Fake Conformal Symmetry in Unimodular Gravity

Understand

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.