Cosmology of F(T) Gravity and k-Essence

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.