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

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6. CONCLUSIONS

The cosmological constant Lambda 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 Omegatot = 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 Omegatot = 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 OmegaM > 0.2 or so is a definite embarrassment. Even the tentative evidence of large-scale velocity flows, which may allow OmegaM approx 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 OmegaM = 1 and a constant bias factor does not provide sufficient power on large spatial scales.

Postulating an OmegaLambda-dominated model seems to solve a lot of problems at once. The cosmological constant supplies the ``missing matter'' to make Omegatot = 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 H0 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 Lambda 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 OmegaLambda (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 OmegaLambda is not really necessary for solving the theorists' problems: OmegaM = 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 Omegalambda 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 H0 (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 H0 (> 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 OmegaLambda 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 Lambda-fashionability and Lambda-rejection, is the existence of a new set of tests - gravitational lens statistics - that have the ability to rule out a dominant OmegaLambda contribution. Both the raw number of expected lenses, and also the statistics of their redshifts, are highly sensitive to OmegaLambda as it approaches 1 along the Omegatot = 1 line (Figure 9). While there are formidable complications to be dealt with, there is a good case that, along the Omega = 1 line, gravitational lens tests already bound OmegaLambda to be less than 0.9, about the same as the bound from the existence of dynamical matter in amounts OmegaM approx 0.1. It is possible that bounds to less than 0.5 can be achieved, by which point Lambda 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 OmegaLambda, particularly since the effects of OmegaLambda are smaller in the higher-redshift past than they are today.

The particle theorist who has no prejudice for Omegatot = 1 might want to know current, observationally secure, bounds on Lambda. For negative Lambda, a bound derives from the minimum age of the universe (Figure 4). Taking OmegaM < 1, t0 > 10 Gyr, and H0 > 40 km/s/Mpc, one gets H0t > 0.40, OmegaLambda > -7, and Lambda > -2 x 10-29 g/cm3. For positive Lambda, 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 OmegaM < 1, one gets OmegaLambda < 2; with H0 < 100 km/s/Mpc, one obtains Lambda < 4 x 10-29 g/cm3. If these bounds seem broad in cosmological terms, astronomers can nevertheless take satisfaction in bounding Lambda to a fractional range of one part in 10120 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 Lambda 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.

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