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Equation

The cosmological constant Λ appears in the Einstein field equations in the form R μ ν − 1 2 R g μ ν + Λ g μ ν = κ T μ ν, {\displaystyle R_{\mu \nu }-{\tfrac {1}{2}}R\,g_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu },} where the Ricci tensor R, Ricci scalar R and the metric tensor g describe the structure of spacetime, the stress–energy tensor T describes the energy density, momentum density and stress at that point in spacetime, and κ = 8 πG / c. The gravitational constant G and the speed of light c are universal constants. When Λ is zero, this reduces to the field equation of general relativity usually used in the 20th century. When T is zero, the field equation describes empty space (a vacuum).

The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ρ (and an associated pressure). In this context, it is commonly moved to the right-hand side of the equation using Λ = κρ. It is common to quote values of energy density directly, though still using the name "cosmological constant". The dimension of Λ is generally understood as length.

Using the values known in 2018 and Planck units for Ω = 0.6889 ± 0.0056 and the Hubble constant H = 67.66 ± 0.42 (km/s)/Mpc = (2.192 7664 ± 0.0136) × 10 s, Λ has the value of Λ = 3 (H 0 c) 2 Ω Λ = 1.1056 × 10 − 52 m − 2 = 2.888 × 10 − 122 l P − 2 {\displaystyle {\begin{aligned}\Lambda =3\,\left({\frac {\,H_{0}\,}{c}}\right)^{2}\Omega _{\Lambda }&=1.1056\times 10^{-52}\ {\text{m}}^{-2}\\&=2.888\times 10^{-122}\,l_{\text{P}}^{-2}\end{aligned}}} where l P {\textstyle l_{\text{P}}} is the Planck length. 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 the universe, as observed. (See Dark energy and Cosmic inflation for details.)