Even the photon propagator must break de Sitter symmetry

TL;DR

This paper demonstrates that the massless vector field propagator in de Sitter space inherently breaks de Sitter symmetry due to gauge constraints, with implications for quantum field theory in cosmological backgrounds.

Contribution

The authors construct a de Sitter symmetry-breaking propagator that satisfies all quantization conditions, revealing a previously overlooked Ward-Takahashi identity.

Findings

The propagator breaks spatial special conformal transformations.

A homogeneous de Sitter breaking term is necessary for a consistent propagator.

Corrections are relevant for interactions in gauge theories.

Abstract

The propagator for the massless vector field in de Sitter space cannot maintain de Sitter invariance in the general covaraint gauge, except in the exactly transverse gauge limit. This is due to a previously overlooked Ward-Takahashi identity that the propagator must satisfy. Here we construct the propagator that satisfies all the conditions of a consistently quantized theory. Our solution preserves cosmological symmetries and dilations, but breaks spatial special conformal transformations. The solution amounts to adding a homogeneous de Sitter breaking term to previously reported de Sitter invariant solutions of the propagator equation of motion. Even though the corrections we report pertain to the gauge sector of the linear theory, they are relevant and have to be accounted for when interactions are included.