Intrinsic non-Gaussianity of ultra slow-roll inflation

TL;DR

This paper investigates the non-Gaussian features of curvature fluctuations during ultra slow-roll inflation, emphasizing the importance of intrinsic non-Gaussianities for primordial black hole formation and introducing a numerical method to analyze their distribution.

Contribution

It introduces a numerical procedure to compute the probability distribution of curvature perturbations, highlighting the significance of intrinsic non-Gaussianities in ultra slow-roll inflation scenarios.

Findings

Intrinsic non-Gaussianities are significant in ultra slow-roll inflation.

The importance of intrinsic non-Gaussianities depends on the phase's rapidity and duration.

The method's limitations highlight the need for non-perturbative approaches.

Abstract

We study the non-Gaussian tail of the curvature fluctuation, $\zeta$, in an inflationary scenario with a transient ultra slow-roll phase that generates a localized large enhancement of the spectrum of $\zeta$. To do so, we implement a numerical procedure that provides the probability distribution of $\zeta$ order by order in perturbation theory. The non-Gaussianities of $\zeta$ can be shown to arise from its non-linear relation to the inflaton fluctuations and from the intrinsic non-Gaussianities of the latter, which stem from its self interactions. We find that intrinsic non-Gaussianities, which have often been ignored to estimate the abundance of primordial black holes in this kind of scenario, are important. The relevance of the intrinsic contribution depends on the rapidity with which the transient ultra slow-roll phase occurs, as well as on its duration. Our method cannot be used accurately when the perturbative in-in formalism fails to apply, highlighting the relevance of developing fully non-perturbative approaches to the problem.