Non-minimal Tinges of Unimodular Gravity

TL;DR

This paper investigates how quantum corrections in unimodular gravity with a non-minimally coupled scalar field can distinguish it from general relativity, especially through their different renormalization group flows at quantum level.

Contribution

It constructs a path integral formulation for unimodular gravity, computes one-loop divergences, and identifies a coupling combination that reveals differences from general relativity at quantum scales.

Findings

Quantum corrections differentiate unimodular gravity from GR when non-minimal coupling is present.

The renormalization group flow of key couplings varies between the two theories.

A specific coupling combination has a physical interpretation related to quantum gravitational effects.

Abstract

Unimodular Gravity is normally assumed to be equivalent to General Relativity for all matters but the character of the Cosmological Constant. Here we discuss this equivalence in the presence of a non-minimally coupled scalar field. We show that when we consider gravitation to be dynamical in a QFT sense, quantum corrections can distinguish both theories if the non-minimal coupling is non-vanishing. In order to show this, we construct a path integral formulation of Unimodular Gravity, fixing the complicated gauge invariance of the theory and computing all one-loop divergences. We find a combination of the couplings in the Lagrangian to which we can assign a physical meaning. It tells whether quantum gravitational phenomena can be ignored or not at a given energy scale. Its renormalization group flow differs depending on if it is computed in General Relativity or Unimodular Gravity.