Primordial black holes in peak theory with a non-Gaussian tail

TL;DR

This paper refines peak theory for primordial black hole (PBH) formation by incorporating critical behavior and non-Gaussian features, revealing significant enhancements in PBH abundance and a unique mass spectrum with a maximum mass.

Contribution

It introduces an improved peak theory framework that accounts for non-Gaussian tails and critical behavior, providing more accurate PBH abundance and mass spectrum predictions.

Findings

PBH abundance is significantly enhanced with exponential tail non-Gaussianity.

The PBH mass spectrum exhibits a distinct maximum mass not seen in simpler models.

Peak theory updates lead to better estimates of PBH formation in inflationary scenarios.

Abstract

In this paper, we update the peak theory for the estimation of the primordial black hole (PBH) abundance, particularly by implementing the critical behavior in the estimation of the PBH mass and employing the averaged compaction function for the PBH formation criterion to relax the profile dependence. We apply our peak theory to a specific non-Gaussian feature called the exponential tail, which is characteristic in ultra slow-roll models of inflation. With this type of non-Gaussianity, the probability of a large perturbation is not suppressed by the Gaussian factor but decays only exponentially, so the PBH abundance is expected to be much enhanced. Not only do we confirm this enhancement even compared to the case of the corresponding nonlinearity parameter $f_\mathrm{NL}=5/2$, but also we find that the resultant PBH mass spectrum has a characteristic maximal mass which is not seen in the simple Press--Schechter approach.