The path integral of unimodular gravity

TL;DR

This paper calculates the one-loop effective action in unimodular gravity from two formulations and finds it matches that of General Relativity, indicating their quantum equivalence.

Contribution

It demonstrates the quantum equivalence of different classical formulations of unimodular gravity by explicit computation of the effective action.

Findings

Effective action is the same in both formulations of unimodular gravity.

The effective action agrees with that of General Relativity.

Supports the quantum equivalence between unimodular gravity and General Relativity.

Abstract

We compute the one-loop effective action in unimodular gravity, starting from two different classical formulations of the theory. We find that the effective action is the same in both cases, and agrees with the one of General Relativity.