6. The gravitational lensing rate
The probability of production of multiple images of a quasar or
a radio source by
gravitational lensing by a foreground galaxy, or of strongly
lensed images of a galaxy by a foreground cluster of galaxies,
adds the relativistic expression for the deflection of light to
the physics of the homogeneous cosmological model.
Fukugita, Futamase, and
Kasai (1990)
and Turner (1990)
point out the value of this test: at small
M0 the
predicted lensing rate is
considerably larger in a flat model with
than in an
open model with
= 0 (as
illustrated in Fig 13.12 in
Peebles, 1993).
The measurement problem for the analysis of quasar lensing
is that quasars that are not lensed are not magnified by
lensing, making them harder to find and the correction for
completeness of detection harder to establish. Present estimates
(Falco, Kochanek, and
Muñoz, 1998;
Helbig et al., 1999)
do not seriously constrain
M0 in an
open model, and in a flat model
(
K0 = 0)
suggest
M0 >
0.36 at
2
. This is close to the
upper bound in Eq. (59).
Earlier indications that the lensing rate in a flat model with
constant
requires
a larger value of
M0 than is
suggested by galaxy dynamics led
Ratra and Quillen (1992)
and Waga and Frieman
(2000)
to investigate the inverse power-law
potential dark energy scalar field case. They showed this
can significantly lower the predicted lensing rate at
K0 = 0
and small
M0. The
lensing rate still
is too uncertain to draw conclusions on this point, but advances
in the measurement certainly will be followed with interest.
The main problem in the interpretation of the rate of strong lensing of galaxies by foreground clusters as a cosmological test is the sensitivity of the lensing cross section to the mass distribution within the cluster (Wu and Hammer, 1993); for the present still somewhat uncertain state of the art see Cooray (1999) and references therein.