  We study the classical and quantum models of a flat
Friedmann-Robertson-Walker (FRW) space-time, coupled to a perfect fluid, in the
context of the consensus and a gauge-fixed Lagrangian frameworks. It is shown
that, either in the usual or in the gauge-fixed actions, 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 for the standard matter, and tending towards a big-rip singularity in
which the scale factor diverges for the phantom fluid. We then employ the
familiar canonical quantization procedure in the given cosmological setting to
find the cosmological wave functions in the corresponding minisuperspace. Using
a gauge-fixed (reduced) Lagrangian, we show that, it may lead to a
Schr\"{o}dinger equation for the quantum-mechanical description of the model
under consideration, the eigenfunctions of which can be used to construct the
time dependent 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.
