  We study the classical and quantum models of a scalar field
Friedmann-Robertson-Walker (FRW) cosmology with an eye to the issue of time
problem in quantum cosmology. We introduce a canonical transformation on the
scalar field sector of the action such that the momentum conjugate to the new
canonical variable appears linearly in the transformed Hamiltonian. Using this
canonical transformation, we show that, it may lead to the identification of a
time parameter for the corresponding dynamical system. In the cases of flat,
closed and open FRW universes the classical cosmological solutions are obtained
in terms of the introduced time parameter. Moreover, this formalism gives rise
to a Schr\"{o}dinger-Wheeler-DeWitt 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 functions in order to investigate the possible corrections to the
classical cosmologies due to quantum effects by means of the many-worlds and
ontological interpretation of quantum cosmology.
