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.