Interaction of Gravitational Waves with Yang-Mills fields

TL;DR

This paper explores how non-Abelian SU(2) Yang-Mills fields interact with gravitational waves, revealing conditions for interaction, perturbative effects, and boundary-dependent frequency changes in different spacetime backgrounds.

Contribution

It provides new solutions and insights into the interaction mechanisms between Yang-Mills fields and gravitational waves in flat and cosmological backgrounds.

Findings

In flat spacetime, no interaction occurs unless Yang-Mills self-interaction is present.

Perturbations exhibit beat patterns and frequency shifts depending on boundary conditions.

In cosmological backgrounds, interaction occurs even without self-interaction, especially in the electroweak phase.

Abstract

In this paper, we discuss the interaction of non-Abelian SU(2) Yang-Mills progressive waves with gravitational waves. We solve and obtain some interesting solutions to pure Yang-Mills equations in different backgrounds, and perturbative solutions induced due to gravitational waves. These perturbations show `beat patterns' and depending on boundary conditions, changes in frequency. In flat space-time, when the Yang-Mills fields and the gravitational waves are in the same direction there is no interaction, unless there is self interaction of the Yang-Mills fields. In the system with non-zero self interaction the amplitudes of the perturbation are inversely proportional to the Yang-Mills coupling constant. In a cosmological background, the Yang-Mills fields and the gravitational wave interact when they are in the same direction even without self interaction of the Yang-Mills progressive fields. We find that in the electroweak symmetry broken phase of the gauge fields, the interactions are perturbative only for an infinitesimal time.