Light Propagation in Inhomogeneous Universes. III. Distributions of Image Separations

Using an analytical model, we compute the distribution of image separations resulting from gravitational lensing of distant sources, for 7 COBE-normalized CDM models with various combinations of Omega_0 and lambda_0. Our model assumes that multiple imaging results from strong lensing by individual galaxies. We model galaxies as nonsingular isothermal spheres, and take into account the finite angular size of the sources. Our model neglects the contribution of the background matter distribution, and assumes that lensing is entirely caused by galaxies. To test the validity of this assumption, we performed a series of ray-tracing experiments to study the effect of the background matter on the distribution of image separations. The analytical model predicts that the distributions of image separations are virtually indistinguishable for flat, cosmological constant models with different values of Omega_0. For models with no cosmological constant, the distributions of image separations do depend upon Omega_0, but this dependence is weak. We conclude that while the number of multiple-imaged sources can put strong constraints on the cosmological parameters, the distribution of image separations does not constrain the cosmological models in any significant way, and mostly provides constraints on the structure of the galaxies responsible for lensing.