Stochastic inflaton wave equation from an expanding environment

Abstract

We discuss the inflaton $\varphi$ 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 $k<<aH$ as well as subhorizon $k>>aH$ 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 approximaions to the stochastic wave equation. A determination of the metric from the stochastic Einstein-Klein-Gordon equations is briefly discussed,

arXiv commentminor changes, 10 pages

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Cited by in corpus (2)

• State-dependent graviton noise in the equation of geodesic deviation
• Power spectrum of stochastic wave and diffusion equations in the warm inflation models