CURVATURE OF THE UNIVERSE AND OBSERVED GRAVITATIONAL LENS IMAGE SEPARATIONS VERSUS REDSHIFT

In a flat k = 0, cosmology with galaxies that approximate singular iso thermal spheres, gravitational lens image separations should be uncorr elated with source redshift. But in an open, k = -1, cosmology, such g ravitational lens image separations become smaller with increasing sou rce redshift. The observed separations do become smaller with increasi ng source redshift, but the effect is even stronger than that expected in an Omega = 0 cosmology. The observations are thus not compatible w ith the ''standard'' gravitational lensing statistics model in a flat universe. We try various open and Bat cosmologies, galaxy mass profile s, galaxy merging and evolution models, and lensing aided by clusters to explain the correlation. We find the data are not compatible with a ny of these possibilities within the 95% confidence limit, leaving us with a puzzle. If we regard the observed result as a statistical fluke , it is worth noting that we are about twice as likely to observe it i n an open universe (with 0 < Omega < 0.4) as we are to observe it in a flat one. Finally, the existence of an observed multiple-image lens s ystem with a source at z = 4.5 places a lower limit on the deceleratio n parameter: q(0) > -2.0.