The quantum gravitational back-reaction on inflation

We describe our recent calculation of two-loop corrections to the expansion rate of an initially inflating universe on the manifold T-3 x R. 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. (C) 1997 Academic Press