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 quasars by intervening galaxies, focusing on uncertainties in galaxy models (including velocity dispersion, luminosity functions, core radii and magnification bias effects) and on the parameters of the galaxy distribution and luminosity functions. In the process we derive new results on magnification biasing for galaxy lenses with non-zero core radii, and on how to infer the proper velocity dispersions appropriate for use in lensing statistics. We argue that the existing data do not disfavor a large cosmological constant. In fact, for a set of reasonable parameter choices, using the results of 5 optical quasar lensing surveys we find that a maximum likelihood analysis favors a value of $\om$ in the range $ \approx 0.25$-0.55 in a flat universe. An open cosmology is not favored by the same statistical analysis. Systematic uncertainties are likely to be dominant, however, as these results are sensitive to uncertainties in our understanding of galaxy luminosity functions, and dark matter velocity dispersions, as well as the choice of lensing survey, and to a lesser extent the existence of core radii. Further observational work will be required before it is possible to definitively distinguish between cosmological models on the basis of gravitational lensing statistics.