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