Abstract
We study a variant of the Chromo-Natural Inflation (CNI) mechanism in which the inflaton interacts only gravitationally with the CNI fields. Integrating out all the non-dynamical scalar fields of the model results in a coupling between the perturbations of the inflaton and of the CNI pseudo-scalar which is significantly greater than the one obtained in the absence of the gauge CNI dynamics. We compute how this greater coupling impacts the power spectrum of the inflaton perturbations that are sourced nonlinearly by the unstable (tensor) gauge CNI modes, and we require that the amplitude of these modes is well below that of the linear perturbations. Combining this result with various constraints, including backreaction effects, the requirement of having observable and dominant sourced gravitational waves (GW), and the current upper bound on the tensor-to-scalar ratio, significantly constrains the range of parameter space where this model can produce an interesting GW signal.