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

Cosmology of F(T) gravity and k-essence