Cosmological constant

The cosmological constant (usually denoted by the capital Greek letter Lambda: Λ) is a value occurring in Einstein's theory of general relativity. The units of Λ are 1/second²; its value is unknown but believed to be positive based on recent observations. The constant is proportional to the energy density of the vacuum ρ:

Λ = 8 π G ρ / (3 c²)

where π is Pi, G is the gravitational constant and c is the speed of light in vacuum.

Einstein initially included the term because he was dissatisfied by the fact that his equations would not allow for a static universe. Gravity would cause a universe which was initially at rest to begin to contract. To counteract the force of gravity, Einstein added an extra term which would produce a repulsive force.

However, this term did not fulfill its intended purpose. First of all, observations by Edwin Hubble indicated that the universe was not at rest but rather was expanding. Second, adding the cosmological constant to Einstein's equations would not lead to a universe at rest because a static universe would still be unstable. A universe at rest 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 vacuum quantum 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 appealling 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 a positive cosmological constant. Observations of an accelerating universe in the late 1990's can be explained by assuming a positive cosmological constant, and as of 2002, this is the most commonly adopted position and is favored over models which assume a type of matter known as quintessence. The value of the cosmological constant that would explain current observations is on the order of 10^-36sec^-2.

Thus the cosmological constant may ironically turn out to be Einstein's greatest prediction.

References:

• Sean M. Carroll: "The Cosmological Constant", http://pancake.uchicago.edu/~carroll/encyc/