Gauge fields and inflation: Chiral gravitational waves, fluctuations, and the Lyth bound

Models of inflation involving non-Abelian gauge field backgrounds can produce gravitational waves at an observable level with a preferred handedness. This asymmetry comes about because the non-Abelian background generates parity violation in the action for perturbations. In the specific model we study, chromonatural inflation, these gravitational waves can be produced at observable levels even when no field makes a super-Planckian field excursion, thus evading a common formulation of the Lyth bound. Unfortunately, when considered in concert with the scalar fluctuations, this chiral enhancement of the gravitational waves makes the model observationally inviable.