Gravitational lensing statistics and constraints on the cosmological constant revisited

We re-analyze constraints on the cosmological constant that can be obtained by examining the statistics of strong gravitational lensing of distant qua sars by intervening galaxies, focusing on uncertainties in galaxy models (i ncluding velocity dispersion, luminosity functions, core radii and magnific ation bias effects) and on the parameters of the galaxy distribution and lu minosity functions. In the process we derive new results on magnification b iasing For galaxy lenses with nonzero core radii, and on how to infer the p roper velocity dispersions appropriate for use in lensing statistics. We ar gue that the existing data do not disfavor a large cosmological constant. I n fact, for a set of reasonable parameter choices, using the results of fiv e optical quasar tensing surveys we find that a maximum likelihood analysis favors a value of Ohm(0) in the range approximate to 0.25 - 0.55 in a fat universe. An open cosmology is not favored by the same statistical analysis . Systematic uncertainties are likely to be dominant, however, as these res ults are sensitive to uncertainties in our understanding of galaxy luminosi ty functions, and dark matter velocity dispersions, as well as the choice o f lensing survey, and to a lesser extent the existence of core radii. Furth er observational work will be required before it is possible to definitivel y distinguish between cosmological models on the basis of gravitational len sing statistics.