Conformal invariant teleparallel cosmology

Abstract

We study teleparallel gravitational theories which are invariant under the conformal transformations. The wide family of the gravitational Lagrangians that are invariant under conformal transformations has been investigated. Cosmological solutions inspired by the observational data for a flat Universe in vacuum have been found. There are significant limitations in adding matter fields to the cosmological models by preserving the conformal symmetry. Friedmann-Robertson-Walker (FRW) equations based on the effective terms of energy density and pressure have been rewritten and the continuity equations for the effective quantities are derived. In vacuum and in the absence of any matter field, the FRW equation has an exact solution, for the Hubble parameter, which is consistent with the cosmological data, in particular, the given analytical solution is in good agreement with the ΛCDM model in the present time. Then the scalar-field-torsion models in the cosmological FRW background have been investigated. Massless scalar field equations are very complex with an exact analytical solution in special limits. We have shown that the Lagrangian scalar field with self-interaction, $V(\varphi ) = \tfrac{1} {{4!}}\mu \varphi ^4$, proves that the conformal symmetry is preserved.