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

Astronomy and physics bring different perspectives to the
``cosmological constant problem.'' Originally introduced by Einstein as
a new term in his gravitational field equations [and later regretted
by him as ``the biggest blunder of my life'' (quoted in
Gamow 1970)],
the cosmological constant, ,
confronts observational astronomers as a
possible additional term in the equation that, according to general
relativity, governs the expansion factor of the universe *R(t)*,

Here _{M} is
the mass density; *k* = - 1, 0, + 1 for a Universe that is
respectively open, ``flat,'' and closed; and *H* is the Hubble constant,
whose observable value at the present epoch *t*_{0} is
denoted *H*_{0}.

Equation 1 says that three competing terms drive the universal expansion: a matter term, a cosmological constant term, and a curvature term. It is convenient to assign symbols to their respective fractional contributions at the present epoch. We define

where zero subscripts refer to the present epoch. Equation 1 then implies

it is also sometimes convenient to define
_{tot} =
_{M} +
_{} = 1 -
_{k}. It is
an observational question whether a non-zero
_{} is required to achieve
consistency in Equation 3. This is the astronomer's cosmological
constant problem.

The Heisenberg uncertainty principle allows particle-antiparticle
pairs spontaneously to appear and disappear. The theoretical particle
physicist thus sees the _{} term
in Equation 3 as an inevitable
concomitant to the _{M}
term. As _{M} is
associated with a density of real
particles, so _{} is associated with virtual,
``vacuum'' states of those
same particles' species - that is, with the energy-momentum density of
their vacuum states. The gravitational effect of these virtual
particles gives the vacuum an energy density
_{vac}
(Zel'dovich 1967).
Although particle physicists do not know how to compute
_{vac} exactly,
theory allows one to estimate its value. Unfortunately, the estimates
disagree with observational limits by a factor of 10^{120}. This is the
physicist's cosmological constant problem.

In this review, we sample both the astronomer's and the physicist's viewpoints. The differing perspectives lead to different perceived goals. An epochal astronomical discovery would be to establish by convincing observation that is non-zero. An important physics discovery, on the other hand, would be to adduce a convincing theoretical model that requires to be exactly zero.

Attempts to measure fundamental cosmological parameters have
consumed enormous observational (and intellectual) resources but have
met with only limited success (see
Sandage 1987
for a historical
review). Hubble's constant *H*_{0} is physically the most
fundamental such
parameter, yet independent determinations via classical techniques
(see reviews by
Tammann 1987 and
de Vaucouleurs 1981)
or the latest new methods
(Tonry 1991,
Roberts et al 1991,
Press et al 1991,
Birkinshaw et al 1991,
Jacoby et al 1990,
Aaronson et al 1989)
give values that vary over a factor of two. Attempts to measure the value
of _{M} have been even
less conclusive (see reviews by
Peebles 1986,
Trimble 1987,
Fukugita 1991).
New results supporting apparently inconsistent values continue to appear (e.g.
Toth & Ostriker 1992,
Richstone et al
1992).

In comparison with *H*_{0} and
_{M}, attempts to
measure _{} have been
infrequent and modest in scope. Moreover, in many respects, the
physical signatures of _{} are
smaller and more subtle than those of
the other two parameters, at least from an observational
perspective. These considerations should severely limit our
expectations for current observational information concerning
_{}.

Table 1 lists five fiducial cosmological models,
parametrized by _{M}
and _{}, which we will refer to in
following sections as Models A
through E. They represent extreme, though not impossible, limits on
the present state of knowledge. In fact, we will see that
distinguishing among these models, and thus among variations in
Equation 3 having dominant versus negligible
_{} terms, is quite
challenging at present.

Model | _{tot}
| _{M}
| _{}
| Description |

A | 1 | 1 | 0 | flat, matter dominated, no |

B | 0.1 | 0.1 | 0 | open, plausible matter, no |

C | 1 | 0.1 | 0.9 | flat, plus plausible matter |

D | 0.01 | 0.01 | 0 | open, minimal matter, no |

E | 1 | 0.01 | 0.99 | flat, plus minimal matter |