Equivalence principles in Weyl transverse gravity

TL;DR

This paper compares general relativity and Weyl transverse gravity, showing they are the only two metric theories in 4D that satisfy the equivalence principle, and explores how weaker forms of the principle are realized in Weyl transverse gravity.

Contribution

It demonstrates the uniqueness of these two theories in obeying the equivalence principle and analyzes the realization of weaker principles in Weyl transverse gravity.

Findings

Only two metric theories in 4D satisfy the equivalence principle.

Weyl transverse gravity can realize weaker equivalence principles.

Matter field behavior in Weyl transverse gravity is clarified.

Abstract

There exist two consistent theories of massless, self-interacting gravitons, which differ by their local symmetries: general relativity and Weyl transverse gravity. We show that these two theories are also the only two metric descriptions of gravity in 4 spacetime dimensions which obey the equivalence principle for test gravitational physics. We further analyse how the weaker formulations of the equivalence principle are realised in Weyl transverse gravity (and its generalisations). The analysis sheds light on the behaviour of matter fields in this theory.