Unimodular gravity vs general relativity: a status report

Abstract

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 cosmological constant problem is considered to be a fundamental open issue in modern physics, UG is preferred over GR.

Using cosmological perturbation theory to distinguish between General Relativity and Unimodular Gravity

“…This is generally considered as, at least, an alleviation of the cosmological constant problem that plagues GR. At quantum level also, it has been argued that UG can shed some light in the issues that appear in GR [6].…”

“…The discussion of the possible equivalence between UG (without cosmological constant) and GR (in presence of a cosmological constant) is intensive, see Refs. [4][5][6] for example. At the cosmological background level, the equivalence seems to be clearly set out.…”

“…Many discussions exist, on the other hand, on the possible equivalence between GR e UG, but the restriction of the invariance of UG to the TD group seems to indicate that this equivalence is not complete, even if it may appear in some contexts (see, for example, Refs. [4][5][6] and references therein).…”

TDiff invariant field theories for cosmology

“…In recent years, interest in gravitational theories with broken diffeomorphisms invariance has grown. The most popular examples being the so-called unimodular gravity theories [1][2][3][4]. Unimodular gravity restricts the determinant of the metric tensor to be a non-dynamical field thus breaking the full diffeomorphisms (Diff) invariance of General Relativity down to transverse diffeomorphisms (TDiff) [5,6].…”

Tidal Deformability of Neutron Stars in Unimodular Gravity

“…The above form of UG works under an important hypothesis that the energy-momentum tensor is covariantly conserved. It turns out that if the conservation of the energy-momentum tensor is imposed, at least in the classical level, UG does correspond to GR with an additional integration constant associated to the cosmological term [14] 1 (see, for a recent review, [16]).…”