F(T) gravity and k-essence

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Modified teleparallel gravity theory with the torsion scalar have 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 derive conditions for the equivalence between of F(T) models with purely kinetic k-essence. We present a new class models of F(T)-gravity and k-essence. We also proposed some new models of generalized gases and knot universes as well as some generalizations of F(T) gravity.