Classical and quantum dynamics of a perfect fluid scalar-metric
  cosmology
  We study the classical and quantum models of a Friedmann-Robertson-Walker
(FRW) cosmology, coupled to a perfect fluid, in the context of the
scalar-metric gravity. Using the Schutz' representation for the perfect fluid,
we show that, under a particular gauge choice, it may lead to the
identification of a time parameter for the corresponding dynamical system. It
is shown that the evolution of the universe based on the classical cosmology
represents a late time power law expansion coming from a big-bang singularity
in which the scale factor goes to zero while the scalar field blows up.
Moreover, this formalism gives rise to a Schr\"{o}dinger-Wheeler-DeWitt (SWD)
equation for the quantum-mechanical description of the model under
consideration, the eigenfunctions of which can be used to construct the wave
function of the universe. We use the resulting wave function in order to
investigate the possibility of the avoidance of classical singularities due to
quantum effects by means of the many-worlds and ontological interpretation of
quantum cosmology.
