Quantum field theory in de Sitter and quasi-de Sitter spacetimes: Revisited

TL;DR

This paper investigates the thermality of the de Sitter horizon in Friedmann coordinates and explores quantum field theory in (approximately) de Sitter spacetimes, analyzing vacuum choices, mode functions, and detector responses.

Contribution

It provides a detailed analysis of de Sitter thermality in Friedmann coordinates and introduces a general method for studying quantum fields in nearly de Sitter spacetimes, including matter effects.

Findings

Thermality can be studied directly in Friedmann coordinates.

Vacuum choices significantly affect mode functions and detector responses.

Derived corrections to thermal spectra due to matter presence.

Abstract

It is possible to associate temperatures with the non-extremal horizons of a large class of spherically symmetric spacetimes using periodicity in the Euclidean sector and this procedure works for the de Sitter spacetime as well. But, unlike e.g., the black hole spacetimes, the de Sitter spacetime also allows a description in Friedmann coordinates. This raises the question of whether the thermality of the de Sitter horizon can be obtained, working entirely in the Friedmann coordinates, without reference to the static coordinates or using the symmetries of de Sitter spacetime. We discuss several aspects of this issue for de Sitter and approximately de Sitter spacetimes, in the Friedmann coordinates (with a time-dependent background and the associated ambiguities in defining the vacuum states). The different choices for the vacuum states, behaviour of the mode functions and the detector response are studied in both (1+1) and (1+3) dimensions. We compare and contrast the differences brought about by the different choices. In the last part of the paper, we also describe a general procedure for studying quantum field theory in spacetimes which are approximately de Sitter and, as an example, derive the corrections to thermal spectrum due to the presence of pressure-free matter.