Observational Constraints on Transverse Gravity: a Generalization of Unimodular Gravity

TL;DR

This paper investigates a modified gravity theory with transverse diffeomorphism symmetry, generalizing unimodular gravity, and analyzes observational constraints, its relation to scalar-tensor theories, and quantum divergence structure.

Contribution

It introduces and constrains a transverse gravity model, extending unimodular gravity, and explores its equivalence to scalar-tensor theories and quantum divergence properties.

Findings

Observational data constrains transverse gravity models.

Transverse gravity is closely related to scalar-tensor theories.

Quantum divergences at one-loop order are discussed.

Abstract

We explore the hypothesis that the set of symmetries enjoyed by the theory that describes gravity is not the full group of diffeomorphisms Diff(M), as in General Relativity, but a maximal subgroup of it, TransverseDiff(M), with its elements having a jacobian equal to unity; at the infinitesimal level, the parameter describing the coordinate change, xi^mu (x), is transverse, i.e., partial_mu(xi^mu)=0. Incidentally, this is the smaller symmetry one needs to propagate consistently a graviton, which is a great theoretical motivation for considering these theories. Also, the determinant of the metric, g, behaves as a "transverse scalar", so that these theories can be seen as a generalization of the better-known unimodular gravity. We present our results on the observational constraints on transverse gravity, in close relation with the claim of equivalence with general scalar-tensor theory. We also comment on the structure of the divergences of the quantum theory to the one-loop order.