Henneaux-Teitelboim Form of the Generalized Unimodular Gravity Action

TL;DR

This paper introduces an alternative formulation of generalized unimodular gravity using the Henneaux-Teitelboim approach, highlighting its gauge structure, spatial nonlocality, and differences from standard diffeomorphism-invariant theories.

Contribution

It extends the Henneaux-Teitelboim method to GUMG, revealing spatial nonlocality and a modified gauge symmetry structure distinct from traditional unimodular gravity.

Findings

Incorporates time reparameterization into GUMG

Reveals spatial nonlocality in the dynamics

Shows the gauge symmetry is extended but not fully diffeomorphism-invariant

Abstract

We propose an alternative description of generalized unimodular gravity (GUMG), extending the Henneaux-Teitelboim approach to unimodular gravity (UMG). The central feature of this formulation is the consistent incorporation of time reparameterization, which enhances the gauge structure and reveals a spatial nonlocality hidden in the dynamics of the original formulation. We examine the resulting dynamics, emphasizing the effects of spatial nonlocality, and outline the constraint structure. We show that the gauge symmetry in the gravitational sector is extended by a functionally incomplete symmetry, as occurs in the unimodular gravity. However, in contrast to the latter, the resulting action is not fully diffeomorphism-invariant.