Scalar tensor teleparallel dark gravity via Noether symmetry

Abstract

In this paper, in the framework of teleparallel gravity we consider scalar tensor theories of gravity in which scalar fields are nonminimal coupled to torsion scalar. Noether symmetry of the Lagrangian of such a theory for the Friedman-Robertson-Walker spacetime 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 (φ) = 3 16 φ 2 and for the potential V (φ) = λφ 2 .

f(T,𝒯) gravity and cosmology

“…The incorporation of non-minimally coupled scalar-torsion theories was performed in [90][91][92][93][94][95][96][97][98], where a scalar field couples non-minimally to the torsion scalar T . Similarly, in [99] nonminimally matter-torsion theories were constructed, where the matter Lagrangian is coupled to a second f (T ) function.…”

Teleparallel quintessence with a nonminimal coupling to a boundary term

“…In recent years an alternative formulation has been considered where the coupling occurs between the scalar field and torsion of the form ξTϕ 2 [51][52][53][54][55][56][57][58][59][60][61][62]. This gives rise to different dynamics and interesting phenomenology, for example phantom behavior and dynamical crossing of the phantom barrier.…”

Scalar-tensor teleparallel wormholes by Noether symmetries

“…After solving the equations, we get the form of metric coefficients, symmetry generators, invariants and the form of torsion and potential functions. This approach has been extensively studied in literature [16][17][18][19][20].…”