Friedmann equations
Equations in physical cosmology
Summary
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. The equations for negative spatial curvature were given by Friedmann in 1924. The physical models built on the Friedmann equations are called FRW or FLRW models and form 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.
Originally created by JHG
11/9/2004, 6:27:46 AM
Modified
4/24/2026, 2:56:15 PM
Recent revisions
Another citation (source with photo)
Dating maintenance tags: {{Cn}}
/* In popular culture */citation moved, cn tag added accordingly
We can discuss a summary of the source. Here is mine. ([[m:Special:MyLanguage/User:Jon Harald Søby/diffedit|diffedit]])
/* History */
link negative spatial curvature
cite 2: link journal
/* Assumptions */ eliminated the metaphor "build upon" which is to state - use the foundation to construct a building (but no such construction is a reality in this context)
/* History */ improved a few grammar issues and typos.
Wording - curvature set by both expansion rate and density
The indents make the citations look funky. Maybe we need a History section that mentions the translations?
changed "location" to copy of source: Petrograd - provides correct context (i.e. [[anachronism]] - Saint Petersburg didn't exist)
retrieved other German codes as version 12:54, 17 November which were inexplicably changed at 02:55, 25 December - although I didn't detail such a change at the time I made the changes
1: separated elements of source
1: doi of German
1: typographical error
1: link journal
1: publishers & translators via https://www.deepdyve.com/lp/springer-journals/on-the-curvature-of-space-eSst0wQ52E
05:17, 25 December: the codes are the same as below in the cite, the difference is below is the translation is the codes location all published 1999 - there aren't any for the German original: can't be the same codes for different sources
1: "location" link
