Perturbations in Chromo-Natural Inflation

Abstract: Chromo-Natural Inflation is the first worked example of a model of inflation in which slow-roll inflation is achieved by "magnetic drift" as opposed to Hubble friction. In this work, we give an account of the perturbations at linear order in this model. Our analysis uncovers two novel phenomena. First, the amplitude of scalar curvature perturbations is not directly tied to the shape of the inflationary potential. This allows the theory to violate na\"ive formulations of the Lyth bound. Second, the tensor sector of the theory is significantly altered from the usual case: the non-Abelian gauge field perturbations have a tensor degree of freedom. One chirality of the this tensor can be exponentially enhanced by a temporary instability near horizon crossing; this chiral instability exists because of the classical gauge field background, which violates parity. These tensor fluctuations of the gauge field also couple to gravitational waves at linear order in perturbation theory and source a chiral spectrum of gravitational waves. This spectrum can be exponentially enhanced over the usual inflationary spectrum due to the instability in the gauge sector. These new features cause the theory in its present form to be in significant tension with current observational data. This is because the new scalar physics leads to a significant reddening of the spectral tilt in the same region of parameter space where the exponential enhancement of the gravitational wave amplitude is small enough to satisfy current constraints on the tensor-to-scalar index. Hence, the model either predicts a spectral tilt that is too red, or it overproduces gravitational waves, or both.