General Markovian Equation for Scalar Fields in a Slowly Evolving Background

TL;DR

This paper develops a general, model-independent quantum kinetic equation for slowly evolving scalar fields in adiabatically changing backgrounds, applicable to cosmological and other physical systems.

Contribution

It introduces a first-principles method to derive a Markovian equation for scalar fields without detailed interaction assumptions, relying on adiabatic and perturbative conditions.

Findings

Derivation of a Markovian equation with effective potential and friction

Applicable to cosmological homogeneous and isotropic systems

Method can extend to include spatial gradients

Abstract

We present a general and model-independent method to obtain an effective Markovian quantum kinetic equation for the expectation value of a slowly evolving scalar field in an adiabatically evolving background from first principles of nonequilibrium quantum field theory. The method requires almost no assumptions about the field's interactions and the composition of the background, except that 1) the coupling constants shall be small enough for perturbation theory to be applicable, 2) there is a clear separation between microphysical time scales and the rate at which bulk properties change, and 3) higher time derivatives of the field remain small. The resulting Markovian equation of motion is expressed in terms of an effective potential and friction coefficients. Motivated by cosmological applications we focus on spatially homogeneous and isotropic systems, but the approach could also be applied to spatial gradients.