Weyl-invariant Kaluza-Klein theory and the teleparallel equivalent of Weyl-invariant general relativity

A simple method is shown to demonstrate that the teleparallel equivalent of general relativity can be generalized to the Weyl-invariant models. We will also show explicitly that Weyl symmetry is preserved step by step throughout the 5D Kaluza-Klein dimensional-reduction process. As a result, the dimensional reduced model will be shown to be a theory with two scalar fields. When a symmetry-breaking potential is introduced, a strong constraint will effectively turn off one of the scalar fields. For heuristic reasons, the stability properties of the power-law solution associated with the resulting one-scalar-field model will be presented explicitly. In particular, all stable modes can be solved explicitly as functions of the free parameter associated with the symmetry-breaking potential.