Non-Gaussian tail of the curvature perturbation in stochastic ultra-slow-roll inflation: implications for primordial black hole production

TL;DR

This paper presents a novel stochastic approach to calculating the probability distribution of curvature perturbations during ultra-slow-roll inflation, revealing a highly non-Gaussian tail that significantly impacts primordial black hole abundance.

Contribution

It introduces the first stochastic calculation of $P(\mathcal{R})$ during USR inflation, capturing non-linearity and non-Markovian effects to assess PBH production.

Findings

Stochastic effects increase PBH abundance by about 10^5 times compared to Gaussian estimates.

The probability distribution $P(\mathcal{R})$ exhibits a highly non-Gaussian tail.

The method accounts for coupled evolution of background and modes with random kicks.

Abstract

We consider quantum diffusion in ultra-slow-roll (USR) inflation. Using the $\Delta N$ formalism, we present the first stochastic calculation of the probability distribution $P(\mathcal{R})$ of the curvature perturbation during USR. We capture the non-linearity of the system, solving the coupled evolution of the coarse-grained background with random kicks from the short wavelength modes, simultaneously with the mode evolution around the stochastic background. This leads to a non-Markovian process from which we determine the highly non-Gaussian tail of $P(\mathcal{R})$. Studying the production of primordial black holes in a viable model, we find that stochastic effects during USR increase their abundance by a factor $\sim 10^5$ compared to the Gaussian approximation.