Markovian Dynamics in de Sitter

TL;DR

This paper demonstrates that from the perspective of a de Sitter observer, out-of-equilibrium scalar fields appear to thermalize in a Markovian manner, supported by a systematic expansion and explicit calculations.

Contribution

It introduces a systematic expansion method for tracing out the environment, revealing Markovian thermalization in de Sitter space and computes the first-order correction to relaxation exponents.

Findings

Out-of-equilibrium states appear thermalized in a Markovian way.

Calculated the $O(rac{rac{1}{4}})$ correction to relaxation exponents.

Validated the Markovian approximation for scalar fields in de Sitter space.

Abstract

The equilibrium state of fields in the causal wedge of a dS observer is thermal, though realistic observers have only partial access to the state. To them, out-of-equilibrium states of a light scalar field appear to thermalize in a Markovian fashion. We show this by formulating a systematic expansion for tracing out the environment. As an example, we calculate the $O(\lambda)$ correction to the result of Starobinsky and Yokoyama for the relaxation exponents of $\lambda \phi^4$ theory.