Quantum fields in the static de Sitter universe
É. T. Akhmedov, K. V. Bazarov, D. V. Diakonov, Ugo Moschella
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 $T=(2\ensuremath{\pi}{)}^{\ensuremath{-}1}$ in the units of de Sitter curvature. We show that propagators with $T\ensuremath{\ne}(2\ensuremath{\pi}{)}^{\ensuremath{-}1}$ 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.