3.4 Gravitational lensing
The volume of space back to a specified redshift, given by
(44), depends sensitively on . 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 (M = 1,
= 0) case, is given by
where as = 1 / (1 + zs).
![]() |
Figure 9. Gravitational lens probabilities
in a flat universe
with |
As shown in Figure (9), the probability rises
dramatically
as is increased to unity as we
keep
fixed.
Thus, the absence of a large number of such lenses would imply an
upper limit on
.
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
< 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
, including statistics of
giant arcs [119],
deep weak-lensing surveys
[120], and
lensing in the Hubble
Deep Field [121].