The Sloan Digital Sky Survey Quasar Lens Search. VI. Constraints on dark energy and the evolution of massive galaxies

We present a statistical analysis of the final lens sample from the Sloan Digital Sky Survey Quasar Lens Search (SQLS). The number distribution of a complete subsample of 19 lensed quasars selected from 50,836source quasars is compared with theoretical expectations, with particular attention given to the selection function. Assuming that the velocity function of galaxies does not evolve with redshift, the SQLS sample constrains the cosmological constant to Ω _Λ= 0.79 ^+0.06 _-0.07(stat.) ^+0.06 _-0.06(syst.) for a flat universe. The dark energy equation of state is found to be consistent with w = -1 when the SQLS is combined with constraints from baryon acoustic oscillation (BAO) measurements or results from the Wilkinson Microwave Anisotropy Probe (WMAP). We also obtain simultaneous constraints on cosmological parameters and redshift evolution of the galaxy velocity function, finding no evidence for redshift evolution at z ≲ 1 in any combinations of constraints. For instance, number density evolution quantified as ν _n≡ dln φ _*/dln (1 + z) and the velocity dispersion evolution ν _σ≡ dln σ _*/dln (1 + z) are constrained to ν _n= 1.06 ^+1.36 _-1.39(stat.) ^+0.33 _-0.64(syst.) and ν _σ= -0.05 ^+0.19 _-0.16(stat.) ^+0.03 _-0.03(syst.), respectively, when the SQLS result is combined with BAO and WMAP for flat models with a cosmological constant. We find that a significant amount of dark energy is preferred even after fully marginalizing over the galaxy evolution parameters. Thus, the statistics of lensed quasars robustly confirm the accelerated cosmic expansion.