Photon propagator in de Sitter space in the general covariant gauge

Abstract

We consider a free photon field in $D$-dimensional de Sitter space, and construct its propagator in the general covariant gauge. Canonical quantization is employed to define the system starting from the classical theory. This guarantees that the propagator satisfies both the equation of motion and subsidiary conditions descending from gauge invariance and gauge fixing. We first construct the propagator as a sum-over-modes in momentum space, carefully accounting for symmetry properties of the state. We then derive the position space propagator in a covariant representation, that is our main result. Our conclusions disagree with previous results as we find that the position space photon propagator necessarily breaks de Sitter symmetry, except in the exact transverse gauge limit.