$k$-essence non-minimally coupled with Gauss-Bonnet invariant for inflation

TL;DR

This paper explores inflationary models involving a scalar field non-minimally coupled to the Gauss-Bonnet invariant, analyzing perturbations and key inflationary parameters within Horndeski theories.

Contribution

It introduces a formalism for calculating perturbations and inflationary observables in $k$-essence models with Gauss-Bonnet coupling, extending previous work.

Findings

Derived expressions for spectral index and tensor-to-scalar ratio.

Supported early-time acceleration with canonical scalar and $k$-essence.

Provided a framework for perturbation analysis in these models.

Abstract

In this paper, we investigated inflationary solutions for a subclass of Horndeski models where a scalar field is non-minimally coupled with the Gauss-Bonnet invariant. Examples of canonical scalar field and $k$-essence to support the early-time acceleration are considered. The formalism to calculate the perturbations in FRW universe and to derive the spectral index and the tensor-to-scalar ratio is furnished.