# Primordial black hole formation with non-Gaussian curvature perturbations

## TL;DR

This paper investigates how non-Gaussian curvature perturbations during inflation influence primordial black hole formation, deriving a non-perturbative relation and identifying a critical amplitude that affects collapse conditions.

## Contribution

It introduces a non-perturbative field redefinition relating Gaussian and non-Gaussian curvature perturbations in inflation, and applies this to primordial black hole formation scenarios.

## Key findings

- Derived a non-perturbative relation between Gaussian and non-Gaussian perturbations.
- Identified a new critical amplitude $zeta_*$ affecting black hole formation.
- Showed that smaller perturbation amplitudes can produce significant black hole abundance.

## Abstract

In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude $\zeta_*$, corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which $\zeta_*$ is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.