Comments on MacDowell–Mansouri gravity and torsion

Abstract

Starting with the MacDowell–Mansouri formulation of gravity with a [Formula: see text] gauge group, we introduce new parameters into the action to include the nondynamical Holst term, and the topological Nieh–Yan and Pontryagin classes. Then, we consider the new parameters as fields and analyze the solutions coming from their equations of motion. The new fields introduce torsional contributions to the theory that modify Einstein’s equations.