New limits on a cosmological constant from statistics of gravitational lensing

We present new limits on cosmological parameters from the statistics of gravitational lensing, based on the recently revised knowledge of the luminosity function and internal dynamics of E/SO galaxies that are essential in lensing high-redshift QSOs. We find that the lens models using updated Schechter parameters for such galaxies, derived from the recent redshift surveys combined with morphological classification, are found to give smaller lensing probabilities than were calculated earlier. Inconsistent adoption of these parameters from a mixture of various galaxy surveys gives rise to systematic biases in the results. We also show that less compact dwarf-type galaxies that largely dominate the faint part of the Schechter form luminosity function contribute little to lensing probabilities, so that earlier lens models overestimate incidents of small separation lenses. Applications of the lens models to the existing lens surveys indicate that reproduction of both the lensing probability of optical sources and the image separations of optical and radio lenses is significantly improved in the revised lens models. The likelihood analyses allow us to conclude that a flat universe with Ω₀ = 0.3^+0.2_-0.1 and Ω₀ + λ₀ = 1 is preferable, and a matter-dominated flat universe with λ₀ = 0 is ruled out at the 98% confidence level. These new limits are unaffected by the inclusion of uncertainties in the lens properties.