The statistics of primordial black holes in a radiation dominated Universe -- recent and new results

Understand

We review the non-linear statistics of Primordial Black Holes that form from the collapse of over-densities in a radiation dominated Universe.

• We focus on the scenario in which large over-densities are generated by rare and Gaussian curvature perturbations during inflation.
• As new results, we show that the mass spectrum follows a power law determined by the critical exponent of the self-similar collapse up to a power spectrum dependent cut-off, and that the abundance related to very narrow power spectra is exponentially suppressed.
• Related to this, we discuss and explicitly show that the Press-Schechter approximation, as well as the statistics of mean profiles, lead to wrong conclusions for the abundance and mass spectrum.