  The classical and quantum models of the Friedmann universe originally filled
with a scalar field and radiation have been studied. The radiation has been
used to specify a reference frame that makes it possible to remove ambiguities
in choosing the time coordinate. Solutions to the Einstein and Schroedinger
equations have been studied under the assumption that the rate of scalar-field
variation is much less than the rate of universe expansion (contraction). It
has been shown that, under certain conditions, the quantum universe can be in
quasistationary states. The probability that the universe goes over to states
with large quantum numbers owing to the interaction of the scalar and
gravitational fields is nonzero. It has been shown that, in the lowest state,
the scale factor is on order of the Planck length. The matter- and
radiation-energy densities in the Planck era have been computed. The possible
scenarios of Universe evolution are discussed.
