  We consider the quantum gravitational back-reaction on an initially
inflating, homogeneous and isotropic universe whose topology is $T^3 \times
\Re$. Although there is no secular effect at one loop, an explicit calculation
shows that two-loop processes act to slow the rate of expansion by an amount
which becomes non-perturbatively large at late times. By exploiting Feynman's
tree theorem we show that all higher loops act in the same sense.
