Stochastic non-attractor inflation

TL;DR

This paper extends stochastic inflation formalism to non-attractor models with sound speed, deriving Langevin equations and analyzing stochastic effects on curvature perturbations and boundary crossing probabilities.

Contribution

It introduces a formalism for stochastic non-attractor inflation with sound speed and calculates stochastic corrections to key inflationary observables.

Findings

Stochastic corrections are of the order of the power spectrum.

Derived Langevin equations for superhorizon perturbations.

Analyzed boundary crossing and hitting probabilities in a dS space with boundaries.

Abstract

We extend the formalism of stochastic inflation to the setup of non-attractor inflation with a sound speed $c_s$. We obtain the Langevin equations for the superhorizon perturbations and calculate the stochastic corrections to curvature perturbation power spectrum. It is shown that the fractional stochastic corrections in mean number of e-folds and power spectrum are at the order of power spectrum. We also calculate the boundary crossing and the first hitting probabilities in a hypothetical dS space with two boundaries in field space. Furthermore, the stochastic corrections in power spectrum in a setup akin to eternal inflation with large diffusion term are calculated.