Stochastic-tail of the curvature perturbation in hybrid inflation

TL;DR

This paper investigates the probability distribution of primordial curvature perturbations in hybrid inflation, revealing exponential tails, upper bounds, and a new mechanism that suppresses primordial black hole formation, with implications for inflationary models.

Contribution

The study confirms exponential-tail behaviors in hybrid inflation and introduces Johnson's S_U-distribution as a novel fitting function for the curvature perturbation PDF, highlighting a new perturbation-reduction mechanism.

Findings

Exponential tails of the curvature perturbation PDF are confirmed.

Effective upper bounds on the perturbation are identified, affecting PBH formation.

A new perturbation-reduction mechanism can suppress PBH formation below the threshold.

Abstract

The exponential-tail behaviours of the probability density function (PDF) of the primordial curvature perturbation are confirmed in the mild-waterfall variants of hybrid inflation with the use of the stochastic formalism of inflation. On top of these tails, effective upper bounds on the curvature perturbation are also observed, corresponding to the exact hilltop trajectory during the waterfall phase. We find that in the model where the leading and higher-order terms in the expansion of the inflaton potential around the critical point are fine-tuned to balance, this upper bound can be significantly reduced, even smaller than the primordial black hole (PBH) threshold, as a novel perturbation-reduction mechanism than the one proposed by Tada and Yamada. It makes PBH formation much difficult compared to the Gaussian or exponential-tail approximation. We also introduce Johnson's $S_U$-distribution as a useful fitting function for the PDF, which reveals a nonlinear mapping between the Gaussian field and the curvature perturbation.