Reconstruction of k-essence inflation in Horndeski gravity

Abstract

In this paper, we analyzed inflation from k-essence in the framework of Horndeski gravity. In the specific, we considered models of canonical scalar field and k-essence with quadratic kinetic term. Viable inflationary models can be reconstructed by starting from the cosmological data. Several possibilities are explored in order to correctly reproduce the spectral index and the tensor-to-scalar ratio of primordial cosmological perturbations.

Reconstruction of inflation from scalar field non-minimally coupled with the Gauss-Bonnet term

“…This result seems to improve the predictivity of the model with respect to the standard framework of GR or other Horndeski theories (see for example Ref. [29]), due to the fact that, when c 2 s is small, the tensor-to-scalar ratio of tensorial perturbations tends to be suppressed, in agreement with cosmological data.…”

“…[26,28] for the framework of General Relativity and of Ref. [29] for Horndeski gravity with the coupling with the Einstein's tensor.…”

“…In this section, we will consider canonical scalar field models where κ = λ = 1 in (28)- (29). Let us start with the case a = 1 in (26).…”

“…In this section, we will generalize our analysis to k-essence models with quadratic kinetic term, namely λ = 2 in (28)- (29). We start with a = 1 in (26), namely we assume (32).…”

“…We will follow the lines of Refs. [26,27,28,29] and we will propose a reconstruction method in order to infer viable models in agreement with the cosmological data. In this respect, we note that one of the most robust predictions of inflation is represented by the possibility of reproducing the cosmological perturbations at the origin of the inhomogeneities of our Friedmann Universe.…”