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.

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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.