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2.3. Number Count of Quasar Lensing

This is a promising new version of the classical number density test. Strong sensitivity to OmegaLambda arises when OmegaLambda is positive and comparable to Omegam. In this case, the universe should have gone through a phase of slower expansion in the recent cosmological past, which should be observed as an accumulation of objects at a specific redshift of order unity. In particular, it should be reflected in the observed rate of lensing of high-redshift quasars by foreground galaxies [7]. The probability of lensing of a source at redshift zs by a population of isothermal spheres of constant comoving density as a function of the cosmological parameters is [1]:

Equation 3 (3)

where da(z1, z2) is the angular diameter distance from z1 to z2. The contours of constant lensing probability in the Omegam - OmegaLambda plane for zs ~ 2 [1] happen to almost coincide with the lines Omegam - OmegaLambda = const. The limits from lensing are thus similar in nature to the limits from SNIa.

Pro: This test shares all the advantages of direct geometrical measures, e.g., being independent of dark matter, fluctuations, GI and galaxy biasing. The high redshifts involved bring about a unique sensitivity to OmegaLambda, compared to the negligible effect that OmegaLambda has on the structure observed at z << 1.

Con: The constraint is weakened if the lensed images are obscured by dust in the early-type galaxies that are responsible for the lensing, especially if E galaxies at z ~ 1 have nuch more dust than low-redshift ones [8]. There is no clear evidence for a strong effect. bullet A similar uncertainty arises if these galaxies had rapid evolution between z ~ 1 and the present; current evidence suggests a weak evolution. bullet The method was criticized for it's sensitivity to the velocity dispersion assumed for the typical lenses and thus to the galaxy luminosity function [9], but the requirement that the distribution of lenses should simultaneously produce the observed distribution of image separations largely invalidates this criticism [10].

Current Results: From the failure to detect the accumulation of lenses, the current limit for a flat model is OmegaLambda < 0.66 (or Omegam > 0.36) at 95% confidence [10] (Fig. 1). If OmegaLambda = 0, this test provides only a weaker bound, Omegam > 0.2 at 90% confidence. Several new lenses are found each year, promising slow but continuous improvement.

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