Palatini gravity with nonmetricity, torsion, and boundaries in metric and connection variables

TL;DR

This paper establishes the equivalence between metric and connection formulations of Palatini gravity with nonmetricity and torsion, using a cohomological approach, and explores implications for singularity detection.

Contribution

It proves the covariant phase space equivalence of metric and connection formulations of Palatini gravity with boundaries, incorporating nonmetricity and torsion, using a cohomological framework.

Findings

Equivalence between metric and connection formulations established.

Implications for singularity identification discussed.

Cohomological approach applied to gravitational theories with boundaries.

Abstract

We prove the equivalence in the covariant phase space of the metric and connection formulations for Palatini gravity, with nonmetricity and torsion, on a spacetime manifold with boundary. To this end, we will rely on the cohomological approach provided by the relative bicomplex framework. Finally, we discuss some of the physical implications derived from this equivalence in the context of singularity identification through curvature invariants.