# Effect of nonlinearity between density and curvature perturbations on the primordial black hole formation

## TL;DR

This paper investigates how nonlinear relationships between density and curvature perturbations influence primordial black hole formation, revealing a slight suppression effect comparable to local non-Gaussianity with f_NL around -1.

## Contribution

It introduces a detailed analysis of nonlinear effects on PBH formation, quantifies non-Gaussianity, and estimates the suppression of PBH abundance during the Radiation era.

## Key findings

- Nonlinear effects slightly suppress PBH formation.
- Larger curvature perturbations are needed due to nonlinearity.
- Suppression is comparable to local non-Gaussianity with f_NL ~ -1.

## Abstract

We study the effect of the nonlinear relation between density and curvature perturbations on the formation of PBHs. By calculating the variance and skewness of the density perturbation we derive the non-Gaussian property. As a criterion for PBH formation, the compaction function is used and it is found that larger curvature perturbations are required due to the nonlinear effect. We estimate the PBH abundance based on the Press-Schechter formalism with non-Gaussian probability density function during Radiation dominated era. It is found that the nonlinear effect slightly suppresses the PBH formation and the suppression is comparable to that expected if the primordial curvature perturbation would have the local form of non-Gaussianity with nonlinear parameter $f_\text{NL} \sim -1$.