QUANTUM-GRAVITY SLOWS INFLATION

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