Unimodular Gravity vs General Relativity: A status report

Unimodular Gravity is an alternative to General Relativity (GR) which, however, is so closely related to the latter that one can wonder to what extent they are different. The different behavior of the cosmological constant in the semiclassical regimes of both frameworks suggests the possible existence of additional contrasting features. UG and GR are based on two different gauge symmetries: UG is based on transverse diffeomorphisms and Weyl rescalings (WTDiff transformations), whereas GR is based on the full group of diffeomorphisms. This difference is related to the existence of a fiduciary background structure, a fixed volume form, in UG theories. In this work we present an overview as complete as possible of situations and regimes in which one might suspect that some differences between these two theories might arise. This overview contains analyses in the classical, semiclassical, and quantum regimes. When a particular situation is well known we make just a brief description of its status. For situations less analyzed in the literature we provide here more complete analyses. Whereas some of these analyses are sparse through the literature, many of them are new. Apart from the completely different treatment they provide for the cosmological constant problem, our results uncover no further differences between them. We conclude that, to the extent that the technical naturalness of the cosmological constant is regarded as a fundamental open issue in modern physics, UG is preferred over GR since the cosmological constant is technically natural in the former.