Scalar tensor teleparallel dark gravity via Noether symmetry

In this paper, in the framework of teleparallel gravity we consider scalar tensor theories of gravity in which scalar field is non-minimal coupled to torsion scalar. Noether symmetry of the Lagrangian of such a theory for the Friedmann–Robertson–Walker space-time is used to determine the explicit forms for the coupling function and for the potential, and it is shown that both must be power-law forms as a functions of the scalar field. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. It is shown that the equation of state parameter in the present model can cross the phantom divide line for a special case with the coupling function $F(\phi) = \frac{3}{16} \phi^{2}$ and for the potential V(ϕ)=λϕ 2