Non-perturbative non-Gaussianity and primordial black holes

TL;DR

This paper introduces a non-perturbative approach to calculate primordial black hole abundance considering arbitrary non-Gaussian distributions of primordial curvature perturbations, revealing the importance of intermediate regimes and non-Gaussian effects on black hole formation.

Contribution

It develops a non-perturbative method relating the curvature perturbation to a Gaussian field for arbitrary distributions, enabling accurate PBH abundance calculations beyond perturbative limits.

Findings

Non-Gaussianity significantly affects PBH formation.

Enhancement of PBH formation occurs in the intermediate regime.

Non-Gaussian effects shape the PBH mass distribution.

Abstract

We present a non-perturbative method for calculating the abundance of primordial black holes given an arbitrary one-point probability distribution function for the primordial curvature perturbation, $P(\zeta)$. A non-perturbative method is essential when considering non-Gaussianities that cannot be treated using a conventional perturbative expansion. To determine the full statistics of the density field, we relate $\zeta$ to a Gaussian field by equating the cumulative distribution functions. We consider two examples: a specific local-type non-Gaussian distribution arising from ultra slow roll models, and a general piecewise model for $P(\zeta)$ with an exponential tail. We demonstrate that the enhancement of primordial black hole formation is due to the intermediate regime, rather than the far tail. We also show that non-Gaussianity can have a significant impact on the shape of the primordial black hole mass distribution.