The de Sitter QED in Coulomb gauge: first order transition amplitudes

TL;DR

This paper develops a framework for calculating first-order transition amplitudes in de Sitter QED within Coulomb gauge, revealing unique effects of de Sitter geometry such as non-vanishing amplitudes due to gravity.

Contribution

It introduces a method to compute de Sitter QED transition amplitudes considering a stable vacuum and highlights gravity's role in enabling first-order electromagnetic particle creation.

Findings

First-order amplitudes are non-zero due to de Sitter geometry.

Electromagnetic particle creation is significant only in strong gravity regimes.

The approach adapts flat space QED techniques to curved de Sitter spacetime.

Abstract

We construct the de Sitter QED in Coulomb gauge assuming that the quantum modes are prepared by a global apparatus which is able to determine a stable and invariant vacuum state, independent on the local coordinates. Then we proceed in traditional manner postulating the appropriate equal-time commutators and anti-commutators of the interacting fields and deriving the perturbation expansion of the scattering operator. In this approach the $in -out$ transitions amplitudes, measured by the same global apparatus, can be calculated exactly by using the reduction formalism and the perturbation procedure as in the flat case but with significant differences due to the de Sitter geometry. A specific feature is that the gravity eliminates the constraints due to the simultaneous momentum-energy conservation giving rise to QED transitions with non-vanishing amplitudes even in the first order of perturbations. Of a special interest could be the first order amplitudes of the electromagnetic particle creation allowed by the expansion of the de Sitter universe. We show that this effect is significant only in the very strong gravity of the early universe.