Annu. Rev. Astron. Astrophys. 1992. 30:
499-542
Copyright © 1992 by . All rights reserved |

The cosmological constant is an idea whose time has come . . . . and gone . . . . and come . . . . and so on. The most recent cycle of interest derives from a mutually supportive combination of aggressive theoretical prejudice and new, suggestive, observations.

Theorists, in aggregate, strongly believe (on the basis of little or
no observational evidence) that
_{tot} = 1. This belief
is not only
supported by the Copernican view that the present cosmological epoch
should not be special, but is also the firm prediction of inflationary
models (which also explain several, other otherwise, mystifying
cosmological puzzles). Nucleosynthetic evidence against baryons
providing more than
_{tot} = 0.1 does not
sway this conviction, but only
fuels equally fervent belief in non-baryonic dark matter.

However, the preponderance of evidence against *any* form of dynamical
matter able to provide _{M} > 0.2 or so is a definite
embarrassment. Even the tentative evidence of large-scale velocity
flows, which may allow _{M}
1, cannot be warmly embraced
by the many
theorists who favor the Cold Dark Matter theory of structure formation
in its canonical form: CDM with
_{M} = 1 and a constant
bias factor does
not provide sufficient power on large spatial scales.

Postulating an _{}-dominated model seems to
solve a lot of problems
at once. The cosmological constant supplies the ``missing matter'' to
make _{tot} = 1. It
modifies CDM to put more (perhaps sufficient) power
on large scales, *and* it does so in a way compatible with anisotropy
limits on the cosmic microwave background. Simultaneously, it cleans
up that old embarrassment: the apparent discrepancy, for larger values
of *H*_{0} in its observationally viable range, between the
age of the universe and the age of globular clusters.

On the observational side, the new cycle of interest in
was for a
time supported by evidence of an excess of faint galaxies in B band
number vs magnitude counts, and by the realization that previous
number vs redshift evidence *against* a significant
_{} (Loh-Spillar) was
flawed in its reliance on an overly simple model for galaxy evolution.

Unfortunately, this new evidence has been undermined by near-IR K band counts that show an opposite trend, and by new appreciation of the importance of selection effects.

Furthermore, while arguably convenient, a non-zero
_{} is not really
necessary for solving the theorists' problems:
_{M} = 1 in the form of
dynamical baryonic plus nonbaryonic dark matter (of unknown
character!) is not ruled out, and is perhaps supported by large-scale
streaming velocities. Closing the universe with
_{} in fact does not
remove the need to postulate nonbaryonic matter, unless one is willing
to have the universe be *older* than 30 Gyr *and* have a very
low value for *H*_{0}
(Figure 10). CDM theory can be
fixed by abandoning the
assumption (made originally as a matter of convenient simplification,
not physical necessity) of a constant bias factor; indeed this may be
forced on the theory by new numerical simulations, and by the COBE
microwave anisotropy measurements.

In terms of ruling *in* a non-zero cosmological constant, the
situation now is not too different than it has been in the past. A
high value of *H*_{0} (> 80 km/s/Mpc, say), combined with
no loss of
confidence in a value 12-14 Gyr as a *minimum* age for some globular
clusters, would effectively prove the existence of a significant
_{}
term. Given such observational results, we would know of no convincing
alternative hypotheses.

What is most different now from in the past, and what provides hope
for breaking the seemingly endless alternation between
-fashionability and
-rejection, is the existence
of a new set of
tests - gravitational lens statistics - that have the ability to rule
*out* a dominant
_{} contribution. Both the raw
number of expected
lenses, and also the statistics of their redshifts, are highly
sensitive to _{} as it approaches 1 along
the _{tot} = 1 line
(Figure 9).
While there are formidable complications to be dealt with, there
is a good case that, along the
_{} to be less than 0.9, about
the same as the bound from
the existence of dynamical matter in amounts
_{M}
0.1. It is possible
that bounds to less than 0.5 can be achieved, by which point
is
rendered uninteresting as a solution for theoretical ills - its
``constituency'' ought to evaporate.

It will never be possible to rule out a sufficiently small
fractional value for _{}, particularly since the
effects of _{} are
smaller in the higher-redshift past than they are today.

The particle theorist who has no prejudice for
_{tot} = 1 might want to
know current, observationally secure, bounds on
. For negative
, a
bound derives from the minimum age of the universe
(Figure 4).
Taking _{M} < 1,
*t*_{0} >
10 Gyr, and *H*_{0} > 40 km/s/Mpc, one gets
*H*_{0}*t* > 0.40,
_{} >
-7, and > -2 x 10^{-29}
g/cm^{3}. For positive
, the best bound derives
from gravitational lens statistics
(Figure 9),
although a bound from
the simple existence of high-redshift objects would be not much less
stringent. Taking
_{M} < 1, one gets
_{} < 2; with
*H*_{0} < 100 km/s/Mpc, one
obtains < 4 x
10^{-29} g/cm^{3}. If these bounds seem broad in cosmological
terms, astronomers can nevertheless take satisfaction in bounding
to
a fractional range of one part in 10^{120} of that allowed by
contemporary particle theory, thus making it the most precisely
measured constant in all of physics. That same precision convinces
most theoretical physicists that
must be precisely zero.

**ACKNOWLEDGMENTS**

We thank many colleagues for responding to our requests for information about their work. For helpful conversations and comments on the manuscript, we thank Robert Brandenberger, Sidney Coleman, George Field, Chris Kochanek, Ramesh Narayan, Jerry Ostriker, Ted Pyne, Martin Rees, George Rybicki, and Helmut Zaglauer. This work was supported in part by NSF grant PHY-91-06678 and by NASA contracts NAGW-931 and NAGW-2448. SMC acknowledges the support of an NSF predoctoral fellowship.