Constraining cosmology with image separation statistics for gravitationally-lensed quasars in the Sloan Digital Sky Survey

The Sloan Digital Sky Survey (SDSS) has successfully compiled data on more than 300,000 quasars. It, therefore, provides the best sample of multiple-image, gravitationally-lensed quasistellar objects (QSOs) with a well-defined selection effect. We use a SDSS Quasar Lens Search (SQLS) sample of lensed quasars to investigate the constraints on the matter density Ω_m and the cosmological constant Ω_Λ. In order to be free from magnification bias, we use only image separation statistics, which requires detailed knowledge of the source’s luminosity function at all redshifts. The maximum-likelihood analysis shows that cosmological models with non-zero cosmological constant are more likely, but the statistical significance is not large enough. Monte-Carlo simulation show that 100 or more lensed QSOs can provide constraints comparable to other major cosmological constraints. It also shows that unless the number of lensed QSOs is an order-of-magnitude larger, the lensing statistics test has a degeneracy in the Ω_Λ−Ω_m parameter space in the direction roughly perpendicular to Ω_Λ + Ω_m = 1 and that the lensing statistics test alone cannot determine Ω_Λ and Ω_m simultaneously. We also derive constraints on the equation-of-state parameter for dark energy.