Primordial Black Hole Dark Matter and the LIGO/Virgo observations

TL;DR

This paper revisits primordial black hole (PBH) merger rates, showing that interactions in PBH clusters significantly reduce predicted rates and suggesting QCD epoch PBHs could account for all dark matter without conflicting with current gravitational wave observations.

Contribution

The study provides a detailed numerical analysis of PBH binary evolution in clusters, reducing merger rate predictions and supporting PBHs as dark matter candidates consistent with LIGO/Virgo data.

Findings

PBH merger rates are reduced by interactions in clusters.

QCD epoch PBHs naturally produce a merger peak around 1 solar mass.

Predicted merger rates for 30 solar mass PBHs align with LIGO/Virgo observations.

Abstract

The LIGO/Virgo collaboration have by now detected the mergers of ten black hole binaries via the emission of gravitational radiation. The hypothesis that these black holes have formed during the cosmic QCD epoch and make up all of the cosmic dark matter, has been rejected by many authors reasoning that, among other constraints, primordial black hole (PBH) dark matter would lead to orders of magnitude larger merger rates than observed. We revisit the calculation of the present PBH merger rate. Solar mass PBHs form clusters at fairly high redshifts, which evaporate at lower redshifts. We consider in detail the evolution of binary properties in such clusters due to three-body interactions between the two PBH binary members and a third by-passing PBH, for the first time, by full numerical integration. A Monte-Carlo analysis shows that formerly predicted merger rates are reduced by orders of magnitude due to such interactions. The natural prediction of PBH dark matter formed during the QCD epoch yields a pronounced peak around $1M_{\odot}$ with a small mass fraction of PBHs on a shoulder around $30M_{\odot}$, dictated by the well-determined equation of state during the QCD epoch. We employ this fact to make a tentative prediction of the merger rate of $\sim 30M_{\odot}$ PBH binaries, and find it very close to that determined by LIGO/Virgo. Furthermore we show that current LIGO/Virgo limits on the existence of $\sim M_{\odot}$ binaries do not exclude QCD PBHs to make up all of the cosmic dark matter. Neither do constraints on QCD PBHs from the stochastic gravitational background, pre-recombination accretion, or dwarf galaxies pose a problem. Microlensing constraints on QCD PBHs should be re-investigated. We caution, however, in this numerically challenging problem some possibly relevant effects could not be treated.