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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, Chromo-Natural 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.