Friedmann equations

The Friedmann equations, also known as the Friedmann–Lemaître (FL) equations, are a set of equations in physical cosmology that govern cosmic expansion in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann in 1922 from Einstein's field equations of gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect fluid with a given mass density $ρ$ and pressure $p$ .^[1] The equations for negative spatial curvature were given by Friedmann in 1924.^[2] The physical models built on the Friedmann equations are called FRW or FLRW models and from the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.

^ Friedman, A (1922). "Über die Krümmung des Raumes". Z. Phys. (in German). 10 (1): 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902. (English translation: Friedman, A (1999). "On the Curvature of Space". General Relativity and Gravitation. 31 (12): 1991–2000. Bibcode:1999GReGr..31.1991F. doi:10.1023/A:1026751225741. S2CID 122950995.). The original Russian manuscript of this paper is preserved in the Ehrenfest archive.
^ Friedmann, A (1924). "Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes". Z. Phys. (in German). 21 (1): 326–332. Bibcode:1924ZPhy...21..326F. doi:10.1007/BF01328280. S2CID 120551579. (English translation: Friedmann, A (1999). "On the Possibility of a World with Constant Negative Curvature of Space". General Relativity and Gravitation. 31 (12): 2001–2008. Bibcode:1999GReGr..31.2001F. doi:10.1023/A:1026755309811. S2CID 123512351.)