Measuring the curvature of the universe with gravitational lensing

The image separations of the gravitational lens systems as a function of th e source redshift depends on the curvature of the universe if lenses can be approximated by singular isothermal spheres. In a flat k = 0 cosmology, im age separations should be uncorrelated with the source redshift. In an open k = -1 cosmology such image separations become smaller with increasing sou rce redshift and vice versa for closed k = +1 cosmology. The observed lens systems do show negative correlation between the image separation versus th e source redshift. However, the negative correlation seen in the data is mu ch stronger than any correlation expected in open or even in empty universe . Therefore, the curvature effect alone cannot explain the observed negativ e correlation. So we explore other possibilities that may explain this stro ng correlations: steeper galaxy mass profile, lens evolution, like merging and infall, and cluster helping. None of them produce strong enough negativ e correlation seen in the data, leaving us with a puzzle. If a rather unlik ely assumption that all lens systems with image separations lager than 3.0 " are "false" lenses [15], correlation becomes insignificant and nothing is troublesome. However, we show that under such image separation distributio n roughly 300 lens systems suffice to test the curvature of Omega = 0.4 ope n universe with 95% confidence, which is well within the reach of future su rveys.