Solving Stochastic Inflation for Arbitrary Potentials

TL;DR

This paper introduces a perturbative method to solve the Langevin equation in inflationary cosmology, enabling explicit calculation of the inflaton field's probability distribution for arbitrary potentials, including backreaction and volume effects.

Contribution

It presents a novel perturbative approach for solving stochastic inflation equations applicable to various models, with explicit probability distribution calculations and analysis of quantum effects.

Findings

Stochastic effects are significant in new inflation models.

Stochastic effects are negligible in hybrid inflation.

Quantum effects can blur classical distinctions in running mass inflation.

Abstract

A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models namely large field, small field, hybrid and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.