A clarification on prevailing misconceptions in unimodular gravity

BENGOCHEA, GABRIEL R.; LEÓN, GABRIEL; PEREZ, ALEJANDRO; SUDARSKY, DANIEL

JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS

IOP PUBLISHING LTD

Año: 2023 vol. 2023

1475-7516

The traditional presentation of Unimodular Gravity (UG) consists on indicating that it is an alternative theory of gravity that restricts the generic diffeomorphism invariance of General Relativity. In particular, as one regularly finds in the literature, unlike General Relativity, UG is invariant only under volume preserving diffeomorphisms. That characterization of UG has led to some confusion and incorrect statements in various treatments on the subject. For instance, sometimes it is claimed (mistakenly) that only spacetime metrics such that |det g_{\mu \nu}| = 1 can be considered as valid solutions of the theory. Additionally, that same (incorrect) statement is often invoked to  argue that some particular gauges (e.g. the Newtonian or synchronous gauge) are not allowed when dealing with cosmological perturbation theory in UG. The present article is devoted to clarify those and other misconceptions regarding the notion of diffeomorphism invariance, in general, and its usage in the context of UG,  in particular.