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.
Highlights
Recent astrophysical data imply that the current expansion of the universe is accelerating [1]
The simplest one is the introduction of the Cosmological Constant Λ in the framework of General Relativity (ΛCDM model), namely an exotic form of energy whose Equation of State (EoS) parameter w is equal to minus one and dynamically remains near this value, but in principle quintessence/phantom-fluid description is not excluded
We introduce the generator of Noether symmetry as [41]
Summary
Recent astrophysical data imply that the current expansion of the universe is accelerating [1]. The existence of an early accelerated epoch, namely the inflation, introduces a new problem to the standard cosmology, and various proposals have been made to construct acceptable inflationary model, including the scalar, spinor SU (2), (non-)abelian vector theory (SU (2)) U (1), etc Another alternative approach to the dark energy puzzle is the modified gravity theories. The fact that the field equations of F (T ) gravity are second order makes these theories simpler than the ones where modification is via curvature invariants, and a deeper investigation on this kind of models is of extreme interest (see [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40] for recent developments).
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