Changes

The '''Cosmological constant''' is the constant <math>\Lambda</math> of Einstein field equation  

The '''Cosmological constant''' is the constant <math>\Lambda</math> of Einstein field equation  

:<math>R_{\mu\nu}-(R/2)g_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}</math>,

:<math>R_{\mu\nu}-(R/2)g_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi G T_{\mu\nu}</math>,

where <math>R_{\mu\nu}</math> is Ricci tensor, <math>R</math> is its contraction, <math>g_{\mu\nu}</math> is metric tensor of spacetime, and <math>T_{\mu\nu}</math> is stress-energy tensor.  

where <math>R_{\mu\nu}</math> is Ricci's tensor, <math>R</math> is its contraction, <math>g_{\mu\nu}</math> is the metric tensor of spacetime, <math>G</math> is Newton's constant of gravitation, and <math>T_{\mu\nu}</math> is the stress-energy tensor. (The experimentally derived constant <math>G</math> has to appear in both Newton's formulation of gravity and the [[General relativity]] formulation, since they are compatible.)

Einstein added the term with '''cosmological constant''' to his gravitational field equations in order to allow the existence of a homogeneous static solutions in the presence of matter, i.e. to make the universe stationary (neither expanding nor contracting). This works when the '''cosmological constant''' has so called Einstein value:  

Einstein added the cosmological constant term to his gravitational field equations in order to allow the existence of a homogeneous static solutions in the presence of matter, i.e. to make the universe stationary (neither expanding nor contracting). This works when the cosmological constant has the so-called Einstein value:  

:<math>\Lambda_E=4\pi G \rho/c^2</math>,  

:<math>\Lambda_E=4\pi G \rho/c^2</math>,  

where <math>G</math> is Newtonian gravitational constant, <math>\rho</math> is [mass] density of space, and <math>c</math> is speed of light in [[vacuum]].

where <math>\rho</math> is the mass density of space and <math>c</math> is the speed of light in vacuo.

==Historical background==

==Historical background==