k-Essence Non-Minimally Coupled with Gauss–Bonnet Invariant for Inflation

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 a Friedmann–Robertson–Walker (FRW) universe and to derive the spectral index and the tensor-to-scalar ratio is furnished.