Stochastic inflationary dynamics beyond slow-roll and consequences for primordial black hole formation

TL;DR

This paper analyzes how quantum diffusion influences inflationary dynamics during ultra-slow-roll phases, confirming the consistency of stochastic inflation with traditional methods and exploring implications for primordial black hole formation.

Contribution

It provides an analytical and numerical comparison of stochastic inflation and Mukhanov-Sasaki solutions during ultra-slow-roll, clarifying quantum noise effects and the quantum-to-classical transition.

Findings

Stochastic inflation results match Mukhanov-Sasaki calculations at linear level.

Quantum noise significantly impacts ultra-slow-roll inflation dynamics.

The study clarifies the quantum-to-classical transition in this context.

Abstract

We consider the impact of quantum diffusion on inflationary dynamics during an ultra-slow-roll phase, which can be of particular significance for the formation of primordial black holes. We show, by means of a fully analytical approach, that the power spectrum of comoving curvature perturbations computed in stochastic inflation matches precisely, at the linear level, the result obtained by solving the Mukhanov-Sasaki equation, even in the presence of an ultra-slow-roll phase. We confirm this result numerically in a model in which the inflaton has a polynomial potential and is coupled quadratically to the Ricci scalar. En route, we assess the role that quantum noise plays in the presence of an ultra-slow-roll phase, and clarify the issue of the quantum-to-classical transition in this scenario.