Interlude 27-1

INTERLUDE 27-1 The Cosmological Constant

Even the greatest minds are fallible. The first scientist to apply general relativity to the universe was, not surprisingly, the theory's inventor, Albert Einstein. When he derived and solved the equations describing the behavior of the universe, Einstein discovered that they predicted a universe that evolved in time. But in 1917 neither he nor anyone else knew about the expansion of the universe, as described by Hubble's law, which would not be discovered for another 10 years.

(Sec. 24.5) At the time, Einstein, like most scientists, believed that the universe was static—that is, unchanging and everlasting. The discovery that there was no static solution to his equations seemed to Einstein to be a near-fatal flaw in his new theory.

To bring his theory into line with his beliefs, Einstein tinkered with his equations, introducing a "fudge factor" now known as the cosmological constant. As illustrated in the accompanying figure, which shows the effect of introducing a cosmological constant into the equations describing the expansion of a critical-density universe, this factor allows many other solutions to Einstein's equations. One of these solutions describes a "coasting" universe, whose radius does in fact remain constant for an indefinite period of time, Einstein took this to be the static universe he expected.

Instead of predicting an evolving cosmos, which would have been one of relativity's greatest triumphs, Einstein yielded to a preconceived notion of the way the universe "should be," unsupported by observational evidence. Later, when the expansion of the universe was discovered and Einstein's equations—without the fudge factor—were found to describe it perfectly, he declared that the cosmological constant was the biggest mistake of his scientific career.

For many researchers—Einstein included—the main problem with the cosmological constant was (and still is) the fact that it had no clear physical interpretation. Einstein introduced it to fix what he thought was a problem with his equations, but he discarded it immediately once he realized that no problem actually existed. Scientists are very reluctant to introduce unknown quantities into their equations purely to make the results "come out right." As a result, the cosmological constant fell out of favor among astronomers for many years.

Since the early 1980s, however, the cosmological constant has made something of a comeback, an it now enjoys a measure of respectability in cosmological circles. One reason for this is that the leading theories of matter and radiation on very small scales (the GUTs described in More Precisely 27-1) now suggest that the universe really did go through an early phase when its evolution was determined by a "cosmological constant" of sorts. As discussed in Section 27.4, this idea is now firmly entrenched in many cosmologists' models of the universe.

Unfortunately, although the GUTs make the idea of a cosmological constant more acceptable, they presently offer no useful means of estimating its value.

A second reason for the cosmological constant's resurgence in popularity is the fact that it offers a possible means of resolving a nagging problem in astronomy—the fact that the measured ages of the oldest stars in our Galaxy, some 12 billion years (Section 20.5), may be greater than the age of the universe, as determined from the Hubble expansion and our best estimates of the cosmic density (Section 26.4), especially if the universe is close to critical density (Section 27.4). Interlude 26-2 discusses the conventional view of how this discrepancy may be resolved by improved observations. The cosmological constant provides a radical alternative. In addition, recent observations of distant Type-I supernovae, which seem to imply that the expansion of the universe is not slowing down, but is actually accelerating (Section 26.4), are readily explained by cosmological models that include a cosmological constant. (See for example the light-green curve in the accompanying figure.)

As indicated in the figure, by carefully adjusting the value of the cosmological constant, theorists can construct mathematical models of the universe that did not expand so rapidly in the past and so are older than the measured value of H₀ suggests. With a suitably chosen cosmological constant, a Hubble constant of 65 km/s/Mpc in a critical-density universe can be reconciled with a cosmic age of 12 billion years, or even much more. In fact, with a sufficiently large cosmological constant, it is even possible to avoid a Big Bang altogether, although this possibility now seems to be quite firmly ruled out by observations of high-redshift quasars and galaxies. Notice, incidentally, that if the cosmological constant does indeed provide the explanation of the cosmic age paradox, it also implies that the universe will expand forever, regardless of the present value of the cosmic mass density.

But before we jump to any conclusions about the cosmological constant and overstate its potential role in solving the outstanding problems of astronomy, it is probably worth remembering the experience of its inventor and bearing in mind that—at least for now—its physical meaning remains completely unknown.