Gauge Theories on de Sitter Spacetime

TL;DR

This paper investigates gauge theories in de Sitter spacetime by analyzing the Euclidean version, constructing an inner product for gauge fields, and deriving a two-point function using spherical harmonics.

Contribution

It introduces a method to analyze gauge theories on de Sitter space via Euclidean techniques and spherical harmonics, providing a new way to compute gauge field correlations.

Findings

Inner product for gauge fields on de Sitter space constructed

Two-point function for gauge fields derived

Relation between de Sitter and four-sphere metrics established

Abstract

In this paper we will analyse the inner product for gauge theories in de Sitter spacetime. This will be done by analysing an Euclidean version of the de Sitter metric. Thus, the de Sitter metric will be related to the metric on a four-sphere. Then scalar spherical harmonics and vector spherical harmonics on a four-sphere will be analysed. An inner product for the gauge fields will be constructed using these modes. Finally, a two point function will be constructed, for gauge fields on de Sitter spacetime.