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3.4 Gravitational lensing

The volume of space back to a specified redshift, given by (44), depends sensitively on OmegaLambda. Consequently, counting the apparent density of observed objects, whose actual density per cubic Mpc is assumed to be known, provides a potential test for the cosmological constant [112, 113, 114, 3] Like tests of distance vs. redshift, a significant problem for such methods is the luminosity evolution of whatever objects one might attempt to count. A modern attempt to circumvent this difficulty is to use the statistics of gravitational lensing of distant galaxies; the hope is that the number of condensed objects which can act as lenses is less sensitive to evolution than the number of visible objects.

In a spatially flat universe, the probability of a source at redshift zs being lensed, relative to the fiducial (OmegaM = 1, OmegaLambda = 0) case, is given by

Equation 53 (53)

where as = 1 / (1 + zs).

Figure 9

Figure 9. Gravitational lens probabilities in a flat universe with OmegaM + OmegaLambda = 1, relative to OmegaM = 1, OmegaLambda = 0, for a source at z = 2.

As shown in Figure (9), the probability rises dramatically as OmegaLambda is increased to unity as we keep Omega fixed. Thus, the absence of a large number of such lenses would imply an upper limit on OmegaLambda.

Analysis of lensing statistics is complicated by uncertainties in evolution, extinction, and biases in the lens discovery procedure. It has been argued [115, 116] that the existing data allow us to place an upper limit of OmegaLambda < 0.7 in a flat universe. However, other groups [117, 118] have claimed that the current data actually favor a nonzero cosmological constant. The near future will bring larger, more objective surveys, which should allow these ambiguities to be resolved. Other manifestations of lensing can also be used to constrain OmegaLambda, including statistics of giant arcs [119], deep weak-lensing surveys [120], and lensing in the Hubble Deep Field [121].

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