Can the conformal factor of the gravitational field be a physical degree of freedom?

TL;DR

This paper investigates whether the conformal factor in gravitational theories can be considered a physical degree of freedom, using gauge-invariant perturbation methods in classical and quantum contexts, and finds it to be non-physical.

Contribution

It demonstrates that the conformal perturbation behaves as a non-physical degree of freedom in both classical and quantum linearized gravity frameworks.

Findings

Conformal perturbation is non-physical in gauge-invariant formulations.

Incompatibility of conformal perturbations with quantum dynamical equations.

Conformal factor does not serve as an independent physical degree of freedom.

Abstract

The role of the conformal factor was analysed in two gauge-invariant perturbative formulations. Using the classical and quantum linearized perturbation approach given by Mukhanov et al \cite{Mukhanov:1990me}, the non-physical behaviour of the conformal perturbation as an isolated degree of freedom is shown. In the quantum gravity context, the restriction to conformal perturbations gives us an incompatibility with the dynamical equations.