Non-Gaussian tails without stochastic inflation

TL;DR

This paper demonstrates that non-Gaussian tails in curvature perturbations during ultra-slow-roll inflation can be derived analytically and numerically using the δN formalism without stochastic inflation, resolving previous discrepancies.

Contribution

It shows that non-Gaussian tails can be obtained analytically without stochastic inflation and clarifies the role of momentum perturbations in previous approaches.

Findings

Non-Gaussian tails depend on the inflation phase space.

Correct accounting of momentum perturbations aligns δN and stochastic approaches.

Analytical and numerical methods agree on tail shapes.

Abstract

We show, both analytically and numerically, that non-Gaussian tails in the probability density function of curvature perturbations arise in ultra-slow-roll inflation from the $\delta N$ formalism, without invoking stochastic inflation. Previously reported discrepancies between both approaches are a consequence of not correctly accounting for momentum perturbations. Once they are taken into account, both approaches agree to an excellent degree. The shape of the tail depends strongly on the phase space of inflation.