Interaction of gravitational waves with Yang–Mills fields

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.