Quantum Gravity and Inflation
  We review some perturbative results obtained in quantum gravity in an
accelerating cosmological background. We then describe a class of non-local,
purely gravitational models which have the correct structure to reproduce the
leading infrared logarithms of quantum gravitational back-reaction during the
inflationary regime. These models end inflation in a distinctive phase of
oscillations with slight and short violations of the weak energy condition and
should, when coupled to matter, lead to rapid reheating. By elaborating this
class of models we exhibit one that has the same behaviour during inflation,
goes quiescent until the onset of matter domination, and induces a small,
positive cosmological constant of about the right size thereafter. We also
briefly comment on the primordial density perturbations that this class of
models predict.
