Transforming to Lorentz Gauge on de Sitter

TL;DR

This paper shows how to transform electromagnetic potentials to Lorentz gauge on de Sitter space, preserving invariance and potentially resolving issues about graviton invariance in this background.

Contribution

It constructs a gauge transformation to Lorentz gauge on de Sitter space, addressing linearization instability and invariance issues in gauge fixing.

Findings

Transformed propagator matches previous de Sitter invariant results

Gauge transformation eliminates unphysical breaking of invariance

Technique may resolve graviton invariance questions

Abstract

We demonstrate that certain gauge fixing functionals cannot be added to the action on backgrounds such as de Sitter in which a linearization instability is present. We also construct the field dependent gauge transformation which carries the electromagnetic vector potential from a convenient, non-de Sitter invariant gauge to the de Sitter invariant, Lorentz gauge. The transformed propagator agrees with the de Sitter invariant result previously found by solving the propagator equation in Lorentz gauge. This shows that the gauge transformation technique will eliminate unphysical breaking of de Sitter invariance introduced by a gauge condition. It is suggested that the same technique can be used to finally resolve the issue of whether or not free gravitons are de Sitter invariant.