Cosmological Einstein-Yang-Mills equations

TL;DR

This paper systematically derives Einstein-Yang-Mills equations for cosmological models with homogeneous spaces, focusing on SU(n) and SO(n) gauge groups, and analyzes the resulting dynamical systems.

Contribution

It introduces a method to construct invariant connections on homogeneous spaces for Einstein-Yang-Mills equations in cosmology, considering specific gauge groups and their representations.

Findings

Derived full evolution equations for simplified cases.

Identified the number of dynamical variables after gauge fixing.

Applied the method to Friedmann-Robertson-Walker and LRS cosmologies.

Abstract

We use a systematic construction method for invariant connections on homogeneous spaces to find the Einstein-SU(n)-Yang-Mills equations for Friedmann-Robertson-Walker and locally rotationally symmetric homogeneous cosmologies. These connections depend on the choice of a homomorphism from the isotropy group into the gauge group. We consider here the cases of the gauge group SU(n) and SO(n) where these homomorphisms correspond to unitary or orthogonal representations of the isotropy group. For some of the simpler cases the full system of the evolution equations are derived, for others we only determine the number of dynamical variables that remain after some mild fixing of the gauge.