Transverse gravity versus observations

TL;DR

This paper explores transverse gravity theories, which differ from General Relativity by having a transverse scalar determinant, and discusses how observational data can constrain these models, especially regarding additional scalar degrees of freedom and equivalence principle violations.

Contribution

It introduces and analyzes transverse gravity models, highlighting their unique features and the observational constraints needed to test their viability against General Relativity.

Findings

Transverse gravity models predict additional scalar degrees of freedom.

These models imply non-equivalence of mass concepts, constrained by equivalence principle tests.

Observational bounds tightly restrict deviations from General Relativity.

Abstract

Theories of gravity invariant under those diffeomorphisms generated by transverse vectors, $\pd_\m\xi^\m=0$ are considered. Such theories are dubbed transverse, and differ from General Relativity in that the determinant of the metric, $g$, is a transverse scalar. We comment on diverse ways in which these models can be constrained using a variety of observations. Generically, an additional scalar degree of freedom mediates the interaction, so the usual constraints on scalar-tensor theories have to be imposed. If the purely gravitational part is Einstein--Hilbert but the matter action is transverse, the models predict that the three {\em a priori} different concepts of mass (gravitational active and gravitational passive as well as inertial) are not equivalent anymore. These transverse deviations from General Relativity are therefore tightly constrained, actually correlated with existing bounds on violations of the equivalence principle, local violations of Newton's third law and/or violation of Local Position Invariance.