Primordial black hole dark matter and LIGO/Virgo merger rate from inflation with running spectral indices: formation in the matter- and/or radiation-dominated universe

Abstract

We study possibilities to explain the whole dark matter abundance by primordial black holes (PBHs) or to explain the merger rate of binary black holes estimated from the gravitational wave detections by LIGO/Virgo. We assume that the PBHs are originated in a radiation-or matter-dominated era from large primordial curvature perturbation generated by inflation. We take a simple model-independent approach considering inflation with large running spectral indices which are parametrized by n s , α s , and β s consistent with the observational bounds. The merger rate is fitted by PBHs with masses of O(10) M produced in the radiation-dominated era. Then the running of running should be β s ∼ 0.025, which can be tested by future observation. On the other hand, the whole abundance of dark matter is consistent with PBHs with masses of asteroids (O(10 −17 ) M ) produced in an early matter-dominated era if a set of running parameters are properly realized. arXiv:1802.06785v4 [astro-ph.CO] 5 Nov 2018 which we are interested [41][42][43][44][45][46][47][48][49][50]. In earlier works including Refs. [37,[51][52][53][54][55][56][57][58][59][60][61][62][63][64][65], the BH merger rate for LIGO/Virgo events and/or the DM abundance in inflationary scenarios have been discussed.Here we do not explicitly introduce features like double inflation [58,62] or additional fields like a curvaton [59, 61, 63] to explain DM or LIGO/Virgo events. It is remarkable and encouraging that such a simple inflationary power spectrum can account for the LIGO/Virgo BH merger rate or the whole DM. The former (latter) is explained by the PBHs of intermediate masses M ∼ O(10)M (asteroid masses M ∼ O(10 −17 )M ). Another feature of this paper is that we consider both cases of BH formation in the radiation-dominated (RD) era and in an early matter-dominated (MD) era. The latter is less extensively studied in the literature, but it is wellmotivated in the inflationary cosmology since e.g. the coherent oscillation phase of the inflaton before reheating behaves as a MD era. For the probability of PBH formations in a MD era, we take into account the effects of anisotropies [66-68] and angular momentum [22], which suppress the PBH formation compared to the case without these effects [66,69]. Differences of this paper from Ref. [59] include the facts that we also consider the running of running parameter β s , that we take into account the effects of angular momentum on the PBH formation rate in the MD era, and that we do not rely on a spectator field.

Sensitivity of primordial black hole abundance on the reheating phase

“…We illustrate this reheating sensitivity in a simplest model of single-field inflation with a quasi-inflection point, which we believe is also manifest itself in other generation models of PBH, for example, double inflation model [61][62][63], double inflection-point model [64], to name just a few. It is worth noting that the reheating sensitivity shown in this paper is different from those interesting discussions where PBHs are formed during slow reheating after inflation [65] or during matter-dominated epoch after inflation but before reheating [66][67][68].…”

Clusters of Primordial Black Holes

“…The PBH as DM with the mass around the same value is also considered in other works, e.g., [94,112]. Contribution to DM can also be maximized with several delta-functions (peaks) at different masses of PBH mass spectrum [111,113].…”

“…So, there are already serious attempts (starting from [120]) to explain such binary BHs existence in the framework of PBH models (e.g., [9,10,26,28,29,46,92,94,[121][122][123][124][125][126]).…”

Clustering of primordial black holes formed in a matter-dominated epoch

“…The efficiency parameter in the early MD epoch has some uncertainty and we assume γ = 1 following Ref. [78]. Unless σ is too large, the value of C 2 is always larger than 5 regardless of uncertainty in estimating the effect of angular momentum.…”