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

10 pages, 3 figures, Published in The European Physical Journal C, Feb. 2013

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• Two scalar field cosmology: Conservation laws and exact solutions
• Invariant solutions and Noether symmetries in Hybrid Gravity
• Scalar-Tensor Gravity Cosmology: Noether symmetries and analytical solutions
• Teleparallel dark energy model with a fermionic field via Noether symmetry
• Dynamical symmetries and observational constraints in scalar field cosmology
• Symmetries of geodesic motion in Gödel-type spacetimes
• Nonminimally coupled scalar field in teleparallel gravity: boson stars
• Symmetries of Differential equations and Applications in Relativistic Physics
• Noether gauge symmetry of Dirac field in $2+1$ dimensional gravity