Adapted from P. Coles, 1999, *The Routledge Critical
Dictionary of the New Cosmology*, Routledge Inc., New York. Reprinted
with the author's permission. To order this book click here:
http://www.routledge-ny.com/books.cfm?isbn=0415923549

A constant originally introduced into the
equations of **general relativity** by Albert **Einstein** himself
in order to
produce a **cosmological model** which discovery by Edwin
**Hubble** of the
**expansion of the Universe**. Later events caused Einstein to regret the
addition of this term, but its legacy still lingers.

What Einstein did was to modify the left hand side of the field
equations (see **Einstein equations**) by changing the terms that involve
the **curvature of spacetime**. This was tantamount to modifying the law
of **gravity** slightly so that on sufficiently large scales he could
balance the universal attraction of gravity with a repulsive force of
his own devising. The effect of the cosmological constant
on
Newton's law for the gravitational force between two masses is to add
a new term to the usual law (which depends on the inverse square of
the separation of masses); the new term is directly proportional to
the separation, instead of depending on the inverse square. On large
scales, therefore, the -term
dominates. If it is positive, can be
understood as a cosmic repulsion; if it is negative, it acts as a
cosmic tension leading to an extra attraction over and above the usual
gravitational force. This modification was not entirely arbitrary,
however, because it is completely consistent with the fundamental
reasoning that led Einstein to general relativity in the first place.

One might imagine that the cosmological constant would have vanished
from the scene with the discovery of the expansion of the Universe,
but that certainly did not happen. With developments in the **Big Bang
theory**, cosmologists began to ponder the consequences of **fundamental
interactions** in the very early Universe. These considerations
concerned the right-hand-side of Einstein's equations, the part of the
theory of general relativity that deals with the properties of
matter. It was realised that the cosmological constant term could just
as easily be put on the left-hand side of the field equations. The
cosmological constant is a vacuum energy density: an energy not
directly associated with matter or radiation, but with `empty' space.

Each time matter changes state (i.e. each time it undergoes a **phase
transition**), some amount of vacuum energy is expected to remain.
Physicists working on the theory of **elementary particles** tried to
calculate the net amount of vacuum energy produced by all the phase
transitions the Universe underwent as it cooled. The answer is
catastrophically large: about 10^{120} times larger than the density of
all the matter in the Universe. Such a result is at odds with
observations, to put it mildly.

Some cosmologists believe that a cosmological constant term is
necessary in order to reconcile the **age of the Universe** with estimates
of the **Hubble constant** and the **density parameter**. But the
size of the
term required corresponds to a vacuum energy density of the same order
as the density of matter, about 10^{120} times smaller than the
predictions of particle physics. Many are deeply uncomfortable about
the size of this discrepancy, and suggest that it means that the
cosmological constant has to be exactly zero.

The cosmological constant also plays a role in the **inflationary
Universe**. The mathematical solution that describes a universe
undergoing inflation, first found by Willem **de Sitter** in 1917,
involves the cosmological constant term (actually that is all it
involves - the de Sitter universe is empty apart from the vacuum
density). The **scalar field** responsible for driving the inflationary
expansion behaves in such a way that the vacuum energy dominates: the
solution in this case is identical to the de Sitter model.

FURTHER READING:

Einstein, A., `Cosmological considerations on the general theory of
relativity', 1917, reprinted in The Principle of Relativity, edited by
H.A. Lorentz et al., (Dover, New York, 1950).
Weinberg, S. `The cosmological constant problem', *Reviews of Modern
Physics*, 1989, **68**, 1.
Goldsmith, D., *Einstein's Greatest Blunder? The Cosmological Constant
and Other Fudge Factors in the Physics of the Universe* (Harvard
University Press, Cambridge, MA, 1995).