m AND 
LIMITS
The subject of the cosmological constant has had a long and
checkered history in cosmology. The reasons for skepticism regarding a
non-zero value of the cosmological constant are many. First, there is
a discrepancy of 
120 orders of
magnitude between current
observational limits and estimates of the vacuum energy density based
on current standard particle theory (e.g.
Carroll, Press and
Turner 1992).
Second, it would require that we are now living at a
special epoch when the cosmological constant has begun to affect the
dynamics of the Universe (other than during a time of inflation). In
addition, it is difficult to ignore the fact that historically a
non-zero has been dragged
out prematurely many times to
explain a number of other apparent crises, and moreover, adding
additional free parameters to a problem always makes it easier to fit
data. Certainly the oft-repeated quote from Einstein to Gamov about
his ``biggest blunder" continues to undermine the credibility of a
non-zero value for .
However, despite the strong arguments that can be made for =
0, there are compelling reasons to keep an open mind on the issue.
First, at present there is no known physical principle that demands
= 0. Although supersymmetry
can provide a mechanism, it is
known that supersymmetry is broken (e.g.,
Weinberg 1989).
Second, unlike the case of Einstein's original arbitrary constant
term, standard particle theory and inflation now provide a physical
interpretation of : it is the
energy density of the vacuum
(e.g., Weinberg
1989).
Third, if theory demands
total = 1, then a number of
observational results can be
explained with a low m and m +
= 1: a) for instance, the
observed large scale
distribution of galaxies, clusters, large voids, and walls is in
conflict with that
predicted by the (standard) cold dark matter model for the origin of
structure (e.g.
Davis et al. 1992;
Peacock & Dodds
1994);
and b) the low values of the matter density based on a number of
methods as described in Section 2. In
addition, the discrepancy between
the ages of the oldest stars and the expansion age can be resolved.
Perhaps the most important reason to keep an open mind is that this is
an issue that ultimately must be resolved by experiment.
The importance of empirically establishing whether there is a non-zero
value of cannot be
overemphasized. However, it underscores
the need for high-accuracy experiments: aspects of the standard model
of particle theory have been tested in the laboratory to precisions
unheard of in most measurements in observational cosmology.
Nevertheless, cosmology offers an opportunity to test the standard
model over larger scales and higher energies than can ever be achieved
by other means. It scarcely needs to be said that overthrowing the
Standard Model (i.e., claiming a measurement of a non-zero value
for ) will require
considerably higher accuracy than is currently available.
What are the current observational limits on ?
In the next sections, limits based on both the observed numbers of
quasars multiply imaged by galaxy ``lenses'' and limits from a
sample of strongly lensed galaxies are briefly discussed.