NO VERY LARGE-SCALE STRUCTURE IN AN OPEN UNIVERSE

We study the effects of negative spatial curvature on the statistics o f inhomogeneities in open cosmological models. In particular we examin e the suppression of large-separation correlations in density and grav itational potential fluctuations and the resulting suppression of larg e-angle correlations in the anisotropy of the microwave background rad iation. We obtain an expression which gives the minimum amount of supp ression of correlations for any statistical distribution described by a ''power spectrum.'' This minimum suppression requires that the corre lations fall off exponentially above the curvature scale. To the exten t that the observed correlations in the temperature anisotropy extend to large angular scales, one can set a lower bound to the radius of cu rvature and hence on Omega(0). A preliminary analysis suggests that th is bound is, in practice, extremely weak, and less stringent than othe r cosmological tests of curvature.