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

Abstract

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.

Nonlinear perturbations from axion-gauge fields dynamics during inflation

“…In this case, if we ignore the contributions to the elements of the matrices in (3.10) that arise from integrating out the metric perturbations (namely, if we set to zero the metric perturbations by hand), one obtains the set of equations written for instance in eqs. (3.17) of [46]. As explicitly proven in [43], adding and then integrating out the metric perturbations provides additional contributions to the matrices C, K, Ω 2 , and then to the equation of motions, which are suppressed by higher order of the slow roll parameters with respect to the leading terms present in eqs.…”

“…This conclusion, however, does not account for the inflaton perturbations that can be produced at the nonlinear level by the t L mode. The power spectrum of these nonlinear scalar perturbations was computed only recently in the CNI model [46], where it was shown that these perturbations can be greater than the ones obtained by the linearized theory for a wide range of parameters. In this work we have repeated the same computation for the spectator model of [55].…”

“…The bump is very well fitted by a log-normal shape. In [46], an accurate fitting function is given in the regime m Q < 4 which we are making use of in the present work as further elaborated in the Appendix C.…”

“…Concerning the CNI sector, different gauge choices were taken in the studies [43] and [45]. We adopt the convention of [45], that we also used in [46]. The freedom of general coordinate transformations allows to eliminate the two modes from δg ij , while the SU(2) fixing eliminates one linear combination of the three modes emerging from δA a i .…”

The Different Regimes of Axion Gauge Field Inflation

“…Refs. [22,56], the primordial black hole production remains irrelevant in the parameter space in question.…”