Primordial black hole abundance from the power spectrum of cosmological perturbations

Abstract

A random field of cosmological perturbations may have rare high peaks which evolve non-linearly after they cross the horizon during the radiation dominated era, forming primordial black holes (PBH). Using recent results for the statistics of large initial overdensities, we will consider a family of well motivated profiles for such overdensities, determining the critical amplitude which causes them to collapse gravitationally. This is relevant for determining the abundance of PBH for a given primordial power spectrum of cosmological perturbations.