A note on classical and quantum unimodular gravity

TL;DR

This paper examines unimodular gravity, showing it is classically equivalent to General Relativity and discussing its quantum aspects, concluding that any differences are due to different quantum theory definitions rather than fundamental distinctions.

Contribution

It clarifies the classical equivalence of unimodular gravity to GR and discusses the subtle quantum equivalence, emphasizing that differences arise from different quantum theory formulations.

Findings

Unimodular gravity is classically a gauge-fixed version of GR.

Quantum equivalence between unimodular gravity and GR can be maintained at high momenta.

Quantum inequivalence indicates different quantum theories sharing the same classical limit.

Abstract

We discuss unimodular gravity at a classical level, and in terms of its extension into the UV through an appropriate path integral representation. Classically, unimodular gravity is simply a gauge fixed version of General Relativity (GR), and as such it yields identical dynamics and physical predictions. We clarify this and explain why there is no sense in which it can "bring a new perspective" to the cosmological constant problem. The quantum equivalence between unimodular gravity and GR is more of a subtle question, but we present an argument that suggests one can always maintain the equivalence up to arbitrarily high momenta. As a corollary to this, we argue that whenever inequivalence is seen at the quantum level, that just means we have defined two different quantum theories that happen to share a classical limit.