Gauge dependence in QED amplitudes in expanding de Sitter space

TL;DR

This paper investigates the gauge dependence of QED transition amplitudes in expanding de Sitter space, revealing issues with gauge invariance linked to mode frequencies at large times and proposing potential solutions.

Contribution

It identifies the source of gauge dependence in QED amplitudes in de Sitter space and suggests conditions for gauge invariance of external field amplitudes.

Findings

Gauge dependence arises from mode frequencies becoming independent of momenta at large times.

Restricting potentials to vanish at infinity can ensure gauge invariance.

Discussion of gauge invariance issues in the full interacting theory.

Abstract

We consider first order transition amplitudes in external fields in QED in the expanding de Sitter space and point out that they are gauge dependent quantities. We examine the gauge variations of the amplitudes assuming a decoupling of the interaction at large times, which allows to conclude that the source of the problem lies in the fact that the frequencies of the modes in the infinite future become independent of the comoving momenta. We show that a possibility to assure the gauge invariance of the external field amplitudes is to restrict to potentials which vanish sufficiently fast at infinite times, and briefly discuss a number of options in the face of the possible gauge invariance violation in the full interacting theory.