Stability analysis of chromo-natural inflation and possible evasion of Lyth's bound

We perform the complete stability study of the model of chromo-natural inflation by Adshead and Wyman, where, due to its coupling to a SU(2) vector, a pseudoscalar inflaton χ slowly rolls on a steep potential. As a typical example, one can consider an axion with a sub-Planckian decay constant f. The model was recently studied by Dimastrogiovanni, Fasiello, and Tolley in the m_g H limit, where m_g is the mass of the fluctuations of the vector field, and H the Hubble rate. We show that the inflationary solution is stable for m_g>2H, while it otherwise experiences a strong instability due to scalar perturbations in the subhorizon regime. The tensor perturbations are instead enhanced at large m_g, while the vector ones remain perturbatively small. Depending on the parameters, this model can give a chiral gravity wave signal that can be detected in ongoing or forthcoming cosmic microwave background experiments. This detection can occur even if, during inflation, the inflaton spans an interval of size Δχ=O(f) which is some orders of magnitude below the Planck scale, evading a well known bound that holds for a free inflaton by Lyth. The spectral tilt of the scalar perturbations typically decreases with decreasing m_g. Therefore the simultaneous requirements of stability, sufficiently small tensor-to-scalar ratio, and sufficiently flat scalar spectrum can pose nontrivial bounds on the parameters of the model.