The probability of primordial black hole formation

Abstract

Primordial black holes might make up dark matter, and their abundance is a sensitive probe of the amount of small-scale fluctuations in the early universe and of the theory of inflation that sourced them. In this thesis, we present a calculation of their formation probability in the radiation era directly from the density matrix of any inflationary state seeding the density perturbations for their production, using the Wigner function to define probability distributions of the relevant quantum fields. For Gaussian states and a Gaussian distribution of the overdensities, this yields a well-defined prescription to link the local power spectrum to the nonlocal probability of a region to collapse. We find corrections to previously found results due to nontrivial momentum correlators, and suggest that these might also influence the formation criteria. Extensions of this method to study non-Gaussianity and shape-dependence of the formation criteria are within reach.