Exact solutions in Einstein-Yang-Mills-Dirac systems

TL;DR

This paper derives exact cosmological solutions in Einstein-Yang-Mills-Dirac theories with SU(2) and SU(4) gauge groups, revealing oscillating Yang-Mills fields, fermion production, and sphaleron-like configurations.

Contribution

It introduces a method to find exact symmetric solutions in EYMD theories and interprets them as cosmological models with novel fermion and gauge field dynamics.

Findings

Oscillating Yang-Mills fields passing between vacua

Fermion energy sign change during evolution

Existence of sphaleron-like static solutions

Abstract

We present exact solutions in Einstein-Yang-Mills-Dirac theories with gauge groups SU(2) and SU(4) in Robertson-Walker space-time $R \times S^3 $, which are symmetric under the action of the group SO(4) of spatial rotations. Our approach is based on the dimensional reduction method for gauge and gravitational fields and relates symmetric solutions in EYMD theory to certain solutions of an effective dynamical system. We interpret our solutions as cosmological solutions with an oscillating Yang-Mills field passing between topologically distinct vacua. The explicit form of the solution for spinor field shows that its energy changes the sign during the evolution of the Yang-Mills field from one vacuum to the other, which can be considered as production or annihilation of fermions. Among the obtained solutions there is also a static sphaleron-like solution, which is a cosmological analogue of the first Bartnik-McKinnon solution in the presence of fermions.