  We analyze the origin of the quasiclassical realm from the no-boundary
proposal for the universe's quantum state in a class of minisuperspace models.
The models assume homogeneous, isotropic, closed spacetime geometries, a single
scalar field moving in a quadratic potential, and a fundamental cosmological
constant. The allowed classical histories and their probabilities are
calculated to leading semiclassical order. We find that for the most realistic
range of parameters analyzed a minimum amount of scalar field is required, if
there is any at all, in order for the universe to behave classically at late
times. If the classical late time histories are extended back, they may be
singular or bounce at a finite radius. The ensemble of classical histories is
time symmetric although individual histories are generally not. The no-boundary
proposal selects inflationary histories, but the measure on the classical
solutions it provides is heavily biased towards small amounts of inflation.
However, the probability for a large number of efoldings is enhanced by the
volume factor needed to obtain the probability for what we observe in our past
light cone, given our present age. Our results emphasize that it is the quantum
state of the universe that determines whether or not it exhibits a
quasiclassical realm and what histories are possible or probable within that
realm.
