Conformal Teleparallel Theories and Weyl Geometry

TL;DR

This paper reviews conformal teleparallel gravity using Weyl geometry, introduces a new invariant model, explores various solutions, and analyzes the universe's energy, expanding the scope beyond traditional TEGR.

Contribution

It presents a Weyl geometric approach to conformal teleparallel gravity, developing an invariant model and exploring its solutions and energy properties.

Findings

Wider class of solutions than TEGR.

Constructed a model invariant under diffeomorphisms, LLT, and WT.

Calculated and analyzed the universe's total and gravitational energies.

Abstract

Despite the fact that General Relativity (GR) has been very successful, many alternative theories of gravity have attracted the attention of a significant number of theoretical physicists. Among these theories, we have theories with conformal symmetry. Here, the use of Weyl geometry to deal with conformal teleparallel gravity is reviewed in great detail. As an application, a model that can be set to be equivalent to the Teleparallel Equivalent of General Relativity (TEGR) and is invariant under diffeomorphisms, local Lorentz transformations (LLT) and Weyl transformations (WT) is created. Some $pp$-wave, spherically symmetric and cosmological solutions are obtained. It turns out that the class of possibles solutions is wider than that of TEGR. In addition, the total and the gravitational energies of the universe are calculated and analyzed.