Conformal teleparallel theories and Weyl geometry

Abstract

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