  We show how, by considering the cumulative effect of tiny quantum
gravitational fluctuations over very large distances, it may be possible to:
($a$) reconcile nucleosynthesis bounds on the density parameter of the Universe
with the predictions of inflationary cosmology, and ($b$) reproduce the
inferred variation of the density parameter with distance. Our calculation can
be interpreted as a computation of the contribution of quantum gravitational
degrees of freedom to the (local) energy density of the Universe.
