Testing Cosmological Models by Gravitational Lensing: I. Method and First Applications

Gravitational lensing directly measures mass density fluctuations along the lines of sight to very distant objects. No assumptions need to be made concerning bias, the ratio of fluctuations in galaxy density to mass density. Hence, lensing is a very useful tool to study the universe at low to moderate redshifts. We describe in detail a new method to trace light rays from redshift zero through a three dimensional mass distribution to high redshift. As an example, this method is applied here to a standard cold dark matter universe. We obtain a variety of results, some of them statistical in nature, others from rather detailed case studies of individual ``lines of sight". Among the former are the frequency of multiply imaged quasars, the distribution of separation of the multiple quasars, and the redshift distribution of lenses: all that as a function of quasar redshift. We find effects from very weak lensing to highly magnified multiple images of high redshift objects, which, for extended background sources, (i.e. galaxies), range from slight deformations of the shapes through tangentially aligned arclets up to giant luminous arcs. Different cosmological models differ, increasingly with redshift, in their predictions for the mass (thus gravitational potential) distributions. Our ultimate goal is to apply this method to a number of cosmogonic models and to eliminate some models whose gravitational lensing properties are inconsistent with those observed.