Cosmology of F(T) gravity and k-essence

TL;DR

This paper reviews $F(T)$ gravity and its connection to k-essence, analyzing models that could explain dark energy through modifications of teleparallel gravity and establishing conditions for their equivalence.

Contribution

It provides a comprehensive reconstruction analysis of $F(T)$ models and introduces a new class of models linking $F(T)$ gravity with k-essence.

Findings

Derived conditions for $F(T)$ and k-essence equivalence

Presented new $F(T)$-gravity models

Enhanced understanding of dark energy explanations

Abstract

This a brief review on $F(T)$ gravity and its relation with k-essence. Modified teleparallel gravity theory with the torsion scalar has recently gained a lot of attention as a possible explanation of dark energy. We perform a thorough reconstruction analysis on the so-called $F(T)$ models, where $F(T)$ is some general function of the torsion term, and deduce the required conditions for the equivalence between of $F(T)$ models with pure kinetic k-essence models. We present a new class of models of $F(T)$-gravity and k-essence.