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 PBH≈ few× 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. Finally, we highlight that accretion can play an important role to relax current constraints on the PBH abundance, which calls for a better modelling of the mass and angular momentum accretion rates at redshift 0z≲3.

No abstract

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 . 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.

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 . 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. arXiv:1810.12224v3 [astro-ph.CO] 30 Jul 2019 1 We briefly comment on the high-mass portion of Fig. 1. The Ultra-Faint Dwarf (UFD) galaxy constraint arises from the fact that PBHs of this mass would cause the dissolution of star clusters observed in UFDs such as Eridanus II [27]; this constraint is strongly weakened in the presence of an intermediate-mass black hole, providing a binding energy that stabilizes the cluster [27,28]. We thank Juan García-Bellido for discussions on this issue. Secondly, we do not show in Fig. 1 the lensing bounds related to the measured luminosities of Supernovae Ia derived in [29,30], which constrain the abundance of PBHs above 1 M . We are not showing also the stronger bounds from CMB arising from disk-accretion [31]. We also omitted the constraints coming from Lyman−α forest observations [32], which overlap with the ones from UFD. Similarly, in the low-mass region, we do not show the constraints from [33] related the production of cosmic rays from evaporating PBHs, given that they overlap with the constraints related to γ−rays produced by the PBHs evaporation.

Primordial black holes may owe their origin to the small-scale enhancement of the comoving curvature perturbation generated during inflation. Their mass fraction at formation is markedly sensitive to possible non-Gaussianities in such large, but rare fluctuations. We discuss a path-integral formulation which provides the exact mass fraction of primordial black holes at formation in the presence of non-Gaussianity. Through a couple of classes of models, one based on single-field inflation and the other on spectator fields, we show that restricting to a Gaussian statistics may lead to severe inaccuracies in the estimate of the mass fraction as well as on the clustering properties of the primordial black holes.

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 O(30)M are likely non-spinning at any redshift, whereas heavier black holes can be nearly extremal up to redshift z ∼ 10. 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.

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 s = S/G N M 2 , where S is the spin and M is the mass of the primordial black hole, is about (Ω dm /π)σ δ 1 − γ 2 . Here, σ 2 δ is the variance of the overdensity at horizon crossing, Ω dm measures the current abundance of the dark matter and the parameter γ is a measure of the width of the power spectrum giving rise to primordial black holes. One has γ = 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 s are at the percent level.

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 O(2 ÷ 3).