Quantum fields in the static de Sitter universe

Abstract

We construct explicit mode expansions of various tree-level propagators in the Rindler -- de Sitter universe, also known as the static (or compact) patch of the de Sitter spacetime. We construct in particular the Wightman functions for thermal states having a generic temperature $T$. We give a fresh simple proof that the only thermal Wightman propagator that respects the de Sitter isometry is the restriction to the Rindler -- de Sitter wedge of the propagator for the Bunch--Davies state. It is the thermal state with $T=(2\pi {)}^{-1}$ in the units of de Sitter curvature. We show that propagators with $T\ne (2\pi {)}^{-1}$ are only time translation invariant and have extra singularities on the boundary of the static patch. We also construct the expansions for the so-called alpha-vacua in the static patch and discuss the flat limit.

arXiv comment20 pages, 2 figures, 1 appendix

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• Isometry invariance of exact correlation functions in various charts of Minkowski and de Sitter spaces
• Is the Euclidean path integral always equal to the thermal partition function?
• On the backreaction issue for the black hole in de Sitter space-time
• De Sitter entropy: on-shell versus off-shell
• Real-time observables in de Sitter thermodynamics
• Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams
• De Sitter scattering amplitudes in the Born approximation
• Vacuum zero point energy of self-interacting quantum fields in dS background