Einstein's universe
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For other topics related to Einstein see Einstein (disambig)
Einstein's universe is a model dust universe which is a solution of Einstein's field equation for value of cosmological constant equal <math>\Lambda_E = 4\pi G\rho/c^2<math>, where <math>G<math> is Newtonian gravitational constant, <math>\rho<math> is density of space, and <math>c<math> is speed of light. Value <math>\Lambda_E<math> is called "Einstein's value of cosmological constant" or alternatively "cosmological constant of Einstein's universe".
The radius of curvature of space of Einstein's universe, called "Einstein's radius", is equal <math>R_E = \Lambda_E^{-1/2} = c/\sqrt{4\pi G\rho}<math>
"Einstein's universe" is one of Friedmann's solutions of Einstein's field equation, for the value of cosmological constant <math>\Lambda_E<math>. This is the only stationary solution of all Friedmann's solutions and because it is stationary it is thought to be non physical by majority of astronomers (about 95% according to some estimates). Those astronomers think that the universe is expanding because there is observed a phenomenon of Hubble redshift and it is interpreted by those astronomers as Doppler shift caused by galaxies moving away from our own Galaxy. Therefore it is thought that the real solution of Einstein's field equation can't be stationary.
A number of other values of cosmological constants has been proposed by various authors and the value zero was particularly popular before 1998. It was even assumed by many authors that placing a cosmological constant in Einstein's field equation was an error on part of Einstein and it was labelled "Einstein's biggest blunder" apparently by Einstein himself. The zero value of cosmological constant predicts a decelerating expansion of the universe. After 1998, when observations established beyond any reasonable doubt that the expansion of the universe looks accelerating the value zero had to be given up and a quest for establishing a real value started and is still going on (2004).