Weyl-Invariant Extension of the Metric-Affine Gravity

Metric-affine geometry provides a nontrivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the spacetime (with nonvanishing torsion and nonmetricity). In this paper, we study the generic form of action in this formalism and then construct the Weyl-invariant version of this theory. It is shown that, in Weitzenbock space, the obtained Weyl-invariant action can cover the conformally invariant teleparallel action. Finally, the related field equations are obtained in the general case.