Quantum thermodynamics of de Sitter space

TL;DR

This paper develops a quantum open system framework for de Sitter space, deriving a master equation that reveals its thermal nature with a temperature proportional to the Hubble parameter, and discusses implications for its thermodynamics and stability.

Contribution

It introduces a Markovian master equation approach to quantum fields in de Sitter space, establishing its thermal properties and thermodynamic behavior from a quantum perspective.

Findings

De Sitter space acts as a thermal bath with temperature h / 2π.

Energy density follows Stefan-Boltzmann law proportional to h^4.

Results support the instability of de Sitter space in the infrared.

Abstract

We consider the local physics of an open quantum system embedded in an expanding three-dimensional space $\mathbf x$, evolving in cosmological time $t$, weakly coupled to a massless quantum field. We derive the corresponding Markovian master equation for the system's nonunitary evolution and show that, for a de Sitter space with Hubble parameter $h = $ const., the background fields act as a physical heat bath with temperature $T_{\rm dS} = h / 2 \pi$. The energy density of this bath obeys the Stefan-Boltzmann law $\rho_{\rm dS} \propto h^4$. We comment on how these results clarify the thermodynamics of de Sitter space and support previous arguments for its instability in the infrared. The cosmological implications are considered in an accompanying letter.