In physical cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe. After the discovery of the Hubble redshift and the introduction of the expanding space paradigm, Einstein abandoned the concept. However, the discovery of cosmic acceleration in the 1990s has renewed interest in a cosmological constant.
where R and g pertain to the structure of spacetime, T pertains to matter (thought of as affecting that structure), and G and c are conversion factors which arise from using traditional units of measurement. When Λ is zero, this reduces to the original field equation of general relativity. When T is zero, the field equation describes empty space (the vacuum). Astronomical observations imply that the constant cannot exceed 10-46 km-2.
The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ρvac (and an associated pressure). In this context it is commonly defined with a proportionality factor of 8π: Λ = 8πρvac, where modern unit conventions of general relativity are followed (otherwise factors of G and c would also appear). It is common to quote values of energy density directly, though still using the name "cosmological constant".
A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, and vice versa. If the energy density is positive, the associated negative pressure will drive an accelerated expansion of empty space; see dark energy and cosmic inflation for details.
In lieu of the cosmological constant, cosmologists often quote the ratio between the energy density due to the cosmological constant and the current critical density of the universe. This ratio is usually called ΩΛ. In a flat universe ΩΛ corresponds to the fraction of the energy density of the Universe which is associated with the cosmological constant. Note that this definition is tied to the critical density of the present cosmological era: the critical density changes with cosmological time, but the energy density due to the cosmological constant remains unchanged throughout the history of the universe.