Fake Conformal Symmetry in Unimodular Gravity

TL;DR

This paper investigates Weyl symmetry in unimodular gravity, revealing that Noether currents for conformal and scale symmetries vanish, and discusses classical and quantum equivalences among various gravitational theories.

Contribution

It demonstrates the vanishing of Noether currents in conformally invariant gravitational theories and clarifies their classical and quantum equivalences.

Findings

Noether currents for Weyl and scale symmetries vanish.

Classical and quantum equivalences among Einstein, scalar-tensor, and WTDiff gravity.

Weyl current in scalar action also vanishes.

Abstract

We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry, identically vanish as in the conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with the conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences among Einstein's general relativity, the conformally invariant scalar-tensor gravity and the Weyl-transverse (WTDiff) gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing.