concept

cosmological constant

The cosmological constant is a term in Einstein's equations representing dark energy driving the accelerated expansion of the universe.
49 related articles · 1 formulas · 3 who worked here

Description

Imagine an infinite balloon that slowly inflates by itself, without any help. The cosmological constant is that very 'spring' inside space that pushes galaxies farther and farther apart.

History

Einstein introduced Λ in 1917 for a static model of the Universe. In the 1920s, Friedmann and Lemaître showed that solutions with and without Λ lead to expansion. After Hubble's discovery, Einstein abandoned it. At the end of the 20th century, two groups of astronomers (Perlmutter, Riess, Schmidt) discovered acceleration from distant supernovae, which resurrected Λ.

How it works

In Einstein's equations, the cosmological constant adds a term Λ g_{μν}. In a homogeneous and isotropic Universe, it manifests as an effective fluid with equation of state p = -ρ c^2, leading to repulsive gravity. In quantum field theory, the predicted vacuum energy is 120 orders of magnitude larger than observed—this is the cosmological constant problem.

Fun fact

Albert Einstein first introduced this concept to make the Universe static, and then called it his 'greatest blunder'—and today we know that the Universe is actually accelerating its expansion!

Concept graph →

Formulas

$$\mathcal{R} = 2\Lambda + 16\pi G \rho + \Theta^i_j \Theta^j_i - \Theta^2$$
Relates spatial curvature to density and velocity gradients.
What is in the formula
\mathcal{R}variableRicci scalar — ricci scalar per metre squared
\LambdavariableCosmological constant — cosmological constant per metre squared
\rhovariableMass density — mass density kilogram per cubic metre
\Theta^i_jvariableExpansion tensor — expansion tensor per second
\ThetavariableExpansion scalar — expansion scalar per second
GconstantNewton's constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared

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