Anisotopic inflation with a non-abelian gauge field in Gauss-Bonnet gravity

TL;DR

This paper explores how Gauss-Bonnet corrections influence anisotropic inflation driven by a non-abelian SU(2) gauge field, revealing that the anisotropy's magnitude and sign are affected by the Gauss-Bonnet term.

Contribution

It introduces a model where Gauss-Bonnet terms are non-minimally coupled to the inflaton and gauge field, showing their impact on anisotropic inflation as an attractor solution.

Findings

Anisotropy is proportional to the sum of slow-roll parameters.

Gauss-Bonnet term can enhance or suppress anisotropy.

Anisotropy can be positive or negative depending on parameters.

Abstract

In presence of Gauss-Bonnet corrections, we study anisotropic inflation aided by a massless $SU(2)$ gauge field where both the gauge field and the Gauss-Bonnet term are non-minimally coupled to the inflaton. In this scenario, under slow-roll approximations, the anisotropic inflation is realized as an attractor solution with quadratic forms of inflaton potential and Gauss-Bonnet coupling function. We show that the degree of anisotropy is proportional to the additive combination of two slow-roll parameters of the theory. The anisotropy may become either positive or negative similar to the non-Gauss-Bonnet framework, a feature of the model for anisotropic inflation supported by a non-abelian gauge field but the effect of Gauss-Bonnet term further enhances or suppresses the generated anisotropy.