Quantum field theory in de Sitter and quasi–de Sitter spacetimes revisited

It is possible to associate temperatures with the nonextremal 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, the behavior 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 the thermal spectrum due to the presence of pressure-free matter