Photon quantization in cosmological spaces

TL;DR

This paper develops a canonical quantization framework for photons in cosmological spacetimes, focusing on gauge choices and constraints, to improve the computation of photon two-point functions relevant for inflationary models.

Contribution

It introduces a gauge-invariant canonical quantization method for photons in cosmological backgrounds, addressing constraint implementation without relying on spacetime symmetries.

Findings

Identifies inconsistencies in existing de Sitter photon propagators.

Establishes subsidiary conditions for physically consistent photon two-point functions.

Provides a framework for loop computations in inflationary cosmology.

Abstract

Canonical quantization of the photon -- a free massless vector field -- is considered in cosmological spacetimes in a two-parameter family of linear gauges that treat all the vector potential components on equal footing. The goal is setting up a framework for computing photon two-point functions appropriate for loop computations in realistic inflationary spacetimes. The quantization is implemented without relying on spacetime symmetries, but rather it is based on the classical canonical structure. Special attention is paid to the quantization of the canonical first-class constraint structure that is implemented as the condition on the physical states. This condition gives rise to subsidiary conditions that the photon two-point functions must satisfy. Some of the de Sitter space photon propagators from the literature are found not to satisfy these subsidiary conditions, bringing into question their consistency.