Cosmology of F (T) Gravity and k-Essence

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.