Quantum Diffusion in Sharp Transition to Non-Slow-Roll Phase

TL;DR

This paper investigates how quantum diffusion influences inflationary dynamics during sharp transitions, revealing that stochastic noise does not push the inflaton beyond classical limits and analyzing the distribution of curvature perturbations.

Contribution

It provides a detailed analysis of quantum diffusion effects during sharp inflationary transitions using the stochastic δN formalism, applicable to various transition models.

Findings

Quantum noise affects coarse-grained fields during sharp transitions.

Noise cannot push the inflaton beyond classically unreachable values.

Curvature perturbation distribution decays faster than e^(-3ζ).

Abstract

Transitions between different inflationary slow-roll scenarios are known to provide short non-slow-roll periods with non-trivial consequences. We consider the effect of quantum diffusion on the inflationary dynamics in a transition process. Using the stochastic {\delta}N formalism, we follow the detailed evolution of noises through a sharp transition modeled by the Starobinsky potential, although some of our results apply to any sharp transition. We find how the stochastic noise induced by the transition affects the coarse-grained fields. We then consider the special case that the potential is flat after the transition. It is found that the particular noise we obtain cannot drive the inflaton past the classically unreachable field values. By deriving the characteristic function, we also study the tail behavior for the distribution of curvature perturbations {\zeta}, which we find to decay faster than e^(-3{\zeta}).