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 $n_\text{s}, \alpha_\text{s}$, and $\beta_\text{s}$ consistent with the observational bounds. The merger rate is fitted by PBHs with masses of $\mathcal{O}(10)$ $M_{\odot}$ produced in the radiation-dominated era. Then the running of running should be $\beta_\text{s} \sim 0.025$, 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 ($\mathcal{O}(10^{-17})~M_{\odot}$) produced in an early matter-dominated era if a set of running parameters are properly realized.