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

1. INTRODUCTION

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),

1.

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 t₀ is denoted H₀.

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

2.

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

3.

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 10¹²⁰. 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 H₀ 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 H₀ 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.

Table 1. Five fiducial cosmological models

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