No Very Large Scale Structure in an Open Universe

We study the effects of negative spatial curvature on the statistics of inhomogeneities in open cosmological models. In particular we examine the suppression of large-separation correlations in density and gravitational potential fluctuations and the resulting suppression of large-angle correlations in the anisotropy of the microwave background radiation. We obtain an expression which gives the {\it minimum} amount of suppression of correlations for any statistical distribution described by a ``power spectrum''. This minimum suppression requires that the correlations fall off exponentially above the curvature scale. To the extent that the observed correlations in the temperature anisotropy extend to large angular scales, one can set a lower bound to the radius of curvature and hence on $\Omega_0$.