Primordial Black Hole Abundances from Peaks Theory

Given the black hole masses observed by LIGO as well as the continued possibility of explaining all of dark matter, there has been a recent renewed interest in primordial black holes (PBHs). In order to understand such phenomena, we need an accurate calculation of the expected abundance of PBHs from inflationary theory. Present computations of the mass spectrum and number density rely on two dubious "rules of thumb" to determine whether or not a primordial perturbation will undergo gravitational collapse. These approximations contribute significant uncertainty to current results, to the extent that most authors do not even estimate their errors. In this presentation, we describe a new method for computing PBH abundances using a combination of peaks theory, numerical relativity simulations and stochastic integration. We present proof of principle results for a simple hybrid inflation model. While computationally intensive, a rigorous error analysis of our method yields 5-10% error bars, improving on previous calculations by orders of magnitude.