Friedmann equations: Difference between revisions

The '''Friedmann equations''', also known as the '''Friedmann-LemaîtreFriedmann–Lemaître''' or ('''FL''') '''equations''', are a set of [[equation]]s in [[physical cosmology]] that govern the [[Expansion of the universe|expansion of space]] in [[Homogeneity (physics)|homogeneous]] and [[Isotropy|isotropic]] models of the universe within the context of [[general relativity]]. They were first derived by [[Alexander Friedmann]] in 1922 from [[Einstein field equations|Einstein's field equations]] of [[gravitation]] for the [[Friedmann–Lemaître–Robertson–Walker metric]] and a [[perfect fluid]] with a given [[Density|mass density]] {{mvar|[[Rho (letter)|ρ]]}} and [[pressure]] {{mvar|p}}.<ref name="af1922">{{cite journal |first=A |last=Friedman |author-link=Alexander Alexandrovich Friedman |title=Über die Krümmung des Raumes |journal=Z. Phys. |volume=10 |year=1922 |issue=1 |pages=377–386 |doi=10.1007/BF01332580 |bibcode = 1922ZPhy...10..377F|s2cid=125190902 |language=de}} (English translation: {{cite journal |first=A |last=Friedman |title=On the Curvature of Space |journal=General Relativity and Gravitation |volume=31 |issue=12 |year=1999 |pages= 1991–2000 |bibcode=1999GReGr..31.1991F |doi=10.1023/A:1026751225741|s2cid=122950995 }}). The original Russian manuscript of this paper is preserved in the [http://ilorentz.org/history/Friedmann_archive Ehrenfest archive].</ref> The equations for negative spatial curvature were given by Friedmann in 1924.<ref name="af1924">{{cite journal |first=A |last=Friedmann |author-link=Alexander Alexandrovich Friedman |title=Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes |journal=Z. Phys. |volume=21 |year=1924 |issue=1 |pages=326–332 |doi=10.1007/BF01328280 |bibcode=1924ZPhy...21..326F|s2cid=120551579 |language=de}} (English translation: {{cite journal |first=A |last=Friedmann |title=On the Possibility of a World with Constant Negative Curvature of Space |journal=General Relativity and Gravitation |volume=31 |issue=12 |year=1999 |pages=2001–2008 |bibcode=1999GReGr..31.2001F |doi=10.1023/A:1026755309811|s2cid=123512351 }})</ref>