First Order formulation of Unimodular Gravity

TL;DR

This paper introduces first order Lagrangian formulations for Weyl invariant Unimodular Gravity, exploring various approaches and their equivalences under specific gauge conditions.

Contribution

It proposes new first order Lagrangian formulations for Weyl invariant Unimodular Gravity and analyzes their equivalences in different gauges.

Findings

Certain first and second order formulations are equivalent in specific gauges.

Multiple alternative formulations of the theory are examined.

The paper advances understanding of the structure of Unimodular Gravity.

Abstract

First order lagrangians for the Weyl invariant formulation of Unimodular Gravity are proposed. Several alternatives are examined; in some of them first and second order are equivalent in a certain gauge only.