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Cosmological constant

The cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is a value occurring in Einstein's theory of general relativity. The units of Λ are 1/second2. The constant is proportional to the energy density of the vacuum ρ:

\Lambda = {{8\pi G} \over {3c^2}} \rho


The term can be positive, negative, or zero and can be thought of as the amount of energy that is embedded in empty space. If it is positive then the expansion of space would release more energy, whereas if it is negative the expansion of space would consume energy. Recent observations indicate that the expansion of the universe is accelerating and if this accleration is due entirely to the cosmological constant, then the value is on the order of 10-35s-2.

Einstein initially included the term because he was dissatisfied by the fact that his equations would not allow for a stationary universe. Gravity would cause a universe which was initially at dynamical equilibrium to begin to contract. To counteract the contraction, Einstein added the cosmological constant which would keep the universe stationary.

However, this term did not fulfill its intended purpose. First of all, observations by Edwin Hubble indicated that the universe was not at equilibrium but rather was expanding. Second, adding the cosmological constant to Einstein's equations might not lead to a universe at equilibrium because, according to certain theories, the universe might still be unstable. According to those theories, a universe at equilibrium which expanded slightly would release the vacuum energy, which would cause more expansion, which would release more energy. Similarly, a universe which contracted slightly would have less energy, which would increase the rate of contraction.

Einstein abandoned the cosmological constant and called it the "biggest blunder" of his life.

The cosmological constant is still of interest, as most grand unified theories predict a non-zero cosmological constant from the energy of quantum vacuum fluctuations. In fact, one theoretical problem in these theories is that the vacuum energy they predict is huge, and would have to be countered by a similarly large negative Λ to avoid an extremely rapidly expanding universe. Some physicists such as Steven Weinberg regard the delicate balance observed as being improbable and best explained by appealing to the anthropic principle.

Moreover, observations suggest that the early universe underwent a period of rapid expansion known as inflation, which can be modelled by assuming an extremely large positive cosmological constant existed at that time (although the most popular models of inflation employ a slowly varying scalar field). In contrast, observations made in the late 1990's of distance-redshift relations can be explained very well by assuming a very small positive cosmological constant exists at present. However, there are other possible causes of an accelerating universe. As of 2004, the cosmological constant model remains favoured by the observations relative to alternative models. Among these less favoured alternative models are forms of dark energy that include quintessence, phantom energy , and kinessence .

The value of the cosmological constant that would explain current observations is on the order of 10-35s-2. This value of the cosmological constant disturbs theorists who, for reasons of symmetry, are uncomfortable with an extremely small cosmological constant that is non-zero. Thus the cosmological constant may ironically turn out to be Einstein's greatest prediction (although without the consequence of a stationary universe that had been Einstein's original motivation for inventing it, unless of course the universe turns out to be stationary after all).


  • Carroll, Sean M., "The Cosmological Constant" (short), "The Cosmological Constant" (extended).

Last updated: 02-06-2005 14:53:18
Last updated: 03-15-2005 09:52:31