  We describe our recent calculation of two-loop corrections to the expansion
rate of an initially inflating universe on the manifold $T^3 \times \Re$. If
correct, our result proves that quantum gravitational effects slow the rate of
inflation by an amount which becomes non-perturbatively large at late times. In
a preliminary discussion of basic issues we show that the expansion rate is a
gauge invariant, and that our ultraviolet regulator does not introduce spurious
time dependence. We also derive a sharp bound on the maximum strength of higher
loop effects.
