The statistics of wide-separation lenses
  The probability that high-redshift sources are gravitationally-lensed with large image separations (i.e., greater than can be produced by galactic deflectors) is determined by the cosmological population of group- and cluster-sized halos. Thus the observed frequency of wide-separation lensed quasars can be used to constrain not only the halo distribution, but also a number of cosmological parameters. A calculation of the optical depth due to collapsed, isothermal halos is a useful guide to the lens statistics, and illustrates that the number of wide-separation lenses is a sensitive probe of the mean density of the universe and the present day density variance whilst being nearly independent of the cosmological constant. 
Daniel J. Mortlock (Cambridge University)