# Reconstruction of k-essence inflation in Horndeski gravity

## TL;DR

This paper explores reconstructing inflationary models within Horndeski gravity using k-essence, aiming to match cosmological data on spectral index and tensor-to-scalar ratio.

## Contribution

It introduces a method to reconstruct viable inflation models in Horndeski gravity with k-essence, aligning theoretical predictions with observational data.

## Key findings

- Successful reconstruction of inflation models matching cosmological observations
- Identification of conditions for spectral index and tensor-to-scalar ratio compatibility
- Exploration of models with quadratic kinetic terms in k-essence

## 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.