We show that high-frequency, small-amplitude oscillations of Newton's constant {ital G} can dramatically alter cosmology even if the frequency is very high compared to the expansion rate. For example, it is possible to have a spatially flat universe in which dynamical tests of {Omega}==(matter density)/(critical density)---tests which attempt to directly measure the mass density of the universe---obtain values less than unity ({Omega}==0.1--0.3, say). The cosmological effects can be obtained in a frequency-amplitude range allowed by all known constraints on {ital G} and its time derivative.