Cosmological consequences of classical flavor-space locked gauge field radiation

We propose a classical SU(2) gauge field in a flavor-space locked configuration as a species of radiation in the early universe, and show that it would have a significant imprint on a primordial stochastic gravitational wave spectrum. In the flavor-space locked configuration, the electric and magnetic fields of each flavor are parallel and mutually orthogonal to other flavors, with isotropic and homogeneous stress-energy. Due to the non-Abelian coupling, the gauge field breaks the symmetry between left- and right-circularly polarized gravitational waves. This broken chiral symmetry results in a unique signal: non-zero cross correlation of the cosmic microwave background temperature and polarization, $TB$ and $EB$, both of which should be zero in the standard, chiral symmetric case. We forecast the ability of current and future CMB experiments to constrain this model. Furthermore, a wide range of behavior is shown to emerge, depending on the gauge field coupling, abundance, and allocation into electric and magnetic field energy density. The fluctuation power of primordial gravitational waves oscillates back and forth into fluctuations of the gauge field. In certain cases, the gravitational wave spectrum is shown to be suppressed or amplified by up to an order of magnitude depending on the initial conditions of the gauge field.