Photon propagator for inflation in the general covariant gauge

TL;DR

This paper derives the photon propagator in power-law inflation within the general covariant gauge, providing explicit expressions and analyzing its properties, including limits and applications to observable quantities.

Contribution

It presents the first explicit construction of the photon propagator in the simple covariant gauge during power-law inflation, including the exact Coulomb gauge propagator in arbitrary dimensions.

Findings

The photon propagator in simple covariant gauge is more complex than scalar cases.

The derived propagator correctly reproduces de Sitter and flat space limits.

Computed observables are consistent with theoretical expectations.

Abstract

Photon propagator for power-law inflation is considered in the general covariant gauges within the canonical quantization formalism. Photon mode functions in covariant gauges are considerably more complicated than their scalar counterparts, except for the special choice of the gauge-fixing parameter we call the simple covariant gauge. We explicitly construct the position space photon propagator in the simple covariant gauge, and find the result considerably more complicated than its scalar counterpart. This is because of the need for explicitly inverting the Laplace operator acting on the scalar propagator, which results in Appell's fourth function. Our propagator correctly reproduces the de Sitter and flat space limits. We use this propagator to compute two simple observables: the off-coincident field strength-field strength correlator and the energy-momentum tensor, both of which yield consistent results. As a spinoff of our computation we also give the exact expression for the Coulomb gauge propagator in power-law inflation in arbitrary dimensions.