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It is a well known result that any formulation of unimodular gravity isclassically equivalent to General Relativity (GR), however a debate exists inthe literature about this equivalence at the quantum level. In this work, weinvestigate the UV quantum structure of a diffeomorphism invariant formulationof unimodular gravity using functional renormalisation group methods in aWilsonian context. We show that the effective action of the unimodular theoryacquires essentially the same form with that of GR in the UV, as well as thatboth theories share similar UV completions within the framework of theasymptotic safety scenario for quantum gravity. Furthermore, we find that inthis context the unimodular theory can appear to be non--predictive due to anincreasing number of relevant couplings at high energies, and explain how thisunwanted feature is in the end avoided.

On the UV structure of quantum unimodular gravity