k-essence in Horndeski 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 earlytime 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.