A fudge too far

Einstein's Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe - Perspectives in Astrophysical Cosmology

December 1, 1995

Cynics often say that there is speculation, speculation squared and cosmology. Cosmology is the study of the large-scale structure and evolution of the universe, a glamorous science that attracts a great deal of media attention. This is partly because the big bang, widely thought to be the event in which the entire universe originated from nothing, is reminiscent of the biblical creation. Thus cosmology has become imbued with theological overtones. But is scientific cosmology credible?

A great many books seek to popularise cosmology but few are careful to distinguish fact from speculation. There are some well-established cosmological facts: the expansion of the universe and the existence of an afterglow from the big bang to name but two. However, much recent interest focuses on the very early universe - a tiny fraction of a second after the big bang - and on the originating event itself. Here the work is almost entirely theoretical and extremely speculative.

These two books, one by astrophysicist and populariser Donald Goldsmith and the other by the Astronomer Royal, Sir Martin Rees, provide welcome antidotes to the wilder claims of many popular cosmology texts.

Goldsmith surveys what he calls cosmological "fudge factors", referring to a tendency among cosmologists to "fix up" their theories in a rather ad hoc way to fit the observational data better. The best-known fudge was made by no less a scientist than Albert Einstein.

In 1915 Einstein published his theory of gravitation, called the general theory of relativity, which still provides the basic mathematical framework for constructing cosmological models. This theory, like Newton's before it, describes gravitation as a universal attractive force. Einstein wished to apply his theory to the universe as a whole, but here he ran into a problem. If the attraction of gravitation between all the stars is unopposed, what is to prevent the universe from collapsing in on itself?

Einstein's response was to introduce a second, repulsive, force into his theory. Known as "the cosmological constant", it describes a strange type of antigravity that grows stronger with distance, unlike all other fundamental forces that weaken with distance. By fixing the strength of the cosmological constant to have a special value, Einstein was able to describe a static universe in which attraction and repulsion precisely balance.

The idea was a failure. Not only is the balancing act unstable, but we know the universe is not static anyway: it is expanding. When Einstein learned about the expansion from Edwin Hubble he dropped the cosmological constant in disgust, deeming it to be "the greatest blunder" of his life.

However, while the expansion of the universe - and by inference its origin in a big bang - are now well established, the fudging has not stopped. A major problem in explaining the universe concerns the spatial organisation of matter. Viewed on the largest scale, the universe resembles a tangled cobweb, with galaxies clustered into clumps, sheets and filaments enfolded by huge voids. How did this complex structure arise?

Astronomers can obtain a snapshot of the early universe by studying the heat radiation left over from the big bang. This would contain imprints of any primordial clumpiness in the distribution of matter. A satellite called COBE (for Cosmic Background Explorer) recently detected faint irregularities in this radiation, suggesting that the universe started out with very slight density variations. Gravity could amplify these variations over time to create the distinctive cosmic structures we see today.

Unfortunately, computer simulations of the amplification process are not wholly convincing. The problem is that the initial state of the universe was simply too smooth to permit the requisite degree of structure to grow in the time available - without some fudging. To accelerate the process, theorists have suggested that the universe contains vast quantities of dark or invisible matter. The extra gravity that this matter contributes might help tug the visible matter into clumps.

This is not idle speculation. Astronomers have good evidence that there is at least some dark matter in the universe. Our galaxy, the Milky Way, rotates about its central bulge. The stars near the periphery are moving so fast they would fly off if they were being restrained solely by the gravitational pull of the visible matter. Evidently there is a lot of unseen stuff there too, holding these stars in their orbits. Similar reasoning suggests that there is also a lot of dark matter between galaxies.

The nature of this dark matter remains a mystery. Theorists have plenty of ideas, ranging from black holes and dim stars to exotic subatomic particles coughed out of the big bang. Here again, theory far outstrips experiment and observation. It is probable that the visible material of a typical galaxy - consisting mainly of stars and gas clouds - is embedded in a huge halo of dark matter. Recent results from Mt Stromlo Observatory in Australia indicate that our galaxy contains a halo of dim stars, but these are unlikely to account for all the dark matter there is.

Meanwhile, theorists have tried modelling the growth of cosmological structure with a cocktail of hypothetical dark matter, which they assume pervades the cosmos. If all the dark matter were in the form of slow-moving macroscopic objects like dwarf stars, then the details of the large-scale structure come out wrong. Likewise, if the dark matter consisted entirely of high-speed subatomic particles the structures that emerge do not fit the observations very well. Some sort of mixture of dark matter species seems to be necessary, an unwelcome complication.

The struggle to square theory and observation has been exacerbated by some new results from the Hubble Space Telescope. The issue concerns the age of the universe. By definition, the universe must be at least as old as the oldest objects within it. Astronomers can date the ancient stars in globular clusters fairly accurately, and ages of 14 or 15 billion years are quoted. However, many cosmologists believe the universe is at most 10 billion years old. Obviously there is a need for more fudging.

To measure the age of the universe as a whole, you have to work backwards from the rate at which it is expanding. If the expansion rate were constant throughout time, it would be a trivial calculation to determine when the big bang occurred, namely, when all the retreating galaxies would have been together in one place. However, gravitation acts as a brake on the rate of expansion by restraining the galaxies in their outward rush. (Ultimately, the gravitation of the universe may be enough to halt the expansion entirely and turn it into collapse.) So the rate of expansion was much higher in the past. It is necessary to take into account this progressive slowing when computing the age of the universe from its present rate of expansion.

Unfortunately, estimating the magnitude of the braking is fraught with problems. The more matter there is in the universe the greater the braking effect. Thus the inferred age of the universe depends on the amount of dark matter, which we do not know for sure. If there is a lot of dark matter then, for a given rate of expansion today, the universe will be younger.

Many theorists are attracted to the idea that there is a lot of dark matter, because their best explanation for the big bang itself, known as the inflationary universe scenario, predicts that the universe should contain about a hundred times as much matter as there is in the stars. Using this high figure, together with ground-based measurements of the rate of expansion, suggests that the big bang occurred anything between about 8 and 12 billion years ago.

The Hubble Space Telescope has also been used to measure the rate of expansion, and its results confirm the shorter end of the above range of ages. This is clearly a major problem for the inflationary universe scenario. It is also a problem more generally, for unless there is virtually no dark matter after all, then the stars are simply too old to fit into a universe expanding as fast as the Hubble space telescope suggests is the case.

One way out is to bring back Einstein's original fudge factor -the cosmological constant - not to recreate a static universe model, but to reduce the gravitational braking effect on the rate of expansion. Because it describes a repulsive force, a cosmological term would combat the tendency for gravity to slow the rate of expansion. This has the effect of stretching the time that has elapsed since the big bang, possibly by enough to extend the age of the universe to 15 billion years or more.

Big bang cosmology is thus left in a curiously unfinished state. Few cosmologists relish the idea of resurrecting the cosmological constant, regarding it as "a fudge too far". But they may be forced to change their minds if the big bang theory is to avoid drastic revision.

These conflicting strands of evidence, and the theoretical machinations that weave them into plausible cosmic histories, are described with skill and wit by Donald Goldsmith. His book is a very readable introduction to this tangled set of topics. The author avoids too many technicalities, and his account is nicely illustrated by simple line drawings and photographs. If I have a criticism, it is that the nature of the cosmological expansion and the old problem of what happened before the big bang are themselves fudged somewhat.

Martin Rees's book is based on a series of lectures, and covers a broader range of topics, including black holes, quasars, cosmic strings and the very early quantum era. However, the technical level is more appropriate to students than to the lay reader. Rees is careful to separate well-founded ideas from speculation. Indeed, he chides some his more gung-ho colleagues for fuelling the media hype over the recent COBE results. "If we claim too often to be stripping the last veil from the face of God, or making discoveries that overthrow all previous ideas, we will surely erode our credibility," he writes.

Although only a slim volume, it is packed full of useful information and provides a lucid and well-balanced survey of the present state of knowledge of cosmology. On the key issue of dark matter, Rees cautions us against "baryon chauvinism". Since Copernicus dethroned mankind from the centre of the universe, it has been prudent not to suppose that there is anything special about earth or its inhabitants. Now it seems that most of the universe could consist of, not the protons and neutrons (baryons) of which earth and humans are made, but of something else entirely.

Cosmological discoveries will continue to bring surprises in the years ahead, so speculative books on the subject tend to have a rather short use-by date. These two volumes are likely to prove more durable because they weigh up competing ideas and provide valuable insights into the practice of cosmology, rather than hitch themselves onto the latest gee-whiz bandwagon.

Paul Davies is professor of natural philsoph, University of Adelaide, Australia.

Einstein's Greatest Blunder? The Cosmological Constant and Other Fudge Factors in the Physics of the Universe

Author - Donald Goldsmith
ISBN - 0 674 24241 6
Publisher - Harvard University Press
Price - £14.50
Pages - 216

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