Stochastic inflaton wave equation from an expanding environment

Abstract

AbstractWe discuss the inflaton $$\phi $$ϕ in an environment of scalar fields $$\chi _{n}$$χn on flat and curved manifolds. We average over the environmental fields $$\chi _{n}$$χn. We study a contribution of superhorizon $$k\ll aH$$k≪aH as well as subhorizon $$k \gg aH$$k≫aH modes $$\chi _{n}(\mathbf{k})$$χn(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 $$\mathbf{k}$$k in $$\chi _{n}(\mathbf{k})$$χn(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.