Quantum thermodynamics of de Sitter space

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 $T_{\mathrm{dS}}=h/2\pi$. The energy density of this bath obeys the Stefan-Boltzmann law ${\rho }_{\mathrm{dS}}\propto h^4$. 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.

14 pages + Appendix (3 pages). v3: added discussion of relation to other approaches to thermal physics in dS, references improved, typos fixed. To appear in PRD

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• Warm Inflation and its Microphysical Basis
• De Sitter Space and Eternity
• Cosmological expansion and local physics
• A Brief History of the GKLS Equation
• Cosmological Particle Production: A Review
• Characters of different secular effects in various patches of de Sitter space
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• Cosmic Purity Lost: Perturbative and Resummed Late-Time Inflationary Decoherence
• Decoherence out of fire: Purity loss in expanding and contracting universes
• In-in formalism for the entropy of quantum fields in curved spacetimes
• An Open Effective Field Theory for light in a medium
• The irreversible relaxation of inflation
• Holographic vacuum energy regularization and corrected entropy of de Sitter space
• Unification of Stochastic and Quantum Thermodynamics in Scalar Field Theory via a Model with Brownian Thermostat
• Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence