  We discuss the effect of quantum stress tensor fluctuations in deSitter
spacetime upon the expansion of a congruence of timelike geodesics. We treat a
model in which the expansion fluctuations begin on a given hypersurface in
deSitter spacetime, and find that this effect tends to grow, in contrast to the
situation in flat spacetime. This growth potentially leads to observable
consequences in inflationary cosmology in the form of density perturbations
which depend upon the duration of the inflationary period. In the context of
our model, the effect may be used to place upper bounds on this duration.
