Abstract
The redshift distribution of galaxy lenses in known gravitational lens systems provides a powerful test that can potentially discriminate amongst cosmological models. However, applications of this elegant test have been curtailed by two factors: our ignorance of how galaxies evolve with redshift, and the absence of methods to deal with the effect of incomplete information in lensing systems. In this paper, we investigate both issues in detail. We explore how to extract the properties of evolving galaxies, assuming that the cosmology is well determined by other techniques. We propose a new nested Monte Carlo method to quantify the effects of incomplete data. We apply the lens-redshift test to an improved sample of seventy lens systems derived from recent observations, primarily from the SDSS, SLACS and the CLASS surveys. We find that the limiting factor in applying the lens-redshift test derives from poor statistics, including incomplete information samples and biased sampling. Many lenses that uniformly sample the underlying true image separation distribution will be needed to use this test as a complementary method to measure the value of the cosmological constant or the properties of evolving galaxies. Planned future surveys by missions like the SNAP satellite or LSST are likely to usher in a new era for strong lensing studies that utilize this test. With expected catalogues of thousands of new strong lenses, the lens-redshift test could offer a powerful tool to probe cosmology as well as galaxy evolution.
Highlights
Gravitational lensing statistics have been used to map the mass distribution in galaxies (Blandford & Narayan 1992; Narayan & Bartelmann 1996; Kochanek 2004) as well as to constrain cosmological parameters (Cheng & Krauss 1998; Chae 2003; Maoz 2005)
We study the recovery bias in the extraction of (i) cosmological constraints with U = P = 0 for the various compiled lens samples, as well as of (ii) galaxy evolution parameters, by fixing the cosmological parameters
Recent results from the SLACS survey suggest that fE ∼ 1, i.e. the lens model velocity dispersions are fairly close to the measured stellar velocity dispersion within an effective radius (Treu et al 2006)
Summary
Gravitational lensing statistics have been used to map the mass distribution in galaxies (Blandford & Narayan 1992; Narayan & Bartelmann 1996; Kochanek 2004) as well as to constrain cosmological parameters (Cheng & Krauss 1998; Chae 2003; Maoz 2005). Systematic errors have plagued the lensing analysis, leading to contradictory results for the derived values of the cosmological constant in a flat Universe (see, for example, Maoz & Rix 1993, K96, Chae et al 2002) These contradictory results were primarily caused by: small number statistics due to the shortage of observed lens systems; assumptions about the relationship between luminosities and masses of galaxies; scatter in the empirical relation between mass and light; and observational biases, mainly the magnification bias. We investigate the lens-redshift test in detail and re-examine the uncertainties that limit its use as a powerful discriminant between cosmological models, as well as its potential to constrain galaxy evolution models We apply this to a new enlarged sample of lenses. We conclude with a discussion of our results and their implication for future observational surveys
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