# Abundance of primordial black holes with local non-Gaussianity in peak theory

## TL;DR

This paper investigates how local non-Gaussianity influences primordial black hole abundance using peak theory, revealing that even small non-Gaussianity significantly impacts formation estimates.

## Contribution

It introduces a method to estimate PBH abundance considering local non-Gaussianity and demonstrates its substantial effect on formation criteria.

## Key findings

- Non-Gaussianity with |f_NL| ~ 1 affects PBH abundance similarly to amplitude changes in the power spectrum.
- The paper provides a PBH formation criterion based on the compaction function.
- Non-Gaussian effects can alter PBH abundance estimates by factors of a few.

## Abstract

We discuss the effect of local type non-Gaussianity on the abundance of primordial black holes (PBH) based on the peak theory. We provide the PBH formation criterion based on the so-called compaction function and use the peak theory statistics associated with the curvature perturbation with the local type non-Gaussianity. Providing a method to estimate the PBH abundance, we demonstrate the effects of non-Gaussianity. It is explicitly shown that the value of non-linear parameter $|f_{\rm NL}| \sim 1$ induces a similar effect to a few factors of difference in the amplitude of the power spectrum.