Quantum fields in the static de Sitter universe

TL;DR

This paper constructs explicit mode expansions of propagators in the static de Sitter universe, analyzing thermal states and alpha-vacua, and clarifies the unique thermal state respecting de Sitter symmetry.

Contribution

It provides explicit mode expansions for propagators in the static de Sitter patch and clarifies the uniqueness of the de Sitter invariant thermal state.

Findings

The de Sitter invariant thermal state has temperature T = (2π)^{-1}.

Propagators with T ≠ (2π)^{-1} have additional singularities.

Explicit expansions for alpha-vacua in the static patch are constructed.

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.