On the UV structure of quantum unimodular gravity

TL;DR

This paper investigates the ultraviolet quantum structure of unimodular gravity, demonstrating its similarity to General Relativity in the UV and discussing its implications for asymptotic safety and predictivity.

Contribution

It shows that unimodular gravity shares the same UV behavior as GR and clarifies how potential issues with predictivity are resolved in the quantum regime.

Findings

Unimodular gravity's effective action matches that of GR in the UV.

Both theories exhibit similar UV completions within asymptotic safety.

Unimodular gravity's apparent non-predictivity at high energies is ultimately avoided.

Abstract

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.