Curvature of the Universe and Observed Gravitational Lens Image Separations versus Redshift

In a flat, k=0 cosmology with galaxies that approximate singular isothermalspheres, gravitational lens image separations should be uncorrelated withsource redshift. But in an open k=-1 cosmology such gravitational lens imageseparations become smaller with increasing source redshift. The observedseparations do become smaller with increasing source redshift but the effect iseven stronger than that expected in an Omega=0 cosmology. The observations arethus not compatible with the "standard" gravitational lensing statistics modelin a flat universe. We try various open and flat cosmologies, galaxy massprofiles, galaxy merging and evolution models, and lensing aided by clusters toexplain the correlation. We find the data is not compatible with any of thesepossibilities within the 95% confidence limit, leaving us with a puzzle. If weregard the observed result as a statistical fluke, it is worth noting that weare about twice as likely to observe it in an open universe (with 0 -2.0.Comment: 21 pages, 4 figures, AASTeX