Statistical physics of the inflaton decaying in an inhomogeneous random environment

TL;DR

This paper develops a stochastic wave equation model for the inflaton field interacting with an inhomogeneous environment, deriving related equations and thermodynamic principles to understand its evolution in an expanding universe.

Contribution

It introduces a novel stochastic wave equation framework for the inflaton in a complex environment, including derivation of the Fokker-Planck equation and thermodynamic laws.

Findings

Derived a stochastic wave equation for the inflaton.

Established the Fokker-Planck equation for probability distribution.

Analyzed Gaussian probability distributions in this context.

Abstract

We derive a stochastic wave equation for an inflaton in an environment of an infinite number of fields. We study solutions of the linearized stochastic evolution equation in an expanding universe. The Fokker-Planck equation for the inflaton probability distribution is derived. The relative entropy (free energy) of the stochastic wave is defined. The second law of thermodynamics for the diffusive system is obtained. Gaussian probability distributions are studied in detail.