Nonlinear perturbations from the coupling of the inflaton to a non-Abelian gauge field, with a focus on Chromo-Natural Inflation

Several models of inflation employing a triplet of SU(2) vectors with spatially orthogonal vacuum expectation values (VEVs) have been recently proposed. One (tensor) combination $t$ of the vector modes is amplified in some momentum range during inflation. Due to the vector VEVs, this combination mixes with gravitational waves (GW) at the linear level, resulting in a GW amplification that has been well studied in the literature. Scalar perturbations in this class of models have been so far studied only at the linear level. We perform a first step toward the nonlinear computation using as an example the original model of Chromo-Natural Inflation. We compute the contribution to the scalar power spectrum arising from the coupling of the combination $t$ to the inflaton. This contribution is mostly controlled by a single parameter of the model (namely, the ratio between the mass of the fluctuations of the vector field and the Hubble rate), and, for a wide range of this parameter, it can significantly affect the phenomenology obtained from the linear theory. This nonlinear contribution is significantly blue, improving the comparison between the two-point function and the Cosmic Microwave Background (CMB) data. This growth can be also relevant for smaller scale phenomenology, such as large scale structure, CMB distortions, and primordial black holes.