Testing the Dark Energy with Gravitational Lensing Statistics

We study the redshift distribution of two samples of early-type gravitational lenses, extracted from a larger collection of 122 systems, to constrain the cosmological constant in the ΛCDM model and the parameters of a set of alternative dark energy models (XCDM, Dvali-Gabadadze-Porrati, and Ricci dark energy models), in a spatially flat universe. The likelihood is maximized for Ω_Λ = 0.70 ± 0.09 when considering the sample excluding the Sloan Lens ACS systems (known to be biased toward large image-separation lenses) and no-evolution, and Ω_Λ = 0.81 ± 0.05 when limiting to gravitational lenses with image separation Δθ > 2'' and no-evolution. In both cases, results accounting for galaxy evolution are consistent within 1σ. The present test supports the accelerated expansion, by excluding the null hypothesis (i.e., Ω_Λ = 0) at more than 4σ, regardless of the chosen sample and assumptions on the galaxy evolution. A comparison between competitive world models is performed by means of the Bayesian information criterion. This shows that the simplest cosmological constant model—that has only one free parameter—is still preferred by the available data on the redshift distribution of gravitational lenses. We perform an analysis of the possible systematic effects, finding that the systematic errors due to sample incompleteness, galaxy evolution, and model uncertainties approximately equal the statistical errors, with present-day data. We find that the largest sources of systemic errors are the dynamical normalization and the high-velocity cutoff factor, followed by the faint-end slope of the velocity dispersion function.