K-essence in Horndeski models

TL;DR

This paper explores a class of Horndeski models with k-essence scalar fields, presenting solutions for early universe inflation and bounce, and analyzing perturbations to derive key inflationary parameters.

Contribution

It introduces a reconstruction method for Horndeski models with k-essence and provides a formalism for perturbation analysis during inflation.

Findings

Solutions for inflation and bounce in the model

Calculation of spectral index and tensor-to-scalar ratio

Framework for perturbation analysis in Horndeski k-essence models

Abstract

In this paper, we investigate a simple class of Horndeski models where the scalar field plays the role of a k-essence fluid. We present several solutions for early-time universe, namely inflation and cosmological bounce, by making use of some reconstruction technique. Moreover, we furnish the formalism to calculate perturbations in FRW space-time and we compute the spectral index and the tensor-to-scalar ratio during inflation.