The Cosmological Constant

When Einstein first realized that the solution of his equations subject to the constraints of the cosmological principle led to universes that were not static, he was dismayed. At the time (the period between 1915 and 1920) the expansion of the Universe had not yet been discovered by Hubble. This led Einstein to make what he later characterized as the "greatest blunder of his life". To get a static Universe, he added a term to his field equations that stabilized the Universe against expansion. This term has come to be known as the cosmological constant or the vacuum energy density. Although consistent with the equations, Einstein's original intuition was that it did not belong. But he felt that the data required a static solution, so he concluded that his original intuition had been wrong and that the cosmological term was necessary.

A Static Solution
With this new term, Einstein obtained a static solution. Later, when Hubble demonstrated that the Universe was actually not static but expanding (see Chapter 24), Einstein realized that he had missed a tremendous opportunity. If he had possessed sufficient confidence in his intuition, he would have predicted that if his theory was right the Universe should be either expanding or contracting, well before there was experimental evidence that it is in fact expanding.
Is the Cosmological Constant Exactly Zero?
The discovery of the expansion of the Universe removed the immediate obvious need for the cosmological constant in Einstein's gravitational theory. However, it is still possible that there is a non-zero cosmological constant. The effect of a small non-zero cosmological constant would be to alter the rate of change for the expansion. To be consistent with the data, if there is a cosmological constant it must be very small. An important unresolved issue in astronomy is whether the cosmological constant is exactly zero, or just very small.

Measuring the Cosmological Constant

The adjacent image shows one of the most distant Type Ia supernovae yet observed, SN1997cj, in the constellation Ursa Major at a distance of about 5 billion light years (Ref). It was discovered in 1997 by the Canada-France-Hawaii Telescope on Mauna Kea, and the Hubble Space Telescope was then used to resolve it from its host galaxy and study the decay of its light curve. By using the standard candle properties of the Type Ia lightcurve, the distance to the supernova could then be determined (see the discussion of Type Ia supernovae in Chapter 21). When this was compared with the redshift of the host galaxy (z = 0.5), it was then possible to estimate the rate of change in the expansion rate of the Universe. (Because Sn1997cj has a redshift of 0.5, it actually exploded about 5 billion years ago and the light of the explosion is just now reaching us. Therefore, this light carries information about the rate of expansion for the Universe some 5 billion years ago.)

An Accelerating Universe?
Analysis of this and related data have led to the claim (Ref) that the Universe is accelerating (rather than decelerating, as we would expect from normal gravitational interactions) because of a finite cosmological constant. If true, this finite cosmological constant would imply that most of the energy of the Universe is neither in matter nor radiation, but tied up in what physicists called the energy density of the vacuum. The acceleration is then a consequence of this energy density that permeates all of "empty" space (see the right panel). However, this result is controversial because there is some dispute over the reliability of Type Ia supernovae as standard candles. The resolution of this controversy is a major issue of current research in astronomy.