  This paper discusses the problem of inflation in the context of
Friedmann-Robertson-Walker Cosmology. We show how, after a simple change of
variables, to quantize the problem in a way which parallels the classical
discussion. The result is that two of the Einstein equations arise as exact
equations of motion and one of the usual Einstein equations (suitably
quantized) survives as a constraint equation to be imposed on the space of
physical states. However, the Friedmann equation, which is also a constraint
equation and which is the basis of the Wheeler-deWitt equation, acquires a
welcome quantum correction that becomes significant for small scale factors. To
clarify the general formalism and explicitly show why we choose to weaken the
statement of the Wheeler-deWitt equation, we apply the general formalism to de
Sitter space. After exactly solving the relevant Heisenberg equations of motion
we give a detailed discussion of the subtleties associated with defining
physical states and the emergence of the classical theory. This computation
provides the striking result that quantum corrections to this long wavelength
limit of gravity eliminate the problem of the {\it big crunch}. We also show
that the same corrections lead to possibly measurable effects on the CMB
radiation. For the sake of completeness, we discuss the special case,
$\Lambda=0$, and its relation to Minkowski space. Finally, we suggest
interesting ways in which these techniques can be generalized to cast light on
the question of chaotic or eternal inflation. In particular, we suggest one can
put an experimental lower bound on the distance to a universe with a scale
factor very different from our own, by looking at its effects on our CMB
radiation.
