One-loop correction to the enhanced curvature perturbation with local-type non-Gaussianity for the formation of primordial black holes

TL;DR

This paper calculates the one-loop correction to the curvature power spectrum with local non-Gaussianities to better understand primordial black hole formation, deriving a perturbativity condition that constrains inflation models.

Contribution

It introduces a detailed calculation of one-loop corrections with local non-Gaussianity parameters and establishes a perturbativity condition to constrain inflationary scenarios for PBH formation.

Findings

Derived a perturbativity condition: |2cAF_NL^2 + 6AG_NL| << 1

Provided constraints on inflation models based on loop correction analysis

Highlighted the significance of non-Gaussianity in PBH abundance predictions

Abstract

As one of the promising candidates of cold dark matter (DM), primordial black holes (PBHs) were formed due to the collapse of over-densed regions generated by the enhanced curvature perturbations during the radiation-dominated era. The enhanced curvature perturbations are expected to be non-Gaussian in some relevant inflation models and hence the higher-order loop corrections to the curvature power spectrum might be non-negligible as well as altering the abundance of PBHs. In this paper, we calculate the one-loop correction to the curvature power spectrum with local-type non-Gaussianities characterizing by $F_{\mathrm{NL}}$ and $G_{\mathrm{NL}}$ standing for the quadratic and cubic non-Gaussian parameters, respectively. Requiring that the one-loop correction be subdominant, we find a perturbativity condition, namely $|2cAF_{\mathrm{NL}}^2+6AG_{\mathrm{NL}}|\ll 1$, where $c$ is a constant coefficient which can be explicitly calculated in the given model and $A$ denotes the variance of Gaussian part of enhanced curvature perturbation, and such a perturbativity condition can provide a stringent constraint on the relevant inflation models for the formation of PBHs.