Scalar Tensor Teleparallel Dark Gravity via Noether Symmetry

TL;DR

This paper explores scalar-tensor teleparallel gravity models, using Noether symmetry to determine specific forms of coupling and potential functions, and analyzes their solutions and cosmological implications.

Contribution

It introduces a method to derive explicit power-law forms of coupling and potential functions in teleparallel scalar-tensor gravity using Noether symmetry.

Findings

Coupling function and potential are power-law forms of the scalar field.

Solutions of field equations are obtained explicitly.

Equation of state can cross the phantom divide line under specific conditions.

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 $F(\phi) = \frac{3}{16} \phi^2$ and for the potential $V(\phi) = \lambda \phi^{2}$.