We revisit the cosmological and astrophysical constraints on the fraction of the dark matter in primordial black holes (PBHs) with an extended mass function. We consider a variety of mass functions, all of which are described by three parameters: a characteristic mass and width and a dark matter fraction. Various observations then impose constraints on the dark matter fraction as a function of the first two parameters. We show how these constraints relate to those for a monochromatic mass function, demonstrating that they usually become more stringent in the extended case than the monochromatic one. Considering only the well-established bounds, and neglecting the ones that depend on additional astrophysical assumptions, we find that there are three mass windows, around $5\times 10^{-16}M_\odot,$ $2\times 10^{-14}M_\odot$ and $25-100M_\odot$, where PBHs can constitute all dark matter. However, if one includes all the bounds, PBHs can only constitute of order $10\%$ of the dark matter.Comment: 9 pages, 3 figures. Added discussion about combined constraints. Accepted for publication in Phys. Rev.

The abundance of primordial black holes (PBHs) in the mass range 0.1 − 10 3 M can potentially be tested by gravitational wave observations due to the large merger rate of PBH binaries formed in the early universe. To put the estimates of the latter on a firmer footing, we first derive analytical PBH merger rate for general PBH mass functions while imposing a minimal initial comoving distance between the binary and the PBH nearest to it, in order to pick only initial configurations where the binary would not get disrupted. We then study the formation and evolution of PBH binaries before recombination by performing N-body simulations. We find that the analytical estimate based on the tidally perturbed 2-body system strongly overestimates the present merger rate when PBHs comprise all dark matter, as most initial binaries are disrupted by the surrounding PBHs. This is mostly due to the formation of compact N-body systems at matter-radiation equality. However, if PBHs make up a small fraction of the dark matter, f PBH 10%, these estimates become more reliable. In that case, the merger rate observed by LIGO imposes the strongest constraint on the PBH abundance in the mass range 2 − 160M . Finally, we argue that, even if most initial PBH binaries are perturbed, the present BH-BH merger rate of binaries formed in the early universe is larger than O(10) Gpc −3 yr −1 f 3

We study the production of primordial black hole (PBH) binaries and the resulting merger rate, accounting for an extended PBH mass function and the possibility of a clustered spatial distribution. Under the hypothesis that the gravitational wave events observed by LIGO were caused by PBH mergers, we show that it is possible to satisfy all present constraints on the PBH abundance, and find the viable parameter range for the lognormal PBH mass function. The non-observation of a gravitational wave background allows us to derive constraints on the fraction of dark matter in PBHs, which are stronger than any other current constraint in the PBH mass range 0.5 − 16M . We show that the predicted gravitational wave background can be observed by the coming runs of LIGO, and its non-observation would indicate that the observed events are not of primordial origin. As the PBH mergers convert matter into radiation, they may have interesting cosmological implications, for example in the context of relieving the tension between high and low redshift measurements of the Hubble constant. However, we find that these effects are suppressed as, after recombination, no more that 1% of dark matter can be converted into gravitational waves.

Within the framework of scalar-tensor theories, we study the conditions that allow single field inflation dynamics on small cosmological scales to significantly differ from that of the large scales probed by the observations of cosmic microwave background. The resulting single field double inflation scenario is characterised by two consequent inflation eras, usually separated by a period where the slow-roll approximation fails. At large field values the dynamics of the inflaton is dominated by the interplay between its non-minimal coupling to gravity and the radiative corrections to the inflaton self-coupling. For small field values the potential is, instead, dominated by a polynomial that results in a hilltop inflation. Without relying on the slow-roll approximation, which is invalidated by the appearance of the intermediate stage, we propose a concrete model that matches the current measurements of inflationary observables and employs the freedom granted by the framework on small cosmological scales to give rise to a sizeable population of primordial black holes generated by large curvature fluctuations. We find that these features generally require a potential with a local minimum. We show that the associated primordial black hole mass function is only approximately lognormal.

We derive a lower bound on the merger rate of primordial black hole (PBH) binaries by estimating the maximal fraction of binaries that were disrupted between formation in the early universe and merger, and computing the merger rate of disrupted binaries. This implies robust constraints on the PBH abundance in the range 1 − 100M . We further show that LIGO/Virgo design sensitivity has the potential to reach the PBH mass range of 10 −2 − 10 3 M . These constraints are stronger if PBH are initially spatially clustered.