Stochastic inflaton wave equation from an expanding environment

Abstract

We discuss the inflaton phi in an environment of scalar fields chi _{n} on flat and curved manifolds. We average over the environmental fields chi _{n}. We study a contribution of superhorizon kll aH as well as subhorizon k gg aH modes chi _{n}(mathbf{k}). As a result we obtain a stochastic wave equation with a friction and noise. We show that in the subhorizon regime in field theory a finite number of fields is sufficient to produce a friction and diffusion owing to the infinite number of degrees of freedom corresponding to different mathbf{k} in chi _{n}(mathbf{k}). We investigate the slow roll and the Markovian approximations to the stochastic wave equation. A determination of the metric from the stochastic Einstein–Klein–Gordon equations is briefly discussed.