  Inflationary quantum gravity simplifies drastically in the leading logarithm
approximation. We show that the only counterterm which contributes in this
limit is the 1-loop renormalization of the cosmological constant. We go further
to make a simplifying assumption about the operator dynamics at leading
logarithm order. This assumption is explicitly implemented at 1- and 2-loop
orders, and we describe how it can be implemented nonperturbatively. We also
compute the expectation value of an invariant observable designed to quantify
the quantum gravitational back-reaction on inflation. Although our dynamical
assumption may not prove to be completely correct, it does have the right time
dependence, it can naturally produce primordial perturbations of the right
strength, and it illustrates how a rigorous application of the leading
logarithm approximation might work in quantum gravity. It also serves as a
partial test of the "null hypothesis" that there are no significant effects
from infrared gravitons.
