Alternative action for generalized unimodular gravity
Phys. Rev. D 113, 044062 – Published 24 February, 2026
DOI: https://doi.org/10.1103/kywx-9csc
Abstract
We present an alternative formulation of generalized unimodular gravity (GUMG), a class of modifications of general relativity characterized by a special partial breaking of general coordinate covariance. The action for this formulation is derived constructively through a sequence of equivalent representations, beginning with the original GUMG setup and extending the configuration space and gauge structure by introducing time parametrization. Our approach, based on a canonical formalism, parallels the method used by Henneaux and Teitelboim to covariantize the action of unimodular gravity (UMG), which was generalized to consistently accommodate a parametrization via local fields for the entire GUMG family. For completeness, we explore the dynamical structure of the theory and provide a detailed account of its gauge properties. A notable consequence of the consistent parametrization is the emergence of explicit spatial delocalization in the action, manifestations of which we carefully examine. Within the GUMG family, we identify a subfamily of models described by a local action: preserving the essential structural features, these models avoid the complications of spatial nonlocality allowing for a clearer analysis. Unimodular gravity possesses dynamical and constraint structures distinct from those of the GUMG family models; however, UMG appears as an exceptional special case within the family, providing valuable comparative insights.
