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Combining constraints from microlensing and Lyman-$\alpha$ forest, we provide a simple argument to show that large spatial clustering of stellar-mass primordial black holes at the time of formation, such as the one induced by the presence of large non-Gaussianities, is ruled out. Therefore, it is not possible to evade existing constraints preventing stellar-mass primordial black holes to be a dominant constituent of the dark matter by boosting their initial clustering., Comment: 5 pages + supplementary material. 2 figures. v2: matching version published in PRL

The formation of Primordial Black Holes (PBHs) through the collapse of large fluctuations in the early universe is a rare event. This manifests itself, for instance, through the non-Gaussian tail of the formation probability. To compute such probability and the abundance of PBHs, the curvature perturbation is frequently adopted. In this note we emphasize that its use does not provide the correct PBH formation probability. Through a path-integral approach we show that the exact calculation of the PBH abundance demands the knowledge of multivariate joint probabilities of the curvature perturbation or, equivalently, of all the corresponding connected correlators., Comment: 13 pages, 1 figure. v2: matching published version

We consider the role of secondary infall and accretion onto an initially overdense perturbation in matter-dominated eras, like the one which is likely to follow the end of inflation. We show that primordial black holes may form through post-collapse accretion, namely the accretion onto an initial overdensity whose collapse has not given rise to a primordial black hole. Accretion may be also responsible for the growth of the primordial black hole masses by orders of magnitude till the end of the matter-dominated era., Comment: 7 pages, 1 figure. v2: matching published version

Making use of both the stochastic approach to the tunneling phenomenon and the threshold statistics, we offer a simple argument to show that critical bubbles may be correlated in first-order phase transitions and biased compared to the underlying scalar field spatial distribution. This happens though only if the typical energy scale of the phase transition is sufficiently high. We briefly discuss possible implications of this result, e.g. the formation of primordial black holes through bubble collisions., Comment: 6 pages, 1 figure. v2: matching published version

The deformability of a compact object under the presence of a tidal perturbation is encoded in the tidal Love numbers (TLNs), which vanish for isolated black holes in vacuum. We show that the TLNs of black holes surrounded by matter fields do not vanish and can be used to probe the environment around binary black holes. In particular, we compute the TLNs for the case of a black hole surrounded by a scalar condensate under the presence of scalar and vector tidal perturbations, finding a strong power-law behavior of the TLN in terms of the mass of the scalar field. Using this result as a proxy for gravitational tidal perturbations, we show that future gravitational-wave detectors like the Einstein Telescope and LISA can impose stringent constraints on the mass of ultralight bosons that condensate around black holes due to accretion or superradiance. Interestingly, LISA could measure the tidal deformability of dressed black holes across the range from stellar-mass ($\approx 10^2 M_\odot$) to supermassive ($\approx 10^7 M_\odot$) objects, providing a measurement of the mass of ultralight bosons in the range $(10^{-17} - 10^{-13}) \, {\rm eV}$ with less than $10\%$ accuracy, thus filling the gap between other superradiance-driven constraints coming from terrestrial and space interferometers. Altogether, LISA and Einstein Telescope can probe tidal effects from dressed black holes in the combined mass range $(10^{-17} - 10^{-11}) \, {\rm eV}$., Comment: 17 pages, 5 figures. v2: matching published version

The next generation of gravitational-wave experiments, such as Einstein Telescope, Cosmic Explorer and LISA, will test the primordial black hole scenario. We provide a forecast for the minimum testable value of the abundance of primordial black holes as a function of their masses for both the unclustered and clustered spatial distributions at formation. In particular, we show that these instruments may test abundances, relative to the dark matter, as low as $10^{-10}$., Comment: 11 pages, 5 figures

The merger rate of primordial black holes depends on their initial clustering. In the absence of primordial non-Gaussianity correlating short and large-scales, primordial black holes are distributed \`a la Poisson at the time of their formation. However, primordial non-Gaussianity of the local-type may correlate primordial black holes on large-scales. We show that future experiments looking for CMB $\mu$-distortion would test the hypothesis of initial primordial black hole clustering induced by local non-Gaussianity, while existing limits already show that significant non-Gaussianity is necessary to induce primordial black hole clustering., Comment: 6 pages, 2 figures. v2: matching published version

We show that black holes with a Schwarzschild radius of the order of the electroweak scale may act as seeds for the baryon number violation within the Standard model via sphaleron transitions. The corresponding rate is faster than the one in the pure vacuum and baryon number violation around black holes can take place during the evolution of the universe after the electroweak phase transition. We show however that this does not pose any threat for a pre-existing baryon asymmetry in the universe., Comment: 6 pages, 2 figures. v2: matching published version

We perform a hierarchical Bayesian analysis of the GWTC-2 catalog to investigate the mixed scenario in which the merger events are explained by black holes of both astrophysical and primordial origin. For the astrophysical scenario we adopt the phenomenological model used by the LIGO/Virgo collaboration and we include the correlation between different parameters inferred from data, the role of the spins in both the primordial and astrophysical scenarios, and the impact of accretion in the primordial scenario. Our best-fit mixed model has a strong statistical evidence relative to the single-population astrophysical model, thus supporting the coexistence of populations of black-hole mergers of two different origins. In particular, our results indicate that the astrophysical mergers account for roughly four times the number of primordial black hole events and predict that third-generation detectors, such as the Einstein Telescope and Cosmic Explorer, should detect up to hundreds of mergers from primordial black hole binaries at redshift $z\gtrsim30$., Comment: 20 pages, 8 figures. v2: matching published version

Mainly motivated by the recent GW190521 mass gap event which we take as a benchmark point, we critically assess if binaries made of a primordial black hole and a black hole of astrophysical origin may form, merge in stellar clusters and reproduce the LIGO/Virgo detection rate. While two previously studied mechanisms -- the direct capture and the three body induced -- seem to be inefficient, we propose a new "catalysis" channel based on the idea that a subsequent chain of single-binary and binary-binary exchanges may lead to the formation of a high mass binary pairs and show that it may explain the recent GW190521 event if the local overdensity of primordial black holes in the globular cluster is larger than a few., Comment: 24 pages, 4 figures. v2: matching published version

The NANOGrav Collaboration has recently published a strong evidence for a stochastic common-spectrum process that may be interpreted as a stochastic gravitational wave background. We show that such a signal can be explained by second-order gravitational waves produced during the formation of primordial black holes from the collapse of sizeable scalar perturbations generated during inflation. This possibility has two predictions: $i$) the primordial black holes may comprise the totality of the dark matter with the dominant contribution to their mass function falling in the range $(10^{-15}\div 10^{-11}) M_\odot$ and $ii$) the gravitational wave stochastic background will be seen as well by the LISA experiment., Comment: 5 pages, 1 figure. v2 : matching version published in PRL

Primordial black holes might comprise a significant fraction of the dark matter in the Universe and be responsible for the gravitational wave signals from black hole mergers observed by the LIGO/Virgo collaboration. The spatial clustering of primordial black holes might affect their merger rates and have a significant impact on the constraints on their masses and abundances. We provide some analytical treatment of the primordial black hole spatial clustering evolution, compare our results with some of the existing N-body numerical simulations and discuss the implications for the black hole merger rates. If primordial black holes contribute to a small fraction of the dark matter, primordial black hole clustering is not relevant. On the other hand, for a large contribution to the dark matter, we argue that the clustering may increase the late time Universe merger rate to a level compatible with the LIGO/Virgo detection rate. As for the early Universe merger rate of black hole binaries formed at primordial epochs, clustering alleviates the LIGO/Virgo constraints, but does not evade them., Comment: 21 pages, 6 figures

The LIGO/Virgo Collaboration has recently observed GW190521, the first binary black hole merger with at least the primary component mass in the mass gap predicted by the pair-instability supernova theory. This observation disfavors the standard stellar-origin formation scenario for the heavier black hole, motivating alternative hypotheses. We show that GW190521 cannot be explained within the Primordial Black Hole (PBH) scenario if PBHs do not accrete during their cosmological evolution, since this would require an abundance which is already in tension with current constraints. On the other hand, GW190521 may have a primordial origin if PBHs accrete efficiently before the reionization epoch., Comment: 7 pages, 4 figures. v2: matching version published in PRL

The black holes detected by current and future interferometers can have diverse origins. Their expected mass and spin distributions depend on the specifics of the formation mechanisms. When a physically motivated prior distribution is used in a Bayesian inference, the parameters estimated from the gravitational-wave data can change significantly, potentially affecting the physical interpretation of certain gravitational-wave events and their implications on theoretical models. As a case study we analyze primordial black holes, which might be formed in the early universe and could comprise at least a fraction of the dark matter. If accretion is not efficient during their cosmic history, primordial black holes are expected to be almost non-spinning. If accretion is efficient, massive binaries tend to be symmetrical and highly spinning. We show that incorporating these priors can significantly change the inferred mass ratio and effective spin of some binary black hole events, especially those identified as high-mass, asymmetrical, or spinning by a standard analysis using agnostic priors. For several events, the Bayes factors are only mildly affected by the new priors, implying that it is hard to distinguish whether merger events detected so far are of primordial or astrophysical origin. In particular, if binaries identified by LIGO/Virgo as strongly asymmetrical (including GW190412) are of primordial origin, their mass ratio inferred from the data can be closer to unity. For GW190412, the latter property is strongly affected by the inclusion of higher harmonics in the waveform model., Comment: 30 pages, 10 figures; v3: This version updates the previous analysis by including the effects of higher harmonics in the waveform model for GW190412. Version accepted in JCAP"

The LIGO and Virgo Interferometers have so far provided 11 gravitational-wave (GW) observations of black-hole binaries. Similar detections are bound to become very frequent in the near future. With the current and upcoming wealth of data, it is possible to confront specific formation models with observations. We investigate here whether current data are compatible with the hypothesis that LIGO/Virgo black holes are of primordial origin. We compute in detail the mass and spin distributions of primordial black holes (PBHs), their merger rates, the stochastic background of unresolved coalescences, and confront them with current data from the first two observational runs, also including the recently discovered GW190412. We compute the best-fit values for the parameters of the PBH mass distribution at formation that are compatible with current GW data. In all cases, the maximum fraction of PBHs in dark matter is constrained by these observations to be $f_{\text{PBH}}\approx {\rm few}\times 10^{-3}$. We discuss the predictions of the PBH scenario that can be directly tested as new data become available. In the most likely formation scenarios where PBHs are born with negligible spin, the fact that at least one of the components of GW190412 is moderately spinning is incompatible with a primordial origin for this event, unless accretion or hierarchical mergers are significant. In the absence of accretion, current non-GW constraints already exclude that LIGO/Virgo events are all of primordial origin, whereas in the presence of accretion the GW bounds on the PBH abundance are the most stringent ones in the relevant mass range. A strong phase of accretion during the cosmic history would favour mass ratios close to unity, and a redshift-dependent correlation between high masses, high spins and nearly-equal mass binaries, with the secondary component spinning faster than the primary., Comment: 38 pages, 17 figures. v2: references added; corrected typo in the value of $\sigma_M$ reported in Ref. [73] mildly affecting the suppression factor. Figs. 10 and 13 updated. Results and conclusions unchanged

We consider the constraints on the fraction of dark matter in the universe in the form of primordial black holes taking into account the crucial role of accretion which may change both their mass and mass function. We show that accretion may drastically weaken the constraints at the present epoch for primordial black holes with masses larger than a few solar masses., Comment: 6 pages, 4 figures. v2 : matching published version

Primordial black holes in the mass range of ground-based gravitational-wave detectors can comprise a significant fraction of the dark matter. Mass and spin measurements from coalescences can be used to distinguish between an astrophysical or a primordial origin of the binary black holes. In standard scenarios the spin of primordial black holes is very small at formation. However, the mass and spin can evolve through the cosmic history due to accretion. We show that the mass and spin of primordial black holes are correlated in a redshift-dependent fashion, in particular primordial black holes with masses below ${\cal O}(30)M_\odot$ are likely non-spinning at any redshift, whereas heavier black holes can be nearly extremal up to redshift $z\sim10$. The dependence of the mass and spin distributions on the redshift can be probed with future detectors such as the Einstein Telescope. The mass and spin evolution affect the gravitational waveform parameters, in particular the distribution of the final mass and spin of the merger remnant, and that of the effective spin of the binary. We argue that, compared to the astrophysical-formation scenario, a primordial origin of black hole binaries might better explain the spin distribution of merger events detected by LIGO-Virgo, in which the effective spin parameter of the binary is compatible to zero except possibly for few high-mass events. Upcoming results from LIGO-Virgo third observation run might reinforce or weaken these predictions., Comment: 13 figures, 31 pages. v2: Section and appendix added. Results unchanged

In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics., Comment: 22 pages, 1 figure, to appear in General Relativity and Gravitation

We elaborate on the mass function of primordial black holes in the case in which the power spectrum of the curvature perturbation is broad. For the case of a broad and flat spectrum, we argue that such a mass function is peaked at the smallest primordial black mass which can be formed and possesses a tail decaying like $M^{-3/2}$, where $M$ is the mass of the primordial black hole., Comment: 14 pages, 3 figures

The issue of the gauge invariance of gravitational waves arises if they are produced in the early universe at second-order in perturbation theory. We address it by dividing the discussion about the gauge invariance in three parts: the production of gravitational waves, their propagation in the real universe, and their measurement., Comment: 26 pages, 3 figures, version accepted by JCAP

An observable stochastic background of gravitational waves is generated whenever primordial black holes are created in the early universe thanks to a small-scale enhancement of the curvature perturbation. We calculate the anisotropies and non-Gaussianity of such stochastic gravitational waves background which receive two contributions, the first at formation time and the second due to propagation effects. The former contribution can be generated if the distribution of the curvature perturbation is characterized by a local and scale-invariant shape of non-Gaussianity. Under such an assumption, we conclude that a sizeable magnitude of anisotropy and non-Gaussianity in the gravitational waves would suggest that primordial black holes may not comply the totality of the dark matter., Comment: 20 pages, 5 figures, version accepted by JCAP

We discuss a novel mechanism to generate gravitational waves in the early universe. A standard way to produce primordial black holes is to enhance at small-scales the overdensity perturbations generated during inflation. The latter, upon horizon re-entry, collapse into black holes. They must be sizeable enough and are therefore associated to rare peaks. There are however less sizeable and much less rare overdensity peaks which do not end up forming primordial black holes and have a non-spherical shape. Upon collapse, they possess a time-dependent non-vanishing mass quadrupole which gives rise to the generation of gravitational waves. By their nature, such gravitational waves are complementary to those sourced at second-order by the very same scalar perturbations responsible for the formation of the primordial black holes. Their amplitude is nevertheless typically about two orders of magnitude smaller and therefore hardly measurable., Comment: 10 pages, 5 figures, matching published version

We study the formation of primordial black holes when they are generated by the collapse of large overdensities in the early universe. Since the density contrast is related to the comoving curvature perturbation by a nonlinear relation, the overdensity statistics is unavoidably non-Gaussian. We show that the abundance of primordial black holes at formation may not be captured by a perturbative approach which retains the first few cumulants of the non-Gaussian probability distribution. We provide two techniques to calculate the non-Gaussian abundance of primordial black holes at formation, one based on peak theory and the other on threshold statistics. Our results show that the unavoidable non-Gaussian nature of the inhomogeneities in the energy density makes it harder to generate PBHs. We provide simple (semi-)analytical expressions to calculate the non-Gaussian abundances of the primordial black holes and show that for both narrow and broad power spectra the gaussian case from threshold statistics is reproduced by increasing the amplitude of the power spectrum by a factor ${\cal O}(2\div 3)$., Comment: 26 pages, 10 figures, matching published version

The LIGO discoveries have rekindled suggestions that primordial black holes (BHs) may constitute part to all of the dark matter (DM) in the Universe. Such suggestions came from 1) the observed merger rate of the BHs, 2) their unusual masses, 3) their low/zero spins, and 4) also from the independently uncovered cosmic infrared background (CIB) fluctuations signal of high amplitude and coherence with unresolved cosmic X-ray background (CXB). Here we summarize the prospects to resolve this important issue with electromagnetic observations using the instruments and tools expected in the 2020's. These prospects appear promising to make significant, and potentially critical, advances. We demonstrate that in the next decade, new space- and ground-borne electromagnetic instruments, combined with concurrent theoretical efforts, should shed critical light on the long-considered link between primordial BHs and DM. Specifically the new data and methodologies under this program will involve: I) Probing with high precision the spatial spectrum of source-subtracted CIB with Euclid and WFIRST, and its coherence with unresolved cosmic X-ray background using eROSITA and Athena, II) Advanced searches for microlensing of Galactic stars by the intervening Galactic Halo BHs with OGLE, Gaia, LSST and WFIRST, III) Supernovae (SNe) lensing in the upcoming surveys with WFIRST, LSST and also potentially with Euclid and JWST, IV) Advanced theoretical work to understand the details of PBH accretion and evolution and their influence on cosmic microwave background (CMB) anisotropies in light of the next generation CMB experiments, V) Better new samples and theoretical understanding involving stability and properties of ultra faint dwarf galaxies, pulsar timing, and cosmological quasar lensing., Comment: Science whitepaper submitted to the Astro2020 Decadal Survey

We study the spin of primordial black holes produced by the collapse of large inhomogeneities in the early universe. Since such primordial black holes originate from peaks, that is, from maxima of the local overdensity, we resort to peak theory to obtain the probability distribution of the spin at formation. We show that the spin is a first-order effect in perturbation theory: it results from the action of first-order tidal gravitational fields generating first-order torques upon horizon-crossing, and from the asphericity of the collapsing object. Assuming an ellipsoidal shape, the typical value of the dimensionless parameter $a_{\rm s}=S/G_N M^2$, where $S$ is the spin and $M$ is the mass of the primordial black hole, is about $\sigma_\delta\sqrt{1-\gamma^2}/2\pi$. Here, $\sigma^2_\delta$ is the variance of the overdensity at horizon crossing and the parameter $\gamma$ is a measure of the width of the power spectrum giving rise to primordial black holes. One has $\gamma=1$ for monochromatic spectra. For these narrow spectra, the suppression arises because the velocity shear, which is strongly correlated with the inertia tensor, tends to align with the principal axis frame of the collapsing object. Typical values of $a_{\rm s}$ are at the percent level., Comment: 29 pages, 7 figures

We explore non-Gaussian features of a massless spin-two field in the Vasiliev theory of higher-spin gravity. The theory contains an infinite tower of interacting gauge fields with increasing spin, and admits four-dimensional asymptotically de Sitter configurations. Using a recent proposal for calculating late-time quantum correlations in Vasiliev theory, we provide an exact formula for the tensor non-Gaussianities of the massless spin-two graviton field. By general symmetry considerations, we relate our result to that produced by a tree-level calculation in a gravitational theory containing an Einstein term and a term cubic in the Weyl tensor. The relative coefficient between the two terms is calculated explicitly, exhibiting a significant contribution from the Weyl cubed term. We discuss potential cosmological implications of our results., Comment: 34 pages, 3 figures

There has recently been renewed interest in the possibility that the dark matter in the universe consists of primordial black holes (PBHs). Current observational constraints leave only a few PBH mass ranges for this possibility. One of them is around $10^{-12} M_\odot$. If PBHs with this mass are formed due to an enhanced scalar-perturbation amplitude, their formation is inevitably accompanied by the generation of gravitational waves (GWs) with frequency peaked in the mHz range, precisely around the maximum sensitivity of the LISA mission. We show that, if these primordial black holes are the dark matter, LISA will be able to detect the associated GW power spectrum. Although the GW source signal is intrinsically non-Gaussian, the signal measured by LISA is a sum of the signal from a large number of independent sources suppressing the non-Gaussianity at detection to an unobservable level. We also discuss the effect of the GW propagation in the perturbed universe. PBH dark matter generically leads to a detectable, purely isotropic, Gaussian and unpolarised GW signal, a prediction that is testable with LISA., Comment: 6 pages, 3 figures, v3: matching published version

The idea that primordial black holes (PBHs) can comprise most of the dark matter of the universe has recently reacquired a lot of momentum. Observational constraints, however, rule out this possibility for most of the PBH masses, with a notable exception around $10^{-12} M_\odot$. These light PBHs may be originated when a sizeable comoving curvature perturbation generated during inflation re-enters the horizon during the radiation phase. During such a stage, it is unavoidable that gravitational waves (GWs) are generated. Since their source is quadratic in the curvature perturbations, these GWs are generated fully non-Gaussian. Their frequency today is about the mHz, which is exactly the range where the LISA mission has the maximum of its sensitivity. This is certainly an impressive coincidence. We show that this scenario of PBHs as dark matter can be tested by LISA by measuring the GW two-point correlator. On the other hand, we show that the short observation time (as compared to the age of the universe) and propagation effects of the GWs across the perturbed universe from the production point to the LISA detector suppress the bispectrum to an unobservable level. This suppression is completely general and not specific to our model., Comment: 22 pages, 12 figures. v3: matching published version

The NEMO Phase-2 tower is the first detector which was operated underwater for more than one year at the "record" depth of 3500 m. It was designed and built within the framework of the NEMO (NEutrino Mediterranean Observatory) project. The 380 m high tower was successfully installed in March 2013 80 km offshore Capo Passero (Italy). This is the first prototype operated on the site where the italian node of the KM3NeT neutrino telescope will be built. The installation and operation of the NEMO Phase-2 tower has proven the functionality of the infrastructure and the operability at 3500 m depth. A more than one year long monitoring of the deep water characteristics of the site has been also provided. In this paper the infrastructure and the tower structure and instrumentation are described. The results of long term optical background measurements are presented. The rates show stable and low baseline values, compatible with the contribution of 40K light emission, with a small percentage of light bursts due to bioluminescence. All these features confirm the stability and good optical properties of the site., Comment: 12 pages, 17 figures

The results of the analysis of the data collected with the NEMO Phase-2 tower, deployed at 3500 m depth about 80 km off-shore Capo Passero (Italy), are presented. Cherenkov photons detected with the photomultipliers tubes were used to reconstruct the tracks of atmospheric muons. Their zenith-angle distribution was measured and the results compared with Monte Carlo simulations. An evaluation of the systematic effects due to uncertainties on environmental and detector parameters is also included. The associated depth intensity relation was evaluated and compared with previous measurements and theoretical predictions. With the present analysis, the muon depth intensity relation has been measured up to 13 km of water equivalent., Comment: submitted to Astroparticle Physics