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

TL;DR

This paper investigates the nonlinear effects of coupling between the inflaton and a non-Abelian gauge field in Chromo-Natural Inflation, revealing significant contributions to scalar perturbations that impact CMB and structure formation.

Contribution

It provides the first nonlinear computation of scalar perturbations in Chromo-Natural Inflation, highlighting the role of gauge-inflaton coupling in inflationary phenomenology.

Findings

Nonlinear scalar power spectrum can be significantly enhanced.

The contribution depends mainly on the vector fluctuation mass ratio.

Results improve the fit to CMB data and have implications for small-scale structures.

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.