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It was not Albert Einstein’s best year. The previous one, 1916, he had published his greatest triumph, the general theory of relativity. But in 1917 he sullied his elegant equations with a term he would later regret, the cosmological constant. There was no evidence for a cosmological constant, but without it, Einstein’s equations showed the Universe to be either expanding or collapsing, contrary to the prevailing belief that it was static.

Had Einstein talked to Vesto Slipher of Lowell Observatory in Arizona, he might not have committed his famous blunder. At the time Slipher was measuring the spectra of other galaxies, in order to work out their velocities. He found that the light from most of them was red shifted – stretched – because they are rushing away from Earth. In 1929 Edwin Hubble used these velocities and his own measurements of these galaxies’ distances from Earth to deduce that the Universe is expanding. Following this discovery, Einstein disowned the cosmological constant, and it lived in infamy thereafter.

Yet during the past five years, the cosmological constant has returned. Its importance lies in its effect on calculations of the age of the Universe, a major problem for astronomers. Logically, the Universe cannot be younger than any of the stars it contains. But according to many astronomers’ estimates, the oldest stars appear to be several billion years older than the Universe itself. There seem to be only two ways out of this contradiction. The more controversial one involves abandoning the central tenet of standard cosmology, the big bang theory, which holds that the Universe was born in a gigantic explosion some 15 billion years ago and has been expanding ever since. The other is to reintroduce a cosmological constant.

Most cosmologists still detest the cosmological constant, however. Not only does it make Einstein’s equations of general relativity less elegant, but it also seems little more than a ‘fudge factor’ invoked to solve the problem about the age of the Universe. It also implies an uncomfortable concept. The cosmological constant represents the repulsive energy of empty space, a sort of antigravity, except that it arises from space rather than mass. In 1990, astronomers discovered a new way to measure the cosmological constant that should soon establish once and for all whether or not the Universe really has a cosmological constant.

In standard cosmology, which has no cosmological constant, the age of the Universe depends on only two parameters. One is the Hubble constant, which is the rate at which the Universe is currently expanding. This can be measured. The other is omega (), the mass density of the Universe. To see how to work out the Universe’s age, first imagine a hypothetical universe which has space but no mass ( = 0). Because there is no mass, there is no gravity to slow this universe’s expansion, so it expands at a steady rate (Figure 1, A).FIG-mg18614201.GIF

HUBBLE TIMEKEEPING

The age of such a universe – the time between now and when it had zero size – is simply the inverse of the Hubble constant. This is called the ‘Hubble time’. The bigger the Hubble constant, the shorter the Hubble time and the younger the universe. The age of a massless universe equals the Hubble time. But the real Universe must have expanded more rapidly in the past than it does today, because the gravitational pull of its mass slows its expansion. The Hubble constant is only the present expansion rate, so if the Universe expanded more rapidly in the past, it must be younger than the Hubble time (Figure 1, B).FIG-mg18614202.GIF

How much younger depends on the size of . Astronomers define in such a way that, if it is less than or equal to 1, the Universe has so little mass that the expansion will continue forever. If exceeds 1, the Universe is so massive that it will some day reverse its expansion and collapse. Both observation and theory suggest that its value lies somewhere between 0.1 and 1.0. The bigger is, the more the expansion has slowed, the faster the Universe once expanded, and the younger the Universe must be. It can be calculated that if is 0.1, the age of the Universe is 90 per cent of the Hubble time; if is 0.2, the age is 85 per cent of the Hubble time; and if is 1.0, the Universe’s age is only 67 per cent of the Hubble time.

To compute the Hubble time, we need to know the Hubble constant, the rate of the Universe’s expansion. In an expanding Universe, the farther a galaxy is from us, the faster it moves away. A galaxy twice as far as another moves away from us twice as fast. For example, if a galaxy 100 megaparsecs from Earth recedes at 5000 kilometres per second, then a galaxy 200 megaparsecs from Earth recedes at 10 000 kilometres per second (a megaparsec is 3.26 million light years). The Hubble constant is therefore expressed in units of kilometres per second per megaparsec. Thus for a Hubble constant of 50, a pair of galaxies 100 megaparsecs apart would be receding from each other at 5000 kilometres per second, galaxies 200 megaparsecs apart would be receding at 10 000 kilometres per second, and so on.

The precise size of the Hubble constant is hotly disputed: different observers of distances to other galaxies find values differing by more than a factor of 2, from 40 to 100 kilometres per second per megaparsec. In recent years, many astronomers have found a high value for the Hubble constant, of around 80 (see ‘Starry signposts to the Universe’, ¿ìè¶ÌÊÓƵ, 6 June 1992). But a value of 50 is still favoured by some, most notably the formidable Allan Sandage of the Carnegie Observatories in California (¿ìè¶ÌÊÓƵ, Science, 18 July 1992).

A Hubble constant of 75, somewhere between these two extremes, gives a Hubble time of only 13 billion years. Whatever the value of , this makes the Universe very young: for equal to 0.1, 0.2, and 1.0 respectively, the age of the Universe works out to only 11.7, 11.0 and 8.7 billion years, if there is no cosmological constant to affect it.

OLDER THAN THE UNIVERSE

Yet our Galaxy contains compact star clusters called globulars that are thought to be older than this. From theories of how stars evolve and observations of stars which are at different stages of their evolution, the ages of some globulars have been estimated at about 15 billion years. There is uncertainty in these ages, but recent work by Young-Wook Lee of Yale University makes things worse. When Lee measured the ages of RR Lyrae stars he found that stars near the Galactic centre are over a billion years older than the oldest globular clusters. He suggests that in galaxies more massive than ours the oldest stars may be another billion years older still (¿ìè¶ÌÊÓƵ, Science, 19 September 1992). So the oldest stars could be at least two billion years older than the oldest globular clusters, which already appear to be older than the Universe.

Now what would happen if a cosmological constant were introduced? The cosmological constant represents the inherent tendency of space to expand; to put it another way, it is the energy of empty space. The bigger such a universe gets, the more empty space there is and the faster that universe expands, which creates still more empty space, leading to faster expansion. Such a universe is a runaway, because it expands exponentially (Figure 1, C).

So if there is a cosmological constant in our Universe, then the larger that constant is, the more slowly the Universe must have expanded in the past (relative to its rate of expansion now) and the older it must be. In fact, a Universe with a large cosmological constant can be twice as old as the Hubble time, and this would allow the Universe to be older than the oldest stars.

MEASURABLE ‘FUDGE-FACTOR’

There is a second argument for a cosmological constant. The most popular model of the big bang, called inflation – which many theorists hold to be valid – suggests that the Universe expanded dramatically when it was just a fraction of a second old. This rapid expansion stretched the Universe so much that it became ‘flat’ – which, in standard cosmology, means is equal to 1. A universe with this value of = 1 will always expand, but it does so more and more slowly, because it lies right on the boundary between a universe that expands forever and one that eventually collapses. However, most observations put at less than 1. For example, the motions of galaxies in clusters and the distribution in space of these clusters indicates that the Universe has only enough mass for to be 0.2 or 0.3 (¿ìè¶ÌÊÓƵ, Science, 3 October 1992).

A cosmological constant could solve the problem. If empty space has energy, that energy counts as mass since, as Einstein showed, mass and energy are equivalent. The cosmological constant could therefore make the Universe flat, even if were much less than 1. In this case, the inflationary theory predicts that and should add up to 1, where is the cosmological constant. Unlike the conventional case in which the Universe gradually slows its expansion, the Universe would expand ever faster. A cosmological constant thus solves two problems at once: the Universe would no longer be younger than its oldest stars, and it would fit in with inflationary theory. A Hubble constant of 75, equal to 0.15, and equal to 0.85 would satisfy almost everyone, giving a flat universe that is 15 billion years old.

The trouble is that this is too easy, for you can pick the cosmological constant to be anything you want. As a result, most cosmologists regard the cosmological constant as a fudge factor. But they now recognise that it can be reliably measured. The cosmological constant affects the distances of distant objects: the greater the cosmological constant, the farther a galaxy with a particular red shift must be. This is because, if there is a cosmological constant, the Universe’s expansion has accelerated since the object emitted its light. So we are now farther from the object than we would be if there were no cosmological constant.

FOCUS ON GRAVITATIONAL LENSES

One way to probe distance is to count the number of faint galaxies. If galaxies are distributed uniformly through space, the greater their distance, the more of them should be visible, because a greater volume of space is being examined. In the late 1980s, astronomers observing at blue wavelengths reported more faint galaxies than they expected. They suggested that a cosmological constant might be responsible. But problems soon emerged. At infrared wavelengths there was no excess of galaxies. In any case looking at high red shifts is looking at the Universe as it was, not as it is. Billions of years ago, galaxies might have been more numerous not because the Universe was bigger than we had thought, but because many galaxies have since merged. Furthermore, galaxies might once have been brighter than they are today, so we might see more of them as we look further back in time, even if their number has remained the same. All in all, then, galaxy counts will probably reveal nothing about the cosmological constant.

In 1990, however, Japanese astronomers led by Masataka Fukugita of Kyoto University and Edwin Turner of Princeton University independently came up with gravitational lensing as a way of measuring the cosmological constant. A gravitational lens is formed when a massive galaxy lies between the observer and a quasar. The galaxy’s gravity bends the quasar’s light, so that two or more images of the galaxy are seen by the observer. The first gravitationally lensed quasar was discovered in the constellation of Ursa Major in 1979, and since then about a dozen more have been found.

Both Fukugita’s team and Turner calculate that the amount of gravitational lensing depends strongly on the cosmological constant. The bigger the cosmological constant, the farther away a quasar with a particular red shift lies, so the greater the chance that the quasar’s light has passed close to a massive galaxy on its way to Earth. As a result, the larger the cosmological constant, the more gravitationally lensed quasars there should be. The effect is huge. For a flat universe, there should be six times as many gravitationally lensed quasars if is 0.9 than if is 0.

ZEROING IN ON THE CONSTANT

From 1990 to 1992, astronomers led by John Bahcall and Dan Maoz of the Institute for Advanced Study in Princeton, New Jersey, searched for gravitationally lensed quasars using ‘dead time’ on the Hubble Space Telescope as it slewed from one object to the next. From exposures taken during this dead time, Bahcall’s team were able to examine 498 quasars. But they found that only a few of them are gravitationally lensed. As the astronomers will report later this year in The Astrophysical Journal, their result suggests that the cosmological constant is small or zero.

In 1992, Christopher Kochanek of Harvard University published a test for the cosmological constant that also uses gravitational lenses. He calculated that if the Universe has a cosmological constant, the average red shift of a lensing galaxy should be much greater than if the cosmological constant were zero. His analysis of the known gravitationally lensed quasars rules against a large cosmological constant, in agreement with Bahcall’s study. Kochanek’s test should become increasingly decisive in the future, because its power grows rapidly with the number of gravitational lenses used in the analysis, and astronomers are searching for more gravitationally lensed quasars. Late last year, for example, a team of radio astronomers at the Jodrell Bank radio telescope in Cheshire discovered several new gravitationally lensed quasars (¿ìè¶ÌÊÓƵ, Science, 5 December 1992).

In these ways, astronomers aim to pin down the size of the cosmological constant. Moreover, the next few years should also see more accurate measurements of the Hubble constant and perhaps of . If all goes to plan, they will find a lower value for the Hubble constant, younger ages for the globular clusters, and possibly, a cosmological constant that is not zero. Then the Universe would be older than its oldest stars, as it must be. On the other hand, the Hubble constant might stay high and the globular clusters stubbornly old, while the cosmological constant is shown to be so close to zero that it has no effect. This would make the Universe younger than its oldest stars. If that happens, cosmologists would then have only one more thing to do: dump the big bang.

Ken Croswell is an astronomer in Berkeley, California. Further reading ‘The cosmological constant’, by Sean M. Carroll, William H. Press, and Edwin L. Turner, Annual Review of Astronomy and Astrophysics, vol 30, p 499 (1992).

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A loitering universe

A universe with a cosmological constant can behave in ways far more bizarre than standard cosmology allows. Early in its life, shortly after the big bang created it, such a universe can ‘loiter’, remaining nearly constant in size as it hesitates over whether to expand or to collapse.

A loiter phase occurs when the cosmological constant, , and the mass density, , fight each other for control of the universe – the cosmological constant struggles to keep the universe expanding, while omega tries to make it collapse. If the two opponents nearly balance each other, the loiter phase can last billions of years, making the universe far older than the age that comes from calculations based on its rate of expansion and mass density.

Did our Universe ever loiter? If it did, the cosmological constant obviously won the battle, because we would not be here if the Universe had collapsed. One sign of a long loiter phase is an abundance of objects at one red shift, corresponding to the time when the Universe held nearly constant in size.

In 1967, Geoffrey Burbidge of the University of California at San Diego reported a large number of quasars with a red shift around 1.95, meaning that the wavelength of the light from these objects has been stretched by 195 per cent. Other astronomers interpreted the result as a sign that the Universe had loitered at this red shift. But more distant quasars have since been found, and they do not congregate around any particular red shift.

The strongest argument that our Universe never loitered comes from the observed value of . The earlier the loiter took place, the smaller the Universe was and the smaller needed to be to have balanced the cosmological constant. This is because in a small universe, when objects are closer together and exert more gravitational force on one another, a particular value of counts for more than in a larger universe. So the greater the red shift at which our Universe loitered, the smaller must be.

In 1985, Richard Gott of Princeton University showed that the loiter red shift must have exceeded the red shift of the most distant gravitationally lensed quasar, and last year Richard McMahon of the University of Cambridge, Mike Irwin of the Royal Greenwich Observatory and Cyril Hazard of the University of Pittsburgh discovered a gravitationally lensed quasar with a red shift of 4.5. This means that no loiter could have occurred unless is less than 0.013 – an impossibly low value.