On the UV structure of quantum unimodular gravity

It is a well known result that any formulation of unimodular gravity is classically equivalent to General Relativity (GR), however a debate exists in the literature about this equivalence at the quantum level. In this work, we investigate the UV quantum structure of a diffeomorphism invariant formulation of unimodular gravity using functional renormalisation group methods in a Wilsonian context. We show that the effective action of the unimodular theory acquires essentially the same form with that of GR in the UV, as well as that both theories share similar UV completions within the framework of the asymptotic safety scenario for quantum gravity. Furthermore, we find that in this context the unimodular theory can appear to be non--predictive due to an increasing number of relevant couplings at high energies, and explain how this unwanted feature is in the end avoided.
Comment: 11 pages plus Appendix; Some clarifying comments added, results unchanged; Version to appear in Physical Review D