravitational wave background. Phys Rev Lett 120:231101. https://doi.org/10.1103/PhysRevLett.120.231101. arXiv:1803.03236 [astro-ph.CO]

Cusin G, Dvorkin I, Pitrou C et al (2019b) Properties of the stochastic astrophysical gravitational wave background: astrophysical sources dependencies. Phys Rev D 100(6):063004. https://doi.org/10.1103/PhysRevD.100.063004. arXiv:1904.07797 [astro-ph.CO]

Cusin G, Dvorkin I, Pitrou C et al (2020) Stochastic gravitational wave background anisotropies in the mHz band: astrophysical dependencies. Mon Not R Astron Soc 493(1):L1-L5. https://doi.org/10.1093/mnrasl/slz182. arXiv:1904.07757 [astro-ph.CO]

Cusin G, Pitrou C, Uzan JP (2017) Anisotropy of the astrophysical gravitational wave background: analytic expression of the angular power spectrum and correlation with cosmological observations. Phys Rev D 96(10):103019. https://doi.org/10.1103/PhysRevD.96.103019. arXiv:1704.06184 [astro-ph.CO]

Cusin G, Pitrou C, Uzan JP (2018b) The signal of the gravitational wave background and the angular correlation of its energy density. Phys Rev D 97(12):123527. https://doi.org/10.1103/PhysRevD.97.123527. arXiv:1711.11345 [astro-ph.CO]

Dalianis I, Kehagias A, Tringas G (2019) Primordial black holes from $\alpha$-attractors. JCAP 01:037. https://doi.org/10.1088/1475-7516/2019/01/037. arXiv:1805.09483 [astro-ph.CO]

Dandoy V, Domcke V, Rompineve F (2023) Search for scalar induced gravitational waves in the International Pulsar Timing Array data release 2 and NANOgrav 12.5 years datasets. SciPost Phys Core 6:060. https://doi.org/10.21468/SciPostPhysCore.6.3.060. arXiv:2302.07901 [astro-ph.CO]
Dasgupta B, Laha R, Ray A (2020) Neutrino and positron constraints on spinning primordial black hole dark matter. Phys Rev Lett 125(10):101101. https://doi.org/10.1103/PhysRevLett.125.101101. arXiv: 1912.01014 [hep-ph]

Datta S, Ghosal A, Samanta R (2021) Baryogenesis from ultralight primordial black holes and strong gravitational waves from cosmic strings. JCAP 08:021. https://doi.org/10.1088/1475-7516/2021/08/ 021. arXiv:2012.14981 [hep-ph]

Davoudiasl H (2019) LIGO/Virgo black holes from a first order quark confinement phase transition. Phys Rev Lett 123(10):101102. https://doi.org/10.1103/PhysRevLett.123.101102. arXiv:1902.07805 [hep-ph]

De Luca V, Bellomo N (2023) Accretion, emission, mass and spin evolution. arXiv e-prints arXiv:2312. 14097 [astro-ph.CO]

De Luca V, Desjacques V, Franciolini G et al (2019a) The initial spin probability distribution of primordial black holes. JCAP 05:018. https://doi.org/10.1088/1475-7516/2019/05/018. arXiv:1903.01179 [astro-ph.CO]

De Luca V, Desjacques V, Franciolini G et al (2019b) Gravitational waves from peaks. JCAP 09:059. https://doi.org/10.1088/1475-7516/2019/09/059. arXiv:1905.13459 [astro-ph.CO]

De Luca V, Desjacques V, Franciolini G et al (2020a) The clustering evolution of primordial black holes. JCAP 11:028. https://doi.org/10.1088/1475-7516/2020/11/028. arXiv:2009.04731 [astro-ph.CO]

De Luca V, Desjacques V, Franciolini G et al (2021a) GW190521 mass gap event and the primordial black hole scenario. Phys Rev Lett 126(5):051101. https://doi.org/10.1103/PhysRevLett.126.051101. arXiv:2009.01728 [astro-ph.CO]

De Luca V, Franciolini G, Kehagias A et al (2019c) The ineludible non-gaussianity of the primordial black hole abundance. JCAP 07:048. https://doi.org/10.1088/1475-7516/2019/07/048. arXiv:1904.00970 [astro-ph.CO]

De Luca V, Franciolini G, Kehagias A et al (2020b) On the gauge invariance of cosmological gravitational waves. JCAP 03:014. https://doi.org/10.1088/1475-7516/2020/03/014. arXiv:1911.09689 [gr-qc]

De Luca V, Franciolini G, Kehagias A et al (2021b) Standard model baryon number violation seeded by black holes. Phys Lett B 819:136454. https://doi.org/10.1016/j.physletb.2021.136454. arXiv:2102. 07408 [astro-ph.CO]

De Luca V, Franciolini G, Kehagias A et al (2022a) Primordial black holes in matter-dominated eras: the role of accretion. Phys Lett B 832:137265. https://doi.org/10.1016/j.physletb.2022.137265. arXiv: 2112.02534 [astro-ph.CO]

De Luca V, Franciolini G, Pani P et al (2020c) Constraints on primordial black holes: the importance of accretion. Phys Rev D 102(4):043505. https://doi.org/10.1103/PhysRevD.102.043505. arXiv:2003. 12589 [astro-ph.CO]

De Luca V, Franciolini G, Pani P et al (2020d) Primordial black holes confront LIGO/Virgo data: current situation. JCAP 06:044. https://doi.org/10.1088/1475-7516/2020/06/044. arXiv:2005.05641 [astro-ph.CO]

De Luca V, Franciolini G, Pani P et al (2020e) The evolution of primordial black holes and their final observable spins. JCAP 04:052. https://doi.org/10.1088/1475-7516/2020/04/052. arXiv:2003.02778 [astro-ph.CO]

De Luca V, Franciolini G, Pani P et al (2021c) Bayesian evidence for both astrophysical and primordial black holes: mapping the GWTC-2 catalog to third-generation detectors. JCAP 05:003. https://doi. org/10.1088/1475-7516/2021/05/003. arXiv:2102.03809 [astro-ph.CO]

De Luca V, Franciolini G, Pani P et al (2021d) The minimum testable abundance of primordial black holes at future gravitational-wave detectors. JCAP 11:039. https://doi.org/10.1088/1475-7516/2021/11/039. arXiv:2106.13769 [astro-ph.CO]

De Luca V, Franciolini G, Riotto A (2020f) On the primordial black hole mass function for broad spectra. Phys Lett B 807:135550. https://doi.org/10.1016/j.physletb.2020.135550. arXiv:2001.04371 [astro-ph.CO]

De Luca V, Franciolini G, Riotto A (2021e) Bubble correlation in first-order phase transitions. Phys Rev D 104(12):123539. https://doi.org/10.1103/PhysRevD.104.123539. arXiv:2110.04229 [hep-ph]

De Luca V, Franciolini G, Riotto A (2021f) Constraining the initial primordial black hole clustering with CMB distortion. Phys Rev D 104(6):063526. https://doi.org/10.1103/PhysRevD.104.063526. arXiv: 2103.16369 [astro-ph.CO]

De Luca V, Franciolini G, Riotto A (2021g) NANOGrav data hints at primordial black holes as dark matter. Phys Rev Lett 126(4):041303. https://doi.org/10.1103/PhysRevLett.126.041303. arXiv:2009.08268 [astro-ph.CO]
De Luca V, Franciolini G, Riotto A et al (2022b) Ruling out initially clustered primordial black holes as dark matter. Phys Rev Lett 129(19):191302. https://doi.org/10.1103/PhysRevLett.129.191302. arXiv: 2208.01683 [astro-ph.CO]

De Luca V, Franciolini G, Riotto A (2023a) Heavy primordial black holes from strongly clustered light black holes. Phys Rev Lett 130(17):171401. https://doi.org/10.1103/PhysRevLett.130.171401. arXiv: 2210.14171 [astro-ph.CO]

De Luca V, Kehagias A, Riotto A (2023b) How well do we know the primordial black hole abundance: the crucial role of nonlinearities when approaching the horizon. Phys Rev D 108(6):063531. https://doi.org/10.1103/PhysRevD.108.063531. arXiv:2307.13633 [astro-ph.CO]

De Luca V, Riotto A (2022) A note on the abundance of primordial black holes: use and misuse of the metric curvature perturbation. Phys Lett B 828:137035. https://doi.org/10.1016/j.physletb.2022.137035. arXiv:2201.09008 [astro-ph.CO]

DeRocco W, Graham PW (2019) Constraining primordial black hole abundance with the galactic 511 keV line. Phys Rev Lett 123(25):251102. https://doi.org/10.1103/PhysRevLett.123.251102. arXiv:1906.07740 [astro-ph.CO]

Defillon G, Granet E, Tinyakov P et al (2014) Tidal capture of primordial black holes by neutron stars. Phys Rev D 90(10):103522. https://doi.org/10.1103/PhysRevD.90.103522. arXiv:1409.0469 [gr-qc]

Delos MS (2019) Evolution of dark matter microhalos through stellar encounters. Phys Rev D 100 (8):083529. https://doi.org/10.1103/PhysRevD.100.083529. arXiv:1907.13133 [astro-ph.CO]

Delos MS, Erickcek AL, Bailey AP et al (2018a) Are ultracompact minihalos really ultracompact? Phys Rev D 97(4):041303. https://doi.org/10.1103/PhysRevD.97.041303. arXiv:1712.05421 [astro-ph.CO]

Delos MS, Erickcek AL, Bailey AP et al (2018b) Density profiles of ultracompact minihalos: implications for constraining the primordial power spectrum. Phys Rev D 98(6):063527. https://doi.org/10.1103/PhysRevD.98.063527. arXiv:1806.07389 [astro-ph.CO]

Delos MS, Franciolini G (2023) Lensing constraints on ultradense dark matter halos. Phys Rev D 107 (8):083505. https://doi.org/10.1103/PhysRevD.107.083505. arXiv:2301.13171 [astro-ph.CO]

Deng H, Vilenkin A (2017) Primordial black hole formation by vacuum bubbles. JCAP 12:044. https://doi.org/10.1088/1475-7516/2017/12/044. arXiv:1710.02865 [gr-qc]

Desjacques V, Riotto A (2018) Spatial clustering of primordial black holes. Phys Rev D 98(12):123533. https://doi.org/10.1103/PhysRevD.98.123533. arXiv:1806.10414 [astro-ph.CO]

Dewdney PE, Hall PJ, Schilizzi RT et al (2009) The square kilometre Array. IEEE Proc 97(8):1482-1496. https://doi.org/10.1109/JPROC.2009.2021005

de Jong E, Aurrekoetxea JC, Lim EA (2022) Primordial black hole formation with full numerical relativity. JCAP 03(03):029. https://doi.org/10.1088/1475-7516/2022/03/029. arXiv:2109.04896 [astro-ph.CO]

De Romeri V, Martínez-Miravé P, Tórtola M (2021) Signatures of primordial black hole dark matter at DUNE and THEIA. JCAP 10:051. https://doi.org/10.1088/1475-7516/2021/10/051. arXiv:2106.05013 [hep-ph]

De Vittori L, Jetzer P, Klein A (2012) Gravitational wave energy spectrum of hyperbolic encounters. Phys Rev D 86:044017. https://doi.org/10.1103/PhysRevD.86.044017. arXiv:1207.5359 [gr-qc]

Di Bari P, Marfatia D, Zhou YL (2021) Gravitational waves from first-order phase transitions in Majoron models of neutrino mass. JHEP 10:193. https://doi.org/10.1007/JHEP10(2021)193. arXiv:2106.00025 [hep-ph]

Dimastrogiovanni E, Fasiello M, Tasinato G (2020) Searching for fossil fields in the gravity sector. Phys Rev Lett 124(6):061302. https://doi.org/10.1103/PhysRevLett.124.061302. arXiv:1906.07204 [astro-ph.CO]

Dolgov A, Silk J (1993) Baryon isocurvature fluctuations at small scales and baryonic dark matter. Phys Rev D 47:4244-4255. https://doi.org/10.1103/PhysRevD.47.4244

Dolgov AD, Naselsky PD, Novikov ID (2000) Gravitational waves, baryogenesis, and dark matter from primordial black holes. arXiv e-prints arXiv:astro-ph/0009407

Domcke V, Garcia-Cely C, Rodd NL (2022) Novel search for high-frequency gravitational waves with low-mass axion haloscopes. Phys Rev Lett 129(4):041101. https://doi.org/10.1103/PhysRevLett.129.041101. arXiv:2202.00695 [hep-ph]

Domcke V, Jinno R, Rubira H (2020) Deformation of the gravitational wave spectrum by density perturbations. JCAP 06:046. https://doi.org/10.1088/1475-7516/2020/06/046. arXiv:2002.11083 [astro-ph.CO]

Domcke V, Muia F, Pieroni M et al (2017) PBH dark matter from axion inflation. JCAP 07:048. https://doi.org/10.1088/1475-7516/2017/07/048. arXiv:1704.03464 [astro-ph.CO]
Domènech G (2020) Induced gravitational waves in a general cosmological background. Int J Mod Phys D 29(03):2050028. https://doi.org/10.1142/S0218271820500285. arXiv:1912.05583 [gr-qc]

Domènech G (2021) Scalar induced gravitational waves review. Universe 7(11):398. https://doi.org/10.3390/universe7110398. arXiv:2109.01398 [gr-qc]

Domènech G, Lin C, Sasaki M (2021) Gravitational wave constraints on the primordial black hole dominated early universe. JCAP 04:062. https://doi.org/10.1088/1475-7516/2021/04/062. arXiv: 2012.08151 [gr-qc]

Domènech G, Passaglia S, Renaux-Petel S (2022) Gravitational waves from dark matter isocurvature. JCAP 03(03):023. https://doi.org/10.1088/1475-7516/2022/03/023. arXiv:2112.10163 [astro-ph.CO]

Domènech G, Pi S (2022) NANOGrav hints on planet-mass primordial black holes. Sci China Phys Mech Astron 65(3):230411. https://doi.org/10.1007/s11433-021-1839-6. arXiv:2010.03976 [astro-ph.CO]

Domènech G, Pi S, Sasaki M (2020) Induced gravitational waves as a probe of thermal history of the universe. JCAP 08:017. https://doi.org/10.1088/1475-7516/2020/08/017. arXiv:2005.12314 [gr-qc]

Domènech G, Sasaki M (2018) Hamiltonian approach to second order gauge invariant cosmological perturbations. Phys Rev D 97(2):023521. https://doi.org/10.1103/PhysRevD.97.023521. arXiv:1709.09804 [gr-qc]

Doré O, et al (2014) Cosmology with the SPHEREX All-Sky Spectral Survey. arXiv e-prints arXiv:1412.4872 [astro-ph.CO]

Drlica-Wagner A, et al (2019) Probing the fundamental nature of dark matter with the large synoptic survey telescope. arXiv:1902.01055

Duechting N (2004) Supermassive black holes from primordial black hole seeds. Phys Rev D 70:064015. https://doi.org/10.1103/PhysRevD.70.064015. arXiv:astro-ph/0406260

Easther R, Flauger R, Gilmore JB (2011) Delayed reheating and the breakdown of coherent oscillations. JCAP 04:027. https://doi.org/10.1088/1475-7516/2011/04/027. arXiv:1003.3011 [astro-ph.CO]

Ellis J, Fairbairn M, Hütsi G et al (2023) Prospects for future binary black hole gravitational wave studies in light of PTA measurements. Astron Astrophys 676:A38. https://doi.org/10.1051/0004-6361/202346268. arXiv:2301.13854 [astro-ph.CO]

Ellis J, Lewicki M (2021) Cosmic string interpretation of NANOGrav pulsar timing data. Phys Rev Lett 126(4):041304. https://doi.org/10.1103/PhysRevLett.126.041304. arXiv:2009.06555 [astro-ph.CO]

Enqvist K, Nurmi S, Podolsky D et al (2008) On the divergences of inflationary superhorizon perturbations. JCAP 04:025. https://doi.org/10.1088/1475-7516/2008/04/025. arXiv:0802.0395 [astro-ph]

Escrivà A, Bagui E, Clesse S (2023) Simulations of PBH formation at the QCD epoch and comparison with the GWTC-3 catalog. JCAP 05:004. https://doi.org/10.1088/1475-7516/2023/05/004. arXiv:2209.06196 [astro-ph.CO]

Escrivà A, Germani C, Sheth RK (2020) Universal threshold for primordial black hole formation. Phys Rev D 101(4):044022. https://doi.org/10.1103/PhysRevD.101.044022. arXiv:1907.13311 [gr-qc]

Escrivà A, Germani C, Sheth RK (2021) Analytical thresholds for black hole formation in general cosmological backgrounds. JCAP 01:030. https://doi.org/10.1088/1475-7516/2021/01/030. arXiv:2007.05564 [gr-qc]

Escrivà A, Tada Y, Yokoyama S et al (2022) Simulation of primordial black holes with large negative non-Gaussianity. JCAP 05(05):012. https://doi.org/10.1088/1475-7516/2022/05/012. arXiv:2202.01028 [astro-ph.CO]

Espinosa JR, Racco D, Riotto A (2018) A cosmological signature of the SM higgs instability: gravitational waves. JCAP 09:012. https://doi.org/10.1088/1475-7516/2018/09/012. arXiv:1804.07732 [hep-ph]

Esser N, Tinyakov P (2023) Constraints on primordial black holes from observation of stars in dwarf galaxies. Phys Rev D 107(10):103052. https://doi.org/10.1103/PhysRevD.107.103052. arXiv:2207.07412 [astro-ph.HE]

Ezquiaga JM, García-Bellido J (2018) Quantum diffusion beyond slow-roll: implications for primordial black-hole production. JCAP 08:018. https://doi.org/10.1088/1475-7516/2018/08/018. arXiv:1805.06731 [astro-ph.CO]

Ezquiaga JM, García-Bellido J, Ruiz Morales E (2018) Primordial black hole production in critical higgs inflation. Phys Lett B 776:345-349. https://doi.org/10.1016/j.physletb.2017.11.039. arXiv:1705.04861 [astro-ph.CO]

Ezquiaga JM, García-Bellido J, Vennin V (2020) The exponential tail of inflationary fluctuations: consequences for primordial black holes. JCAP 03:029. https://doi.org/10.1088/1475-7516/2020/03/029. arXiv:1912.05399 [astro-ph.CO]
Ezquiaga JM, García-Bellido J, Vennin V (2022 [arXiv:2207.06317]) Massive galaxy clusters like El Gordo hint at primordial quantum diffusion. Phys Rev Lett arXiv:2207.06317 [astro-ph.CO]

Facchinetti G, Lucca M, Clesse S (2023) Relaxing CMB bounds on primordial black holes: the role of ionization fronts. Phys Rev D 107(4):043537. https://doi.org/10.1103/PhysRevD.107.043537. arXiv: 2212.07969 [astro-ph.CO]

Feng JX, Zhang F, Gao X (2023) Scalar induced gravitational waves from Chern-Simons gravity during inflation era. JCAP 07:047. https://doi.org/10.1088/1475-7516/2023/07/047. arXiv:2302.00950 [gr-qc]

Fernandez N, Profumo S (2019) Unraveling the origin of black holes from effective spin measurements with LIGO-Virgo. JCAP 08:022. https://doi.org/10.1088/1475-7516/2019/08/022. arXiv:1905.13019 [astro-ph.HE]

Ferrante G, Franciolini G, Iovino AJunior et al (2023a) Primordial black holes in the curvaton model: possible connections to pulsar timing arrays and dark matter. JCAP 06:057. https://doi.org/10.1088/1475-7516/2023/06/057. arXiv:2305.13382 [astro-ph.CO]

Ferrante G, Franciolini G, Iovino AJunior et al (2023b) Primordial non-Gaussianity up to all orders: theoretical aspects and implications for primordial black hole models. Phys Rev D 107(4):043520. https://doi.org/10.1103/PhysRevD.107.043520. arXiv:2211.01728 [astro-ph.CO]

Ferreira RZ (2020) Non-Gaussianities in models of inflation with large and negative entropic masses. JCAP 08:034. https://doi.org/10.1088/1475-7516/2020/08/034. arXiv:2003.13410 [astro-ph.CO]

Ferreira RZ, Notari A, Pujolas O et al (2023) Gravitational waves from domain walls in pulsar timing array datasets. JCAP 02:001. https://doi.org/10.1088/1475-7516/2023/02/001. arXiv:2204.04228 [astro-ph.CO]

Ferrer F, Masso E, Panico G et al (2019) Primordial black holes from the QCD axion. Phys Rev Lett 122 (10):101301. https://doi.org/10.1103/PhysRevLett.122.101301. arXiv:1807.01707 [hep-ph]

Figueroa DG, Pieroni M, Ricciardone A et al (2024) Cosmological background interpretation of pulsar timing array data. Phys Rev Lett 132(17):171002. https://doi.org/10.1103/PhysRevLett.132.171002. arXiv:2307.02399 [astro-ph.CO]

Finelli F, Brandenberger RH (1999) Parametric amplification of gravitational fluctuations during reheating. Phys Rev Lett 82:1362-1365. https://doi.org/10.1103/PhysRevLett.82.1362. arXiv:hep-ph/9809490

Finkelstein SL, Bagley MB, Haro PA et al (2022b) A long time ago in a galaxy far, far away: a candidate z 12 galaxy in early JWST CEERS imaging. Astrophys J Lett 940(2):L55. https://doi.org/10.3847/2041-8213/ac966e. arXiv:2207.12474 [astro-ph.GA]

Finkelstein SL, Bagley MB, Arrabal Haro P, et al (2022a) A long time ago in a galaxy far, far away: a candidate z 12 Galaxy in Early JWST CEERS Imaging. arXiv e-prints arXiv:2207.12474. arXiv:2207.12474 [astro-ph.GA]

Firouzjahi H (2023) One-loop corrections in power spectrum in single field inflation. JCAP 10:006. https://doi.org/10.1088/1475-7516/2023/10/006. arXiv:2303.12025 [astro-ph.CO]

Firouzjahi H, Nassiri-Rad A, Noorbala M (2019) Stochastic ultra slow roll inflation. JCAP 01:040. https://doi.org/10.1088/1475-7516/2019/01/040. arXiv:1811.02175 [hep-th]

Firouzjahi H, Riotto A (2023) Sign of non-Gaussianity and the primordial black holes abundance. Phys Rev D 108(12):123504. https://doi.org/10.1103/PhysRevD.108.123504. arXiv:2309.10536 [astro-ph.CO]

Firouzjahi H, Riotto A (2024) Primordial Black Holes and loops in single-field inflation. JCAP 02:021. https://doi.org/10.1088/1475-7516/2024/02/021. arXiv:2304.07801 [astro-ph.CO]

Firouzjahi H, Talebian A (2023) Induced gravitational waves from ultra slow-roll inflation and pulsar timing arrays observations. JCAP 10:032. https://doi.org/10.1088/1475-7516/2023/10/032. arXiv:2307.03164 [gr-qc]

Flanagan EE, Hughes SA (2005) The basics of gravitational wave theory. New J Phys 7:204. https://doi.org/10.1088/1367-2630/7/1/204. arXiv:gr-qc/0501041

Flores MM, Kusenko A, Sasaki M (2024) Revisiting formation of primordial black holes in a supercooled first-order phase transition. Phys Rev D 110(1):015005. https://doi.org/10.1103/PhysRevD.110.015005. arXiv:2402.13341 [hep-ph]

Franciolini G, Baibhav V, De Luca V et al (2022a) Searching for a subpopulation of primordial black holes in LIGO-Virgo gravitational-wave data. Phys Rev D 105(8):083526. https://doi.org/10.1103/PhysRevD.105.083526. arXiv:2105.03349 [gr-qc]

Franciolini G, Cotesta R, Loutrel N et al (2022b) How to assess the primordial origin of single gravitational-wave events with mass, spin, eccentricity, and deformability measurements. Phys Rev D 105(6):063510. https://doi.org/10.1103/PhysRevD.105.063510. arXiv:2112.10660 [astro-ph.CO]
Franciolini G, Iovino AJunior, Vaskonen V (2023) Recent gravitational wave observation by pulsar timing arrays and primordial black holes: the importance of non-gaussianities. Phys Rev Lett 131 (20):201401. https://doi.org/10.1103/PhysRevLett.131.201401. arXiv:2306.17149 [astro-ph.CO]

Franciolini G, Iovino AJ, Taoso M et al (2024a) Perturbativity in the presence of ultraslow-roll dynamics. Phys Rev D 109(12):123550. https://doi.org/10.1103/PhysRevD.109.123550. arXiv:2305.03491 [astro-ph.CO]

Franciolini G, Kehagias A, Matarrese S et al (2018) Primordial black holes from inflation and non-gaussianity. JCAP 03:016. https://doi.org/10.1088/1475-7516/2018/03/016. arXiv:1801.09415 [astro-ph.CO]

Franciolini G, Kritos K, Berti E et al (2022c) Primordial black hole mergers from three-body interactions. Phys Rev D 106(8):083529. https://doi.org/10.1103/PhysRevD.106.083529. arXiv:2205.15340 [astro-ph.CO]

Franciolini G, Maharana A, Muia F (2022d) Hunt for light primordial black hole dark matter with ultrahigh-frequency gravitational waves. Phys Rev D 106(10):103520. https://doi.org/10.1103/PhysRevD.106.103520. arXiv:2205.02153 [astro-ph.CO]

Franciolini G, Musco I, Pani P et al (2022e) From inflation to black hole mergers and back again: gravitational-wave data-driven constraints on inflationary scenarios with a first-principle model of primordial black holes across the QCD epoch. Phys Rev D 106(12):123526. https://doi.org/10.1103/PhysRevD.106.123526. arXiv:2209.05959 [astro-ph.CO]

Franciolini G, Pani P (2022) Searching for mass-spin correlations in the population of gravitational-wave events: The GWTC-3 case study. Phys Rev D 105(12):123024. https://doi.org/10.1103/PhysRevD.105.123024. arXiv:2201.13098 [astro-ph.HE]

Franciolini G, Racco D, Rompineve F (2024b) Footprints of the QCD crossover on cosmological gravitational waves at pulsar timing arrays. Phys Rev Lett 132(8):081001. https://doi.org/10.1103/PhysRevLett.132.081001. arXiv:2306.17136 [astro-ph.CO]

Franciolini G, Urbano A (2022) Primordial black hole dark matter from inflation: the reverse engineering approach. Phys Rev D 106(12):123519. https://doi.org/10.1103/PhysRevD.106.123519. arXiv:2207.10056 [astro-ph.CO]

Franciolini G (2021) Primordial black holes: from theory to gravitational wave observations. PhD thesis, Geneva U., Dept. Theor. Phys., https://doi.org/10.13097/archive-ouverte/unige:156136, arXiv:2110.06815

Freese K, Frieman JA, Olinto AV (1990) Natural inflation with pseudo - Nambu-Goldstone bosons. Phys Rev Lett 65:3233-3236. https://doi.org/10.1103/PhysRevLett.65.3233

Freese K, Galstyan I, Sandick P et al (2022) Neutrino point source searches for dark matter spikes. JCAP 08:065. https://doi.org/10.1088/1475-7516/2022/08/065. arXiv:2202.01126 [astro-ph.CO]

Freigang J, Lust D, Nian GE et al (2023) Cosmic acceleration and turns in the Swampland. JCAP 11:080. https://doi.org/10.1088/1475-7516/2023/11/080. arXiv:2306.17217 [hep-th]

Fujita T, Kawasaki M, Tada Y et al (2013) A new algorithm for calculating the curvature perturbations in stochastic inflation. JCAP 12:036. https://doi.org/10.1088/1475-7516/2013/12/036. arXiv:1308.4754 [astro-ph.CO]

Fumagalli J, Bhattacharya S, Peloso M et al (2024) One-loop infrared rescattering by enhanced scalar fluctuations during inflation. JCAP 04:029. https://doi.org/10.1088/1475-7516/2024/04/029. arXiv:2307.08358 [astro-ph.CO]

Fumagalli J, Garcia-Saenz S, Pinol L et al (2019) Hyper-non-gaussianities in inflation with strongly nongeodesic motion. Phys Rev Lett 123(20):201302. https://doi.org/10.1103/PhysRevLett.123.201302. arXiv:1902.03221 [hep-th]

Fumagalli J, Palma GA, Renaux-Petel S et al (2022a) Primordial gravitational waves from excited states. JHEP 03:196. https://doi.org/10.1007/JHEP03(2022)196. arXiv:2111.14664 [astro-ph.CO]

Fumagalli J, Pieroni M, Renaux-Petel S et al (2022b) Detecting primordial features with LISA. JCAP 07 (07):020. https://doi.org/10.1088/1475-7516/2022/07/020. arXiv:2112.06903 [astro-ph.CO]

Fumagalli J, Renaux-Petel S, Ronayne JW et al (2023) Turning in the landscape: a new mechanism for generating primordial black holes. Phys Lett B 841:137921. https://doi.org/10.1016/j.physletb.2023.137921. arXiv:2004.08369 [hep-th]

Fumagalli J, Renaux-Petel S, Witkowski LT (2021a) Oscillations in the stochastic gravitational wave background from sharp features and particle production during inflation. JCAP 08:030. https://doi.org/10.1088/1475-7516/2021/08/030. arXiv:2012.02761 [astro-ph.CO]
Fumagalli J, Renaux-Petel S, Witkowski LT (2021b) Resonant features in the stochastic gravitational wave background. JCAP 08:059. https://doi.org/10.1088/1475-7516/2021/08/059. arXiv:2105.06481 [astro-ph.CO]

Fumagalli J (2023) Absence of one-loop effects on large scales from small scales in non-slow-roll dynamics. arXiv e-prints arXiv:2305.19263 [astro-ph.CO]

Gaggero D, Bertone G, Calore F et al (2017) Searching for primordial black holes in the radio and X-ray sky. Phys Rev Lett 118(24):241101. https://doi.org/10.1103/PhysRevLett.118.241101. arXiv:1612.00457 [astro-ph.HE]

Garcia-Saenz S, Pinol L, Renaux-Petel S et al (2023) No-go theorem for scalar-trispectrum-induced gravitational waves. JCAP 03:057. https://doi.org/10.1088/1475-7516/2023/03/057. arXiv:2207.14267 [astro-ph.CO]

Garcia-Saenz S, Renaux-Petel S (2018) Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of sound. JCAP 11:005. https://doi.org/10.1088/1475-7516/2018/11/005. arXiv:1805.12563 [hep-th]

Garcia-Saenz S, Renaux-Petel S, Ronayne J (2018) Primordial fluctuations and non-Gaussianities in sidetracked inflation. JCAP 07:057. https://doi.org/10.1088/1475-7516/2018/07/057. arXiv:1804.11279 [astro-ph.CO]

García-Bellido J (2017) Massive primordial black holes as dark matter and their detection with gravitational waves. J Phys Conf Ser 840(1):012032. https://doi.org/10.1088/1742-6596/840/1/012032. arXiv:1702.08275 [astro-ph.CO]

García-Bellido J (2019) Primordial black holes and the origin of the matter-antimatter asymmetry. Phil Trans Roy Soc Lond A 377(2161):20190091. https://doi.org/10.1098/rsta.2019.0091

García-Bellido J, Carr B, Clesse S (2021a) Primordial black holes and a common origin of baryons and dark matter. Universe 8(1):12. https://doi.org/10.3390/universe8010012. arXiv:1904.11482 [astro-ph.CO]

García-Bellido J, Clesse S (2018) Constraints from microlensing experiments on clustered primordial black holes. Phys Dark Univ 19:144–148. https://doi.org/10.1016/j.dark.2018.01.001. arXiv:1710.04694 [astro-ph.CO]

García-Bellido J, Clesse S, Fleury P (2018) Primordial black holes survive SN lensing constraints. Phys Dark Univ 20:95–100. https://doi.org/10.1016/j.dark.2018.04.005. arXiv:1712.06574 [astro-ph.CO]

García-Bellido J, Jaraba S, Kuroyanagi S (2022) The stochastic gravitational wave background from close hyperbolic encounters of primordial black holes in dense clusters. Phys Dark Univ 36:101009. https://doi.org/10.1016/j.dark.2022.101009. arXiv:2109.11376 [gr-qc]

García-Bellido J, Linde AD, Wands D (1996) Density perturbations and black hole formation in hybrid inflation. Phys Rev D 54:6040–6058. https://doi.org/10.1103/PhysRevD.54.6040. arXiv:astro-ph/9605094

García-Bellido J, Murayama H, White G (2021b) Exploring the early Universe with Gaia and Theia. JCAP 12(12):023. https://doi.org/10.1088/1475-7516/2021/12/023. arXiv:2104.04778 [hep-ph]

García-Bellido J, Nesseris S (2017) Gravitational wave bursts from Primordial Black Hole hyperbolic encounters. Phys Dark Univ 18:123–126. https://doi.org/10.1016/j.dark.2017.10.002. arXiv:1706.02111 [astro-ph.CO]

García-Bellido J, Nesseris S (2018) Gravitational wave energy emission and detection rates of Primordial Black Hole hyperbolic encounters. Phys Dark Univ 21:61–69. https://doi.org/10.1016/j.dark.2018.06.001. arXiv:1711.09702 [astro-ph.HE]

García-Bellido J, Nuño Siles JF, Ruiz Morales E (2021c) Bayesian analysis of the spin distribution of LIGO/Virgo black holes. Phys Dark Univ 31:100791. https://doi.org/10.1016/j.dark.2021.100791. arXiv:2010.13811 [astro-ph.CO]

García-Bellido J, Papageorgiou A, Peloso M et al (2024) A flashing beacon in axion inflation: recurring bursts of gravitational waves in the strong backreaction regime. JCAP 01:034. https://doi.org/10.1088/1475-7516/2024/01/034. arXiv:2303.13425 [astro-ph.CO]

García-Bellido J, Peloso M, Ünal C (2016) Gravitational waves at interferometer scales and primordial black holes in axion inflation. JCAP 12:031. https://doi.org/10.1088/1475-7516/2016/12/031. arXiv:1610.03763 [astro-ph.CO]

García-Bellido J, Peloso M, Ünal C (2017) Gravitational wave signatures of inflationary models from primordial black hole dark matter. JCAP 09:013. https://doi.org/10.1088/1475-7516/2017/09/013. arXiv:1707.02441 [astro-ph.CO]

García-Bellido J, Ruiz Morales E (2017) Primordial black holes from single field models of inflation. Phys Dark Univ 18:47–54. https://doi.org/10.1016/j.dark.2017.09.007. arXiv:1702.03901 [astro-ph.CO]
García-Bellido J (2018) Primordial Black Holes. PoS EDSU2018:042. https://doi.org/10.22323/1.335.0042

García-Bellido J, Hawkins M (2024) Reanalysis of the MACHO constraints on PBH in the light of Gaia DR3 data. arXiv e-prints arXiv:2402.00212 [astro-ph.GA]

Garriga J, Sakellariadou M (1993) Effects of friction on cosmic strings. Phys Rev D 48:2502-2515. https://doi.org/10.1103/PhysRevD.48.2502. arXiv:hep-th/9303024

Garriga J, Vilenkin A (1993) Black holes from nucleating strings. Phys Rev D 47:3265-3274. https://doi.org/10.1103/PhysRevD.47.3265. arXiv:hep-ph/9208212

Garriga J, Vilenkin A, Zhang J (2016) Black holes and the multiverse. JCAP 02:064. https://doi.org/10.1088/1475-7516/2016/02/064. arXiv:1512.01819 [hep-th]

Ge S (2020) Sublunar-mass primordial black holes from closed axion domain walls. Phys Dark Univ 27:100440. https://doi.org/10.1016/j.dark.2019.100440. arXiv:1905.12182 [hep-ph]

Geller M, Hook A, Sundrum R et al (2018) Primordial anisotropies in the gravitational wave background from cosmological phase transitions. Phys Rev Lett 121(20):201303. https://doi.org/10.1103/PhysRevLett.121.201303. arXiv:1803.10780 [hep-ph]

Geller SR, Qin W, McDonough E et al (2022) Primordial black holes from multifield inflation with nonminimal couplings. Phys Rev D 106(6):063535. https://doi.org/10.1103/PhysRevD.106.063535. arXiv:2205.04471 [hep-th]

Germani C, Musco I (2019) Abundance of primordial black holes depends on the shape of the inflationary power spectrum. Phys Rev Lett 122(14):141302. https://doi.org/10.1103/PhysRevLett.122.141302. arXiv:1805.04087 [astro-ph.CO]

Ghosh T, Ghoshal A, Guo HK et al (2024) Did we hear the sound of the Universe boiling? Analysis using the full fluid velocity profiles and NANOGrav 15-year data. JCAP 05:100. https://doi.org/10.1088/1475-7516/2024/05/100. arXiv:2307.02259 [astro-ph.HE]

Ghoshal A, Strumia A (2024) Probing the Dark Matter density with gravitational waves from super-massive binary black holes. JCAP 02:054. https://doi.org/10.1088/1475-7516/2024/02/054. arXiv:2306.17158 [astro-ph.CO]

Ginés EU, Mena O, Witte SJ (2022) Revisiting constraints on WIMPs around primordial black holes. Phys Rev D 106(6):063538. https://doi.org/10.1103/PhysRevD.106.063538. arXiv:2207.09481 [astro-ph.CO]

Glicenstein JF, Barnacka A, Vivier M, et al (2013) Limits on Primordial Black Hole evaporation with the H.E.S.S. array of Cherenkov telescopes. In: 33rd International Cosmic Ray Conference, p 0930, arXiv:1307.4898

Goncharov B et al (2021) On the evidence for a common-spectrum process in the search for the nanohertz gravitational-wave background with the parkes pulsar timing array. Astrophys J Lett 917(2):L19. https://doi.org/10.3847/2041-8213/ac17f4. arXiv:2107.12112 [astro-ph.HE]

Gong JO (2022) Analytic integral solutions for induced gravitational waves. Astrophys J 925(1):102. https://doi.org/10.3847/1538-4357/ac3a6c. arXiv:1909.12708 [gr-qc]

Gong JO, Stewart ED (2001) The density perturbation power spectrum to second order corrections in the slow roll expansion. Phys Lett B 510:1-9. https://doi.org/10.1016/S0370-2693(01)00616-5. arXiv:astro-ph/0101225 [astro-ph]

Gong Y, Yue B, Cao Y et al (2023) Fuzzy dark matter as a solution to reconcile the stellar mass density of high-z massive galaxies and reionization history. Astrophys J 947(1):28. https://doi.org/10.3847/1538-4357/acc109. arXiv:2209.13757 [astro-ph.CO]

Gorghetto M, Hardy E, Nicolaescu H (2021) Observing invisible axions with gravitational waves. JCAP 06:034. https://doi.org/10.1088/1475-7516/2021/06/034. arXiv:2101.11007 [hep-ph]

Gorton M, Green AM (2022) Effect of clustering on primordial black hole microlensing constraints. JCAP 08(08):035. https://doi.org/10.1088/1475-7516/2022/08/035. arXiv:2203.04209 [astro-ph.CO]

Gosenca M, Adamek J, Byrnes CT et al (2017) 3D simulations with boosted primordial power spectra and ultracompact minihalos. Phys Rev D 96(12):123519. https://doi.org/10.1103/PhysRevD.96.123519. arXiv:1710.02055 [astro-ph.CO]

Gould A (1992) Femtolensing of gamma-ray bursters. Astrophys J Lett 386:L5. https://doi.org/10.1086/186279

Gouttenoire Y (2023) First-order phase transition interpretation of pulsar timing array signal is consistent with solar-mass black holes. Phys Rev Lett 131(17):171404. https://doi.org/10.1103/PhysRevLett.131.171404. arXiv:2307.04239 [hep-ph]

Gouttenoire Y, Vitagliano E (2024) Domain wall interpretation of the PTA signal confronting black hole overproduction. Phys Rev D 110(6):L061306. https://doi.org/10.1103/PhysRevD.110.L061306. arXiv:2306.17841 [gr-qc]
Gouttenoire Y, Volansky T (2024) Primordial black holes from supercooled phase transitions. Phys Rev D 110(4):043514. https://doi.org/10.1103/PhysRevD.110.043514. arXiv:2305.04942 [hep-ph]

Gow AD, Assadullahi H, Jackson JHP et al (2023) Non-perturbative non-Gaussianity and primordial black holes. EPL 142(4):49001. https://doi.org/10.1209/0295-5075/acd417. arXiv:2211.08348 [astro-ph.CO]

Gow AD, Byrnes CT, Cole PS et al (2021) The power spectrum on small scales: robust constraints and comparing PBH methodologies. JCAP 02:002. https://doi.org/10.1088/1475-7516/2021/02/002. arXiv:2008.03289 [astro-ph.CO]

Gow AD, Byrnes CT, Hall A et al (2020) Primordial black hole merger rates: distributions for multiple LIGO observables. JCAP 01:031. https://doi.org/10.1088/1475-7516/2020/01/031. arXiv:1911.12685 [astro-ph.CO]

Gow AD, Byrnes CT, Cole PS, et al (2020) The power spectrum on small scales: robust constraints and comparing PBH methodologies. arXiv e-prints arXiv:2008.03289. arXiv:2008.03289 [astro-ph.CO]

Graham PW, Rajendran S, Varela J (2015) Dark matter triggers of supernovae. Phys Rev D 92(6):063007. https://doi.org/10.1103/PhysRevD.92.063007. arXiv:1505.04444 [hep-ph]

Green AM (2016) Microlensing and dynamical constraints on primordial black hole dark matter with an extended mass function. Phys Rev D 94(6):063530. https://doi.org/10.1103/PhysRevD.94.063530. arXiv:1609.01143 [astro-ph.CO]

Green AM (2017) Astrophysical uncertainties on stellar microlensing constraints on multi-Solar mass primordial black hole dark matter. Phys Rev D 96(4):043020. https://doi.org/10.1103/PhysRevD.96.043020. arXiv:1705.10818 [astro-ph.CO]

Green AM, Liddle AR (1997) Constraints on the density perturbation spectrum from primordial black holes. Phys Rev D 56:6166-6174. https://doi.org/10.1103/PhysRevD.56.6166. arXiv:astro-ph/9704251

Green AM, Liddle AR, Riotto A (1997) Primordial black hole constraints in cosmologies with early matter domination. Phys Rev D 56:7559-7565. https://doi.org/10.1103/PhysRevD.56.7559. arXiv:astro-ph/9705166

Green AM, Malik KA (2001) Primordial black hole production due to preheating. Phys Rev D 64:021301. https://doi.org/10.1103/PhysRevD.64.021301. arXiv:hep-ph/0008113 [hep-ph]

Groot Nibbelink S, van Tent BJW (2002) Scalar perturbations during multiple field slow-roll inflation. Class Quant Grav 19:613-640. https://doi.org/10.1088/0264-9381/19/4/302. arXiv:hep-ph/0107272

Groot Nibbelink S, van Tent BJW (2000) Density perturbations arising from multiple field slow roll inflation. arXiv e-prints arXiv:hep-ph/0011325

Gröbner M, Jetzer P, Haney M et al (2020) A note on the gravitational wave energy spectrum of parabolic and hyperbolic encounters. Class Quant Grav 37(6):067002. https://doi.org/10.1088/1361-6382/ab6be2. arXiv:2001.05187 [gr-qc]

Guo HK, Shu J, Zhao Y (2019a) Using LISA-like Gravitational wave detectors to search for primordial black holes. Phys Rev D 99(2):023001. https://doi.org/10.1103/PhysRevD.99.023001. arXiv:1709.03500 [astro-ph.CO]

Guo HK, Sinha K, Sun C (2019b) Probing boson stars with extreme mass ratio inspirals. JCAP 09:032. https://doi.org/10.1088/1475-7516/2019/09/032. arXiv:1904.07871 [hep-ph]

Guo HK, Miller A (2022) Searching for mini extreme mass ratio inspirals with gravitational-wave detectors. arXiv e-prints arXiv:2205.10359 [astro-ph.IM]

Guzzetti M, Bartolo N, Liguori M et al (2016) Gravitational waves from inflation. Riv Nuovo Cim 39 (9):399-495. https://doi.org/10.1393/ncr/i2016-10127-1. arXiv:1605.01615 [astro-ph.CO]

Hall A, Gow AD, Byrnes CT (2020) Bayesian analysis of LIGO-Virgo mergers: primordial vs. astrophysical black hole populations. Phys Rev D 102:123524. https://doi.org/10.1103/PhysRevD.102.123524. arXiv:2008.13704 [astro-ph.CO]

Hamadache C et al (2006) Galactic bulge microlensing optical depth from eros-2. Astron Astrophys 454:185-199. https://doi.org/10.1051/0004-6361:20064893. arXiv:astro-ph/0601510

Harada T, Yoo CM, Kohri K (2013) Threshold of primordial black hole formation. Phys Rev D 88 (8):084051. https://doi.org/10.1103/PhysRevD.88.084051. [Erratum: Phys. Rev. D 89, 029903 (2014)] arXiv:1309.4201 [astro-ph.CO]

Harada T, Yoo CM, Kohri K et al (2016) Primordial black hole formation in the matter-dominated phase of the Universe. Astrophys J 833(1):61. https://doi.org/10.3847/1538-4357/833/1/61. arXiv:1609.01588 [astro-ph.CO]
Harada T, Yoo CM, Kohri K et al (2017) Spins of primordial black holes formed in the matter-dominated phase of the Universe. Phys Rev D 96(8):083517. https://doi.org/10.1103/PhysRevD.96.083517. [Erratum: Phys. Rev. D 99, 069904 (2019)] arXiv:1707.03595 [gr-qc]

Harada T, Yoo CM, Kohri K et al (2021) Spins of primordial black holes formed in the radiation-dominated phase of the universe: first-order effect. Astrophys J 908(2):140. https://doi.org/10.3847/1538-4357/abd9b9. arXiv:2011.00710 [astro-ph.CO]

Harikane Y, Ouchi M, Oguri M, et al (2023) A comprehensive study of galaxies at z ~ 9–16 found in the early JWST data: ultraviolet luminosity functions and cosmic star formation history at the pre-reionization epoch. Astrophys J Suppl 265(1). https://doi.org/10.3847/1538-4365/acaaa9, arXiv: 2208.01612 [astro-ph.GA]

Hartwig T, Volonteri M, Bromm V et al (2016) Gravitational waves from the remnants of the first stars. Mon Not R Astron Soc 460(1):L74–L78. https://doi.org/10.1093/mnrasl/slw074. arXiv:1603.05655 [astro-ph.GA]

Hasinger G (2020) Illuminating the dark ages: cosmic backgrounds from accretion onto primordial black hole dark matter. JCAP 07:022. https://doi.org/10.1088/1475-7516/2020/07/022. arXiv:2003.05150 [astro-ph.CO]

Hawking S (1971) Gravitationally collapsed objects of very low mass. Mon Not R Astron Soc 152:75

Hawking SW (1975) Particle creation by black holes. Commun Math Phys 43:199–220. https://doi.org/10.1007/BF02345020. ([Erratum: Commun. Math. Phys. 46, 206 (1976)])

Hawking SW (1989) Black holes from cosmic strings. Phys Lett B 231:237–239. https://doi.org/10.1016/0370-2693(89)90206-2

Hawking SW (1990) Gravitational radiation from collapsing cosmic string loops. Phys Lett B 246:36–38. https://doi.org/10.1016/0370-2693(90)91304-T

Hawking SW, Moss IG, Stewart JM (1982) Bubble collisions in the very early universe. Phys Rev D 26:2681. https://doi.org/10.1103/PhysRevD.26.2681

Hawkins MRS (1993) Gravitational microlensing, quasar variability and missing matter. Nature 366 (6452):242–245. https://doi.org/10.1038/366242a0

Hawkins MRS (2007) Timescale of variation and the size of the accretion disc in active galactic nuclei. Astron Astrophys 462:581. https://doi.org/10.1051/0004-6361:20066283. arXiv:astro-ph/0611491

Hawkins MRS (2015) A new look at microlensing limits on dark matter in the Galactic halo. Astron Astrophys 575:A107. https://doi.org/10.1051/0004-6361/201425400. arXiv:1503.01935 [astro-ph.CO]

Hawkins MRS (2020a) SDSS J1004+4112: the case for a galaxy cluster dominated by primordial black holes. Astron Astrophys 643:A10. https://doi.org/10.1051/0004-6361/202038670. arXiv:2010.15007 [astro-ph.CO]

Hawkins MRS (2020b) The signature of primordial black holes in the dark matter halos of galaxies. Astron Astrophys 633:A107. https://doi.org/10.1051/0004-6361/201936462. arXiv:2001.07633 [astro-ph.CO]

Hawkins MRS (2022) New evidence for a cosmological distribution of stellar mass primordial black holes. Mon Not R Astron Soc 512(4):5706–5714. https://doi.org/10.1093/mnras/stac863. arXiv:2204.09143 [astro-ph.CO]

Heggie DC (1975) Binary evolution in stellar dynamics. Mon Not R Astron Soc 173:729–787. https://doi.org/10.1093/mnras/173.3.729

Hektor A, Hütsi G, Marzola L et al (2018) Constraining primordial black holes with the EDGES 21 cm absorption signal. Phys Rev D 98(2):023503. https://doi.org/10.1103/PhysRevD.98.023503. arXiv:1803.09697 [astro-ph.CO]

Helfer T, Aurrekoetxea JC, Lim EA (2019) Cosmic string loop collapse in full general relativity. Phys Rev D 99(10):104028. https://doi.org/10.1103/PhysRevD.99.104028. arXiv:1808.06678 [gr-qc]

Hellings RW, Downs GS (1983) Upper limits on the isotropic gravitational radiation background from pulsar timing analysis. Astrophys J Lett 265:L39–L42. https://doi.org/10.1086/183954

Herman N, Füzfa A, Lehoucq L et al (2021) Detecting planetary-mass primordial black holes with resonant electromagnetic gravitational-wave detectors. Phys Rev D 104(2):023524. https://doi.org/10.1103/PhysRevD.104.023524. arXiv:2012.12189 [gr-qc]

Herman N, Lehoucq L, Füzfa A (2023) Electromagnetic antennas for the resonant detection of the stochastic gravitational wave background. Phys Rev D 108(12):124009. https://doi.org/10.1103/PhysRevD.108.124009. arXiv:2203.15668 [gr-qc]

Hertzberg MP, Nurmi S, Schiappacasse ED et al (2021) Shining primordial black holes. Phys Rev D 103 (6):063025. https://doi.org/10.1103/PhysRevD.103.063025. arXiv:2011.05922 [hep-ph]
Hertzberg MP, Schiappacasse ED, Yanagida TT (2020) Implications for dark matter direct detection in the presence of LIGO-motivated primordial black holes. Phys Lett B 807:135566. https://doi.org/10.1016/j.physletb.2020.135566. arXiv:1910.10575 [astro-ph.CO]

Hertzberg MP, Yamada M (2018) Primordial black holes from polynomial potentials in single field inflation. Phys Rev D 97(8):083509. https://doi.org/10.1103/PhysRevD.97.083509. arXiv:1712.09750 [astro-ph.CO]

Hidalgo JC, Urena-Lopez LA, Liddle AR (2012) Unification models with reheating via Primordial Black Holes. Phys Rev D 85:044055. https://doi.org/10.1103/PhysRevD.85.044055. arXiv:1107.5669 [astro-ph.CO]

Hindmarsh M, Kume J (2023) Multi-messenger constraints on Abelian-Higgs cosmic string networks. JCAP 04:045. https://doi.org/10.1088/1475-7516/2023/04/045. arXiv:2210.06178 [astro-ph.CO]

Hook A, Marques-Tavares G, Racco D (2021) Causal gravitational waves as a probe of free streaming particles and the expansion of the Universe. JHEP 02:117. https://doi.org/10.1007/JHEP02(2021)117. arXiv:2010.03568 [hep-ph]

Hooper D, Ireland A, Krnjaic G (2023) Cosmological magnetic fields from primordial Kerr-Newman black holes. Phys Rev D 107(10):103524. https://doi.org/10.1103/PhysRevD.107.103524. arXiv:2206.04066 [astro-ph.CO]

Hooper D, Krnjaic G, McDermott SD (2019) Dark radiation and superheavy dark matter from black hole domination. JHEP 08:001. https://doi.org/10.1007/JHEP08(2019)001. arXiv:1905.01301 [hep-ph]

Hotchkiss S, Mazumdar A, Nadathur S (2011) Inflection point inflation: WMAP constraints and a solution to the fine-tuning problem. JCAP 06:002. https://doi.org/10.1088/1475-7516/2011/06/002. arXiv:1101.6046 [astro-ph.CO]

Hoyle F, Lyttleton RA (1939) The effect of interstellar matter on climatic variation. Proceedings of the Cambridge Philosophical Society 35(3):405. https://doi.org/10.1017/S0305004100021150

Hoyle F, Lyttleton RA (1940a) On the accretion of interstellar matter by stars. Proc Cambridge Philos Soc 36(3):325. https://doi.org/10.1017/S0305004100017369

Hoyle F, Lyttleton RA (1940b) On the physical aspects of accretion by stars. Proc Cambridge Philos Soc 36(4):424. https://doi.org/10.1017/S0305004100017461

Hwang JC, Jeong D, Noh H (2017) Gauge dependence of gravitational waves generated from scalar perturbations. Astrophys J 842(1):46. https://doi.org/10.3847/1538-4357/aa74be. arXiv:1704.03500 [astro-ph.CO]

Hütsi G, Koivisto T, Raidal M et al (2021a) Cosmological black holes are not described by the Thakurta metric: LIGO-Virgo bounds on PBHs remain unchanged. Eur Phys J C 81(11):999. https://doi.org/10.1140/epjc/s10052-021-09803-4. arXiv:2105.09328 [astro-ph.CO]

Hütsi G, Raidal M, Urrutia J et al (2023) Did JWST observe imprints of axion miniclusters or primordial black holes? Phys Rev D 107(4):043502. https://doi.org/10.1103/PhysRevD.107.043502. arXiv:2211.02651 [astro-ph.CO]

Hütsi G, Raidal M, Vaskonen V et al (2021c) Two populations of LIGO-Virgo black holes. JCAP 03:068. https://doi.org/10.1088/1475-7516/2021/03/068. arXiv:2012.02786 [astro-ph.CO]

Hütsi G, Raidal M, Veermäe H (2019) Small-scale structure of primordial black hole dark matter and its implications for accretion. Phys Rev D 100(8):083016. https://doi.org/10.1103/PhysRevD.100.083016. arXiv:1907.06533 [astro-ph.CO]

Hütsi G, Koivisto T, Raidal M, et al (2021b) Reply to "Comment on: Cosmological black holes are not described by the Thakurta metric". arXiv e-prints arXiv:2106.02007 [astro-ph.CO]

Iacconi L, Assadullahi H, Fasiello M et al (2022) Revisiting small-scale fluctuations in $\alpha$-attractor models of inflation. JCAP 06(06):007. https://doi.org/10.1088/1475-7516/2022/06/007. arXiv:2112.05092 [astro-ph.CO]

Inayoshi K, Hirai R, Kinugawa T et al (2017) Formation pathway of Population III coalescing binary black holes through stable mass transfer. Mon Not R Astron Soc 468(4):5020–5032. https://doi.org/10.1093/mnras/stx757. arXiv:1701.04823 [astro-ph.HE]

Inman D, Ali-Haïmoud Y (2019) Early structure formation in primordial black hole cosmologies. Phys Rev D 100(8):083528. https://doi.org/10.1103/PhysRevD.100.083528. arXiv:1907.08129 [astro-ph.CO]

Inomata K, Braglia M, Chen X et al (2023) Questions on calculation of primordial power spectrum with large spikes: the resonance model case. JCAP 04:011. https://doi.org/10.1088/1475-7516/2023/04/011. arXiv:2211.02586 [astro-ph.CO]

Inomata K, Kawasaki M, Mukaida K et al (2017) Inflationary primordial black holes for the LIGO gravitational wave events and pulsar timing array experiments. Phys Rev D 95(12):123510. https://doi.org/10.1103/PhysRevD.95.123510. arXiv:1611.06130 [astro-ph.CO]
Inomata K, Kawasaki M, Mukaida K et al (2018) Double inflation as a single origin of primordial black holes for all dark matter and LIGO observations. Phys Rev D 97(4):043514. https://doi.org/10.1103/PhysRevD.97.043514. arXiv:1711.06129 [astro-ph.CO]

Inomata K, Kawasaki M, Mukaida K et al (2020) Gravitational wave production right after a primordial black hole evaporation. Phys Rev D 101(12):123533. https://doi.org/10.1103/PhysRevD.101.123533. arXiv:2003.10455 [astro-ph.CO]

Inomata K, Kawasaki M, Mukaida K et al (2021a) NANOGrav results and LIGO-Virgo primordial black holes in axionlike curvaton models. Phys Rev Lett 126(13):131301. https://doi.org/10.1103/PhysRevLett.126.131301. arXiv:2011.01270 [astro-ph.CO]

Inomata K, Kohri K, Nakama T et al (2019a) Enhancement of gravitational waves induced by scalar perturbations due to a sudden transition from an early matter era to the radiation era. Phys Rev D 100 (4):043532. https://doi.org/10.1103/PhysRevD.100.043532. arXiv:1904.12879 [astro-ph.CO]

Inomata K, Kohri K, Nakama T et al (2019b) Gravitational waves induced by scalar perturbations during a gradual transition from an early matter era to the radiation era. JCAP 10:071. https://doi.org/10.1088/1475-7516/2019/10/071. arXiv:1904.12878 [astro-ph.CO]

Inomata K, Kohri K, Terada T (2024) Detected stochastic gravitational waves and subsolar-mass primordial black holes. Phys Rev D 109(6):063506. https://doi.org/10.1103/PhysRevD.109.063506. arXiv:2306.17834 [astro-ph.CO]

Inomata K, McDonough E, Hu W (2021b) Primordial black holes arise when the inflaton falls. Phys Rev D 104(12):123553. https://doi.org/10.1103/PhysRevD.104.123553. arXiv:2104.03972 [astro-ph.CO]

Inomata K, McDonough E, Hu W (2022) Amplification of primordial perturbations from the rise or fall of the inflaton. JCAP 02(02):031. https://doi.org/10.1088/1475-7516/2022/02/031. arXiv:2110.14641 [astro-ph.CO]

Inomata K, Nakama T (2019) Gravitational waves induced by scalar perturbations as probes of the small-scale primordial spectrum. Phys Rev D 99(4):043511. https://doi.org/10.1103/PhysRevD.99.043511. arXiv:1812.00674 [astro-ph.CO]

Inomata K, Terada T (2020) Gauge independence of induced gravitational waves. Phys Rev D 101 (2):023523. https://doi.org/10.1103/PhysRevD.101.023523. arXiv:1912.00785 [gr-qc]

Inoue Y, Kusenko A (2017) New X-ray bound on density of primordial black holes. JCAP 10:034. https://doi.org/10.1088/1475-7516/2017/10/034. arXiv:1705.00791 [astro-ph.CO]

Ioka K, Chiba T, Tanaka T et al (1998) Black hole binary formation in the expanding universe: three body problem approximation. Phys Rev D 58:063003. https://doi.org/10.1103/PhysRevD.58.063003. arXiv:astro-ph/9807018

Ivanov P (1997) Nonlinear metric perturbations and production of primordial black holes. Phys Rev D 57:7145-7154. https://doi.org/10.1103/PhysRevD.57.7145. arXiv:astro-ph/9708224

Ivanov VR, Ketov SV, Pozdeeva EO et al (2022) Analytic extensions of Starobinsky model of inflation. JCAP 03(03):058. https://doi.org/10.1088/1475-7516/2022/03/058. arXiv:2111.09058 [gr-qc]

Ivanov P, Naselsky P, Novikov I (1994) Inflation and primordial black holes as dark matter. Phys Rev D 50:7173-7178. https://doi.org/10.1103/PhysRevD.50.7173

Jackson JHP, Assadullahi H, Koyama K et al (2022) Numerical simulations of stochastic inflation using importance sampling. JCAP 10:067. https://doi.org/10.1088/1475-7516/2022/10/067. arXiv:2206.11234 [astro-ph.CO]

Jain RK, Chingangbam P, Gong JO et al (2009) Punctuated inflation and the low CMB multipoles. JCAP 01:009. https://doi.org/10.1088/1475-7516/2009/01/009. arXiv:0809.3915 [astro-ph]

Jain RK, Chingangbam P, Sriramkumar L et al (2010) The tensor-to-scalar ratio in punctuated inflation. Phys Rev D 82:023509. https://doi.org/10.1103/PhysRevD.82.023509. arXiv:0904.2518 [astro-ph.CO]

James-Turner C, Weil DPB, Green AM et al (2020) Constraints on the cosmic string loop collapse fraction from primordial black holes. Phys Rev D 101(12):123526. https://doi.org/10.1103/PhysRevD.101.123526. arXiv:1911.12658 [astro-ph.CO]

Jangra P, Kavanagh BJ, Diego JM (2023) Impact of dark matter spikes on the merger rates of Primordial Black Holes. JCAP 11:069. https://doi.org/10.1088/1475-7516/2023/11/069. arXiv:2304.05892 [astro-ph.CO]

Jaraba S, Garcia-Bellido J (2021) Black hole induced spins from hyperbolic encounters in dense clusters. Phys Dark Univ 34:100882. https://doi.org/10.1016/j.dark.2021.100882. arXiv:2106.01436 [gr-qc]

Jedamzik K (1997) Primordial black hole formation during the QCD epoch. Phys Rev D 55:5871-5875. https://doi.org/10.1103/PhysRevD.55.R5871. arXiv:astro-ph/9605152
Jedamzik K (2020) Primordial black hole dark matter and the LIGO/Virgo observations. JCAP 09:022. https://doi.org/10.1088/1475-7516/2020/09/022. arXiv:2006.11172 [astro-ph.CO]

Jedamzik K (2021) Consistency of primordial black hole dark matter with LIGO/Virgo merger rates. Phys Rev Lett 126(5):051302. https://doi.org/10.1103/PhysRevLett.126.051302. arXiv:2007.03565 [astro-ph.CO]

Jedamzik K, Lemoine M, Martin J (2010) Collapse of small-scale density perturbations during preheating in single field inflation. JCAP 09:034. https://doi.org/10.1088/1475-7516/2010/09/034. arXiv:1002.3039 [astro-ph.CO]

Jedamzik K, Niemeyer JC (1999) Primordial black hole formation during first order phase transitions. Phys Rev D 59:124014. https://doi.org/10.1103/PhysRevD.59.124014. arXiv:astro-ph/9901293

Jedamzik K, Sigl G (2000) On metric preheating. Phys Rev D 61:023519. https://doi.org/10.1103/PhysRevD.61.023519. arXiv:hep-ph/9906287

Jenkins AC, O'Shaughnessy R, Sakellariadou M et al (2019a) Anisotropies in the astrophysical gravitational-wave background: the impact of black hole distributions. Phys Rev Lett 122 (11):111101. https://doi.org/10.1103/PhysRevLett.122.111101. arXiv:1810.13435 [astro-ph.CO]

Jenkins AC, Romano JD, Sakellariadou M (2019b) Estimating the angular power spectrum of the gravitational-wave background in the presence of shot noise. Phys Rev D 100(8):083501. https://doi.org/10.1103/PhysRevD.100.083501. arXiv:1907.06642 [astro-ph.CO]

Jenkins AC, Sakellariadou M (2018) Anisotropies in the stochastic gravitational-wave background: formalism and the cosmic string case. Phys Rev D 98(6):063509. https://doi.org/10.1103/PhysRevD.98.063509. arXiv:1802.06046 [astro-ph.CO]

Jenkins AC, Sakellariadou M (2019) Shot noise in the astrophysical gravitational-wave background. Phys Rev D 100(6):063508. https://doi.org/10.1103/PhysRevD.100.063508. arXiv:1902.07719 [astro-ph.CO]

Jenkins AC, Sakellariadou M, Regimbau T et al (2018) Anisotropies in the astrophysical gravitational-wave background: predictions for the detection of compact binaries by LIGO and Virgo. Phys Rev D 98(6):063501. https://doi.org/10.1103/PhysRevD.98.063501. arXiv:1806.01718 [astro-ph.CO]

Jenkins AC, Sakellariadou M (2020) Primordial black holes from cusp collapse on cosmic strings. arXiv e-prints arXiv:2006.16249 [astro-ph.CO]

Jeong D, Kamionkowski M (2012) Clustering fossils from the early universe. Phys Rev Lett 108 (25):251301. https://doi.org/10.1103/PhysRevLett.108.251301. arXiv:1203.0302 [astro-ph.CO]

Jin JH, Chen ZC, Yi Z et al (2023) Confronting sound speed resonance with pulsar timing arrays. JCAP 09:016. https://doi.org/10.1088/1475-7516/2023/09/016. arXiv:2307.08687 [astro-ph.CO]

Joana C (2022) Gravitational dynamics in Higgs inflation: preinflation and preheating with an auxiliary field. Phys Rev D 106(2):023504. https://doi.org/10.1103/PhysRevD.106.023504. arXiv:2202.07604 [astro-ph.CO]

Juan JI, Serpico PD, Franco Abellán G (2022) The QCD phase transition behind a PBH origin of LIGO/Virgo events? JCAP 07(07):009. https://doi.org/10.1088/1475-7516/2022/07/009. arXiv:2204.07027 [astro-ph.CO]

Jung TH, Okui T (2021) Primordial black holes from bubble collisions during a first-order phase transition. arXiv e-prints arXiv:2110.04271 [hep-ph]

Kadota K, Silk J (2021) Boosting small-scale structure via primordial black holes and implications for sub-GeV dark matter annihilation. Phys Rev D 103(4):043530. https://doi.org/10.1103/PhysRevD.103.043530. arXiv:2012.03698 [astro-ph.CO]

Kadota K, Tashiro H (2022) Primordial black hole dark matter in the presence of p-wave WIMP annihilation. JCAP 03(03):045. https://doi.org/10.1088/1475-7516/2022/03/045. arXiv:2112.04179 [astro-ph.CO]

Kalaja A, Bellomo N, Bartolo N et al (2019) From primordial black holes abundance to primordial curvature power spectrum (and back). JCAP 10:031. https://doi.org/10.1088/1475-7516/2019/10/031. arXiv:1908.03596 [astro-ph.CO]

Kallosh R, Linde A (2022) Dilaton-axion inflation with PBHs and GWs. JCAP 08(08):037. https://doi.org/10.1088/1475-7516/2022/08/037. arXiv:2203.10437 [hep-th]

Kamenshchik AY, Tronconi A, Vardanyan T et al (2019) Non-canonical inflation and primordial black holes production. Phys Lett B 791:201–205. https://doi.org/10.1016/j.physletb.2019.02.036. arXiv:1812.02547 [gr-qc]

Kannike K, Marzola L, Raidal M et al (2017) Single field double inflation and primordial black holes. JCAP 09:020. https://doi.org/10.1088/1475-7516/2017/09/020. arXiv:1705.06225 [astro-ph.CO]
Kapadia SJ, Lal Pandey K, Suyama T et al (2021) Search for the stochastic gravitational-wave background induced by primordial curvature perturbations in LIGO's second observing run. Astrophys J Lett 910 (1):L4. https://doi.org/10.3847/2041-8213/abe86e. arXiv:2009.05514 [gr-qc]

Kapadia SJ, Pandey KL, Suyama T et al (2020) Prospects for probing ultralight primordial black holes using the stochastic gravitational-wave background induced by primordial curvature perturbations. Phys Rev D 101(12):123535. https://doi.org/10.1103/PhysRevD.101.123535. arXiv:2005.05693 [astro-ph.CO]

Karam A, Koivunen N, Tomberg E et al (2023) Anatomy of single-field inflationary models for primordial black holes. JCAP 03:013. https://doi.org/10.1088/1475-7516/2023/03/013. arXiv:2205.13540 [astro-ph.CO]

Karnesis N et al (2024) The Laser Interferometer Space Antenna mission in Greece White Paper. Int J Mod Phys D 33(07n08):2450027. https://doi.org/10.1142/S0218271824500275. arXiv:2209.04358 [gr-qc]

Kashlinsky A (2016) LIGO gravitational wave detection, primordial black holes and the near-IR cosmic infrared background anisotropies. Astrophys J Lett 823(2):L25. https://doi.org/10.3847/2041-8205/823/2/L25. arXiv:1605.04023 [astro-ph.CO]

Kashlinsky A, Arendt RG, Atrio-Barandela F et al (2018) Looking at cosmic near-infrared background radiation anisotropies. Rev Mod Phys 90(2):025006. https://doi.org/10.1103/RevModPhys.90.025006. arXiv:1802.07774 [astro-ph.CO]

Kashlinsky A, Arendt RG, Mather J et al (2005) Tracing the first stars with fluctuations of the cosmic infrared background. Nature 438(7064):45–50. https://doi.org/10.1038/nature04143. arXiv:astro-ph/0511105 [astro-ph]

Kashlinsky A, et al (2019) Electromagnetic probes of primordial black holes as dark matter. arXiv e-prints arXiv:1903.04424 [astro-ph.CO]

Katz A, Kopp J, Sibiryakov S et al (2018) Femtolensing by dark matter revisited. JCAP 12:005. https://doi.org/10.1088/1475-7516/2018/12/005. arXiv:1807.11495 [astro-ph.CO]

Kavanagh BJ, Gaggero D, Bertone G (2018) Merger rate of a subdominant population of primordial black holes. Phys Rev D 98(2):023536. https://doi.org/10.1103/PhysRevD.98.023536. arXiv:1805.09034 [astro-ph.CO]

Kawai S, Kim J (2021) Primordial black holes from Gauss-Bonnet-corrected single field inflation. Phys Rev D 104(8):083545. https://doi.org/10.1103/PhysRevD.104.083545. arXiv:2108.01340 [astro-ph.CO]

Kawana K, Xie KP (2022) Primordial black holes from a cosmic phase transition: the collapse of Fermi-balls. Phys Lett B 824:136791. https://doi.org/10.1016/j.physletb.2021.136791. arXiv:2106.00111 [astro-ph.CO]

Kawasaki M, Kitajima N, Yanagida TT (2013) Primordial black hole formation from an axionlike curvaton model. Phys Rev D 87(6):063519. https://doi.org/10.1103/PhysRevD.87.063519. arXiv:1207.2550 [hep-ph]

Kawasaki M, Kohri K, Moroi T (2005a) Big-Bang nucleosynthesis and hadronic decay of long-lived massive particles. Phys Rev D 71:083502. https://doi.org/10.1103/PhysRevD.71.083502. arXiv:astro-ph/0408426

Kawasaki M, Kohri K, Moroi T (2005b) Hadronic decay of late-decaying particles and Big-Bang Nucleosynthesis. Phys Lett B 625:7–12. https://doi.org/10.1016/j.physletb.2005.08.045. arXiv:astro-ph/0402490

Kawasaki M, Kusenko A, Tada Y et al (2016) Primordial black holes as dark matter in supergravity inflation models. Phys Rev D 94(8):083523. https://doi.org/10.1103/PhysRevD.94.083523. arXiv:1606.07631 [astro-ph.CO]

Kawasaki M, Kusenko A, Yanagida TT (2012) Primordial seeds of supermassive black holes. Phys Lett B 711:1–5. https://doi.org/10.1016/j.physletb.2012.03.056. arXiv:1202.3848 [astro-ph.CO]

Kawasaki M, Nakatsuka H (2019) Effect of nonlinearity between density and curvature perturbations on the primordial black hole formation. Phys Rev D 99(12):123501. https://doi.org/10.1103/PhysRevD.99.123501. arXiv:1903.02994 [astro-ph.CO]

Kawasaki M, Nakatsuka H (2021) Gravitational waves from type II axion-like curvaton model and its implication for NANOGrav result. JCAP 05:023. https://doi.org/10.1088/1475-7516/2021/05/023. arXiv:2101.11244 [astro-ph.CO]

Kawasaki M, Sugiyama N, Yanagida T (1998) Primordial black hole formation in a double inflation model in supergravity. Phys Rev D 57:6050–6056. https://doi.org/10.1103/PhysRevD.57.6050. arXiv:hep-ph/9710259
Kehagias A, Musco I, Riotto A (2019) Non-gaussian formation of primordial black holes: effects on the threshold. JCAP 12:029. https://doi.org/10.1088/1475-7516/2019/12/029. arXiv:1906.07135 [astro-ph.CO]

Keith C, Hooper D, Blinov N et al (2020) Constraints on primordial black holes from big bang nucleosynthesis revisited. Phys Rev D 102(10):103512. https://doi.org/10.1103/PhysRevD.102.103512. arXiv:2006.03608 [astro-ph.CO]

Keith C, Hooper D, Linden T et al (2022) Sensitivity of future gamma-ray telescopes to primordial black holes. Phys Rev D 106(4):043003. https://doi.org/10.1103/PhysRevD.106.043003. arXiv:2204.05337 [astro-ph.HE]

Kelley LZ, Blecha L, Hernquist L (2017) Massive black hole binary mergers in dynamical galactic environments. Mon Not R Astron Soc 464(3):3131–3157. https://doi.org/10.1093/mnras/stw2452. arXiv:1606.01900 [astro-ph.HE]

Kelly PL et al (2018) Extreme magnification of an individual star at redshift 1.5 by a galaxy-cluster lens. Nat Astron 2(4):334–342. https://doi.org/10.1038/s41550-018-0430-3. arXiv:1706.10279 [astro-ph.GA]

Khlopov MY (2010) Primordial black holes. Res Astron Astrophys 10:495–528. https://doi.org/10.1088/1674-4527/10/6/001. arXiv:0801.0116 [astro-ph]

Khlopov M, Malomed BA, Zeldovich IB (1985) Gravitational instability of scalar fields and formation of primordial black holes. Mon Not R Astron Soc 215:575–589

Khlopov MY, Polnarev AG (1980) Primordial black holes as a cosmological test of grand unification. Phys Lett B 97:383–387. https://doi.org/10.1016/0370-2693(80)90624-3

Kim H (2021) A constraint on light primordial black holes from the interstellar medium temperature. Mon Not R Astron Soc 504(4):5475–5484. https://doi.org/10.1093/mnras/stab1222. arXiv:2007.07739 [hep-ph]

Kim HI, Lee CH (1996) Constraints on the spectral index from primordial black holes. Phys Rev D 54:6001–6007. https://doi.org/10.1103/PhysRevD.54.6001

Kim JE, Nilles HP, Peloso M (2005) Completing natural inflation. JCAP 01:005. https://doi.org/10.1088/1475-7516/2005/01/005. arXiv:hep-ph/0409138

King SF, Marfatia D, Rahat MH (2024) Toward distinguishing Dirac from Majorana neutrino mass with gravitational waves. Phys Rev D 109(3):035014. https://doi.org/10.1103/PhysRevD.109.035014. arXiv:2306.05389 [hep-ph]

Kinugawa T, Inayoshi K, Hotokezaka K et al (2014) Possible indirect confirmation of the existence of Pop III massive stars by gravitational wave. Mon Not R Astron Soc 442(4):2963–2992. https://doi.org/10.1093/mnras/stu1022. arXiv:1402.6672 [astro-ph.HE]

Kinugawa T, Miyamoto A, Kanda N et al (2016) The detection rate of inspiral and quasi-normal modes of Population III binary black holes which can confirm or refute the general relativity in the strong gravity region. Mon Not R Astron Soc 456(1):1093–1114. https://doi.org/10.1093/mnras/stv2624. arXiv:1505.06962 [astro-ph.SR]

Kinugawa T, Nakamura T, Nakano H (2020) Chirp mass and spin of binary black holes from first star remnants. Mon Not R Astron Soc 498(3):3946–3963. https://doi.org/10.1093/mnras/staa2511. arXiv:2005.09795 [astro-ph.HE]

Kitajima N, Lee J, Murai K et al (2024) Gravitational waves from domain wall collapse, and application to nanohertz signals with QCD-coupled axions. Phys Lett B 851:138586. https://doi.org/10.1016/j.physletb.2024.138586. arXiv:2306.17146 [hep-ph]

Kitajima N, Tada Y, Yokoyama S et al (2021) Primordial black holes in peak theory with a non-Gaussian tail. JCAP 10:053. https://doi.org/10.1088/1475-7516/2021/10/053. arXiv:2109.00791 [astro-ph.CO]

Klein A, et al (2022) The last three years: multiband gravitational-wave observations of stellar-mass binary black holes. arXiv e-prints arXiv:2204.03423 [astro-ph.HE]

Kocsis B, Gaspar ME, Marka S (2006) Detection rate estimates of gravity-waves emitted during parabolic encounters of stellar black holes in globular clusters. Astrophys J 648:411–429. https://doi.org/10.1086/505641. arXiv:astro-ph/0603441

Kocsis B, Sesana A (2011) Gas-driven massive black hole binaries: signatures in the nHz gravitational wave background. Mon Not R Astron Soc 411(3):1467–1479. https://doi.org/10.1111/j.1365-2966.2010.17782.x. arXiv:1002.0584 [astro-ph.CO]

Kocsis B, Suyama T, Tanaka T et al (2018) Hidden universality in the merger rate distribution in the primordial black hole scenario. Astrophys J 854(1):41. https://doi.org/10.3847/1538-4357/aaa7f4. arXiv:1709.09007 [astro-ph.CO]
Kofman L, Linde AD, Starobinsky AA (1994) Reheating after inflation. Phys Rev Lett 73:3195–3198.
https://doi.org/10.1103/PhysRevLett.73.3195. arXiv:hep-th/9405187

Kofman L, Linde AD, Starobinsky AA (1997) Towards the theory of reheating after inflation. Phys Rev D 56:3258–3295. https://doi.org/10.1103/PhysRevD.56.3258. arXiv:hep-ph/9704452

Kohri K, Nakama T, Suyama T (2014) Testing scenarios of primordial black holes being the seeds of supermassive black holes by ultracompact minihalos and CMB µ-distortions. Phys Rev D 90 (8):083514. https://doi.org/10.1103/PhysRevD.90.083514. arXiv:1405.5999 [astro-ph.CO]

Kohri K, Terada T (2018) Semianalytic calculation of gravitational wave spectrum nonlinearly induced from primordial curvature perturbations. Phys Rev D 97(12):123532. https://doi.org/10.1103/PhysRevD.97.123532. arXiv:1804.08577 [gr-qc]

Kohri K, Terada T (2021) Solar-mass primordial black holes explain NANOGrav hint of gravitational waves. Phys Lett B 813:136040. https://doi.org/10.1016/j.physletb.2020.136040. arXiv:2009.11853 [astro-ph.CO]

Kohri K, Yokoyama J (2000) Primordial black holes and primordial nucleosynthesis. 1. Effects of hadron injection from low mass holes. Phys Rev D 61:023501. https://doi.org/10.1103/PhysRevD.61.023501. arXiv:astro-ph/9908160

Kokubu T, Kyutoku K, Kohri K et al (2018) Effect of inhomogeneity on primordial black hole formation in the matter dominated era. Phys Rev D 98(12):123024. https://doi.org/10.1103/PhysRevD.98.123024. arXiv:1810.03490 [astro-ph.CO]

Kolb EW, Tkachev II (1994) Large amplitude isothermal fluctuations and high density dark matter clumps. Phys Rev D 50:769–773. https://doi.org/10.1103/PhysRevD.50.769. arXiv:astro-ph/9403011

Kopp M, Hofmann S, Weller J (2011) Separate universes do not constrain primordial black hole formation. Phys Rev D 83:124025. https://doi.org/10.1103/PhysRevD.83.124025. arXiv:1012.4369 [astro-ph.CO]

Kotok E, Naselsky P (1998) Blue spectra and induced formation of primordial black holes. Phys Rev D 58:103517. https://doi.org/10.1103/PhysRevD.58.103517. arXiv:astro-ph/9806139

Kou XX, Tian C, Zhou SY (2021) Oscillon preheating in full general relativity. Class Quant Grav 38 (4):045005. https://doi.org/10.1088/1361-6382/abd09f. arXiv:1912.09658 [gr-qc]

Koushiappas SM, Loeb A (2017a) Dynamics of dwarf galaxies disfavor stellar-mass black holes as dark matter. Phys Rev Lett 119(4):041102. https://doi.org/10.1103/PhysRevLett.119.041102. arXiv:1704.01668 [astro-ph.GA]

Koushiappas SM, Loeb A (2017b) Maximum redshift of gravitational wave merger events. Phys Rev Lett 119(22):221104. https://doi.org/10.1103/PhysRevLett.119.221104. arXiv:1708.07380 [astro-ph.CO]

Kouvaris C, Tinyakov P, Tytgat MHG (2018) NonPrimordial solar mass black holes. Phys Rev Lett 121 (22):221102. https://doi.org/10.1103/PhysRevLett.121.221102. arXiv:1804.06740 [astro-ph.HE]

Kozaczuk J, Lin T, Villarama E (2022) Signals of primordial black holes at gravitational wave interferometers. Phys Rev D 105(12):123023. https://doi.org/10.1103/PhysRevD.105.123023. arXiv:2108.12475 [astro-ph.CO]

Kristiano J, Yokoyama J (2024a) Constraining primordial black hole formation from single-field inflation. Phys Rev Lett 132(22):221003. https://doi.org/10.1103/PhysRevLett.132.221003. arXiv:2211.03395 [hep-th]

Kristiano J, Yokoyama J (2024b) Note on the bispectrum and one-loop corrections in single-field inflation with primordial black hole formation. Phys Rev D 109(10):103541. https://doi.org/10.1103/PhysRevD.109.103541. arXiv:2303.00341 [hep-th]

Kritos K, De Luca V, Franciolini G et al (2021) The astro-primordial black hole merger rates: a reappraisal. JCAP 05:039. https://doi.org/10.1088/1475-7516/2021/05/039. arXiv:2012.03585 [gr-qc]

Kuhnel F, Matas A, Starkman GD et al (2020) Waves from the centre: probing PBH and other macroscopic dark matter with LISA. Eur Phys J C 80(7):627. https://doi.org/10.1140/epjc/s10052-020-8183-4. arXiv:1811.06387 [gr-qc]

Labbé I, van Dokkum P, Nelson E et al (2023) A population of red candidate massive galaxies 600 myr after the big bang. Nature 616(7956):266–269. https://doi.org/10.1038/s41586-023-05786-2. arXiv:2207.12446 [astro-ph.GA]

Laguna P, Larson SL, Spergel D et al (2010) Integrated Sachs-Wolfe effect for gravitational radiation. Astrophys J Lett 715:L12. https://doi.org/10.1088/2041-8205/715/1/L12. arXiv:0905.1908 [gr-qc]

Laha R (2019) Primordial black holes as a dark matter candidate are severely constrained by the galactic center 511 keV γ-ray line. Phys Rev Lett 123(25):251101. https://doi.org/10.1103/PhysRevLett.123.251101. arXiv:1906.09994 [astro-ph.HE]
Laha R, Lu P, Takhistov V (2021) Gas heating from spinning and non-spinning evaporating primordial black holes. Phys Lett B 820:136459. https://doi.org/10.1016/j.physletb.2021.136459. arXiv:2009.11837 [astro-ph.CO]

Laha R, Muñoz JB, Slatyer TR (2020) INTEGRAL constraints on primordial black holes and particle dark matter. Phys Rev D 101(12):123514. https://doi.org/10.1103/PhysRevD.101.123514. arXiv:2004.00627 [astro-ph.CO]

Lazarides G, Maji R, Shafi Q (2023) Superheavy quasistable strings and walls bounded by strings in the light of NANOGrav 15 year data. Phys Rev D 108(9):095041. https://doi.org/10.1103/PhysRevD.108.095041. arXiv:2306.17788 [hep-ph]

Lewicki M, Toczek P, Vaskonen V (2023) Primordial black holes from strong first-order phase transitions. JHEP 09:092. https://doi.org/10.1007/JHEP09(2023)092. arXiv:2305.04924 [astro-ph.CO]

Li TS et al (2017) Farthest neighbor: The distant Milky Way satellite Eridanus II. Astrophys J 838(1):8. https://doi.org/10.3847/1538-4357/aa6113. arXiv:1611.05052 [astro-ph.GA]

Li T, Liao J (2022) Electron-target experiment constraints on light dark matter produced in primordial black hole evaporation. Phys Rev D 106(5):055043. https://doi.org/10.1103/PhysRevD.106.055043. arXiv:2203.14443 [hep-ph]

Li SL, Shao L, Wu P et al (2021) NANOGrav signal from first-order confinement-deconfinement phase transition in different QCD-matter scenarios. Phys Rev D 104(4):043510. https://doi.org/10.1103/PhysRevD.104.043510. arXiv:2101.08012 [astro-ph.CO]

Libanore S, Artale MC, Karagiannis D et al (2022) Clustering of gravitational wave and supernovae events: a multitracer analysis in luminosity distance space. JCAP 02(02):003. https://doi.org/10.1088/1475-7516/2022/02/003. arXiv:2109.10857 [astro-ph.CO]

Libanore S, Liguori M, Raccanelli A (2023) Signatures of primordial black holes in gravitational wave clustering. JCAP 08:055. https://doi.org/10.1088/1475-7516/2023/08/055. arXiv:2306.03087 [astro-ph.CO]

Lin J, Gao Q, Gong Y et al (2020) Primordial black holes and secondary gravitational waves from k and G inflation. Phys Rev D 101(10):103515. https://doi.org/10.1103/PhysRevD.101.103515. arXiv:2001.05909 [gr-qc]

Lin J, Gao S, Gong Y et al (2023) Primordial black holes and scalar induced gravitational waves from Higgs inflation with noncanonical kinetic term. Phys Rev D 107(4):043517. https://doi.org/10.1103/PhysRevD.107.043517. arXiv:2111.01362 [gr-qc]

Linde AD (1994) Hybrid inflation. Phys Rev D 49:748-754. https://doi.org/10.1103/PhysRevD.49.748. arXiv:astro-ph/9307002

Linde A, Mooij S, Pajer E (2013) Gauge field production in supergravity inflation: local non-gaussianity and primordial black holes. Phys Rev D 87(10):103506. https://doi.org/10.1103/PhysRevD.87.103506. arXiv:1212.1693 [hep-th]

Linde AD, Westphal A (2008) Accidental inflation in string theory. JCAP 03:005. https://doi.org/10.1088/1475-7516/2008/03/005. arXiv:0712.1610 [hep-th]

Liu J, Bian L, Cai RG et al (2022) Primordial black hole production during first-order phase transitions. Phys Rev D 105(2):L021303. https://doi.org/10.1103/PhysRevD.105.L021303. arXiv:2106.05637 [astro-ph.CO]

Liu B, Bromm V (2020a) Gravitational waves from Population III binary black holes formed by dynamical capture. Mon Not R Astron Soc 495(2):2475-2495. https://doi.org/10.1093/mnras/staa1362. arXiv:2003.00065 [astro-ph.CO]

Liu B, Bromm V (2020b) The population III origin of GW190521. Astrophys J Lett 903(2):L40. https://doi.org/10.3847/2041-8213/abc552. arXiv:2009.11447 [astro-ph.GA]

Liu B, Bromm V (2022) Accelerating early massive galaxy formation with primordial black holes. Astrophys J Lett 937(2):L30. https://doi.org/10.3847/2041-8213/ac927f. arXiv:2208.13178 [astro-ph.CO]

Liu L, Chen ZC, Huang QG (2024) Implications for the non-Gaussianity of curvature perturbation from pulsar timing arrays. Phys Rev D 109(6):L061301. https://doi.org/10.1103/PhysRevD.109.L061301. arXiv:2307.01102 [astro-ph.CO]

Liu J, Guo ZK, Cai RG (2020) Primordial black holes from cosmic domain walls. Phys Rev D 101(2):023513. https://doi.org/10.1103/PhysRevD.101.023513. arXiv:1908.02662 [astro-ph.CO]

Lovell CC, Harrison I, Harikane Y et al (2022) Extreme value statistics of the halo and stellar mass distributions at high redshift: are JWST results in tension with ΛCDM? Mon Not R Astron Soc 518(2):2511-2520. https://doi.org/10.1093/mnras/stac3224. arXiv:2208.10479 [astro-ph.GA]
Lu Y, Ali A, Gong Y et al (2020) Gauge transformation of scalar induced gravitational waves. Phys Rev D 102(8):083503. https://doi.org/10.1103/PhysRevD.102.083503(2020). arXiv:2006.03450 [gr-qc]

Lu P, Takhistov V, Gelmini GB et al (2021) Constraining primordial black holes with dwarf galaxy heating. Astrophys J Lett 908(2):L23. https://doi.org/10.3847/2041-8213/abdcb6. arXiv:2007.02213 [astro-ph.CO]

Lucca M, Schöneberg N, Hooper DC et al (2020) The synergy between CMB spectral distortions and anisotropies. JCAP 02:026. https://doi.org/10.1088/1475-7516/2020/02/026. arXiv:1910.04619 [astro-ph.CO]

Luo Y, Hanasoge S, Tromp J et al (2012) Detectable seismic consequences of the interaction of a primordial black hole with Earth. Astrophys J 751:16. https://doi.org/10.1088/0004-637X/751/1/16. arXiv:1203.3806 [astro-ph.CO]

Lyth DH (2012) The hybrid inflation waterfall and the primordial curvature perturbation. JCAP 05:022. https://doi.org/10.1088/1475-7516/2012/05/022. arXiv:1201.4312 [astro-ph.CO]

Lyth DH, Malik KA, Sasaki M (2005) A general proof of the conservation of the curvature perturbation. JCAP 05:004. https://doi.org/10.1088/1475-7516/2005/05/004. arXiv:astro-ph/0411220

Lyth DH, Riotto A (1999) Particle physics models of inflation and the cosmological density perturbation. Phys Rept 314:1–146. https://doi.org/10.1016/S0370-1573(98)00128-8. arXiv:hep-ph/9807278

Lyth DH, Wands D (2002) Generating the curvature perturbation without an inflaton. Phys Lett B 524:5–14. https://doi.org/10.1016/S0370-2693(01)01366-1. arXiv:hep-ph/0110002

López-Coto R, Doro M, de Angelis A et al (2021) Prospects for the observation of Primordial Black Hole evaporation with the Southern Wide field of view Gamma-ray Observatory. JCAP 08:040. https://doi.org/10.1088/1475-7516/2021/08/040. arXiv:2103.16895 [astro-ph.HE]

MacGibbon JH, Brandenberger RH, Wichoski UF (1998) Limits on black hole formation from cosmic string loops. Phys Rev D 57:2158–2165. https://doi.org/10.1103/PhysRevD.57.2158. arXiv:astro-ph/9707146

Mack KJ, Ostriker JP, Ricotti M (2007) Growth of structure seeded by primordial black holes. Astrophys J 665:1277–1287. https://doi.org/10.1086/518998. arXiv:astro-ph/0608642

Madge E, Morgante E, Puchades-Ibáñez C et al (2023) Primordial gravitational waves in the nano-Hertz regime and PTA data–towards solving the GW inverse problem. JHEP 10:171. https://doi.org/10.1007/JHEP10(2023)171. arXiv:2306.14856 [hep-ph]

Maeso DN, Marzola L, Raidal M et al (2022) Primordial black holes from spectator field bubbles. JCAP 02 (02):017. https://doi.org/10.1088/1475-7516/2022/02/017. arXiv:2112.01505 [astro-ph.CO]

Maggiore M (2000) Gravitational wave experiments and early universe cosmology. Phys Rept 331:283–367. https://doi.org/10.1016/S0370-1573(99)00102-7. arXiv:gr-qc/9909001

Maggiore M et al (2020) Science case for the einstein telescope. JCAP 03:050. https://doi.org/10.1088/1475-7516/2020/03/050. arXiv:1912.02622 [astro-ph.CO]

Maggiore M (2008) Gravitational Waves: Volume 1: Theory and Experiments. Gravitational Waves, OUP Oxford

Maldacena J (2021) Comments on magnetic black holes. JHEP 04:079. https://doi.org/10.1007/JHEP04 (2021)079. arXiv:2004.06084 [hep-th]

Mandic V, Bird S, Cholis I (2016) Stochastic gravitational-wave background due to primordial binary black hole mergers. Phys Rev Lett 117(20):201102. https://doi.org/10.1103/PhysRevLett.117.201102. arXiv:1608.06699 [astro-ph.CO]

Manshanden J, Gaggero D, Bertone G et al (2019) Multi-wavelength astronomical searches for primordial black holes. JCAP 06:026. https://doi.org/10.1088/1475-7516/2019/06/026. arXiv:1812.07967 [astro-ph.HE]

Margalit A, Contaldi CR, Pieroni M (2020) Phase decoherence of gravitational wave backgrounds. Phys Rev D 102(8):083506. https://doi.org/10.1103/PhysRevD.102.083506. arXiv:2004.01727 [astro-ph.CO]

Martin J, Papanikolaou T, Pinol L et al (2020a) Metric preheating and radiative decay in single-field inflation. JCAP 05:003. https://doi.org/10.1088/1475-7516/2020/05/003. arXiv:2002.01820 [astro-ph.CO]

Martin J, Papanikolaou T, Vennin V (2020b) Primordial black holes from the preheating instability in single-field inflation. JCAP 01:024. https://doi.org/10.1088/1475-7516/2020/01/024. arXiv:1907.04236 [astro-ph.CO]

Martinelli M, Scarcella F, Hogg NB et al (2022) Dancing in the dark: detecting a population of distant primordial black holes. JCAP 08(08):006. https://doi.org/10.1088/1475-7516/2022/08/006. arXiv:2205.02639 [astro-ph.CO]