This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| Friedmann models | |
|---|---|
| Name | Friedmann models |
| Field | Cosmology |
| Introduced | 1922 |
| Introduced by | Alexander Friedmann |
| Key people | Alexander Friedmann, Albert Einstein, Georges Lemaître, Edwin Hubble, Stephen Hawking, George Gamow, Alan Guth, Roger Penrose, Jim Peebles, Yakov Zel'dovich, Andrei Sakharov, John Wheeler, Subrahmanyan Chandrasekhar, Robert Dicke, Richard Tolman, Hermann Bondi, Thomas Gold, Robert Wald, Kip Thorne, John Barrow |
Friedmann models are solutions of the Einstein field equations describing homogeneous and isotropic expanding or contracting Universes under the assumptions of the Cosmological principle and a perfect-fluid stress–energy tensor. They form the backbone of modern Big Bang cosmology and interface with observational programs such as the Hubble Space Telescope, Planck, Wilkinson Microwave Anisotropy Probe and surveys like Sloan Digital Sky Survey and Two-degree Field Galaxy Redshift Survey. Friedmann models underpin theoretical work by researchers affiliated with institutions such as Princeton University, Cambridge University, California Institute of Technology, Universität Göttingen, and St. Petersburg State University.
Friedmann models derive from the FLRW metric and the Einstein field equations originally developed by Alexander Friedmann and later refined by Georges Lemaître, Howard Robertson, and Arthur Walker. They incorporate parameters measured by collaborations including Planck, WMAP, BICEP2, Large Hadron Collider experiments, and telescopes such as Vera C. Rubin Observatory, Subaru Telescope, Keck Observatory, and Very Large Array. The models connect theoretical constructs from General relativity to empirical results from projects like Type Ia supernova searches led by teams including members from Lawrence Berkeley National Laboratory and Carnegie Institution for Science.
The mathematical formulation uses the FLRW metric with scale factor a(t), curvature constant k, and matter content described by an energy density ρ and pressure p. Friedmann equations follow from Einstein field equations with cosmological constant Λ, terms appearing in works by Albert Einstein and later discussions by Richard Tolman and George Gamow. Conservation equations relate to thermodynamic analyses by Lev Landau, Ralph Alpher, and Robert Herman. Initial conditions reference singularity theorems proved by Stephen Hawking and Roger Penrose and analyses by John Wheeler and Robert Dicke.
Classification uses curvature k = +1, 0, −1 leading to closed, flat, and open geometries respectively, discussed in monographs by Eddington, Arthur Eddington, Friedrich Engels (note: historical contemporaries), and textbooks by Steven Weinberg, Sean Carroll, Charles Misner, Kip Thorne, and Jerome Friedman (distinct author). Models are further categorized by dominant components: radiation-dominated era studied by George Gamow and Ralph Alpher, matter-dominated regimes analyzed by Jim Peebles and Yakov Zel'dovich, and Λ-dominated epochs popularized by A. G. Riess, Saul Perlmutter, and Brian Schmidt.
Exact and approximate solutions include power-law expansion, exponential inflationary expansion proposed by Alan Guth and refined by Andrei Linde and Paul Steinhardt, and oscillatory models considered by Richard Tolman. Perturbative treatments trace to studies by Lifshitz and modern perturbation frameworks by Viatcheslav Mukhanov and Matias Zaldarriaga. Numerical studies rely on codes developed by groups at Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Princeton University, and collaborations with NASA and ESA.
Predicted observables include cosmic microwave background anisotropies measured by COBE, WMAP, Planck, and ground-based arrays like Atacama Cosmology Telescope and South Pole Telescope. Distance–redshift relations connect to the Hubble Law discovered by Edwin Hubble and refined by Allan Sandage and modern teams including Adam Riess. Nucleosynthesis predictions match abundances measured in observations led by Margaret Burbidge, Geoffrey Burbidge, and spectroscopic surveys at Keck Observatory, Very Large Telescope, and Arecibo Observatory. Large-scale structure predictions are tested against data from 2dFGRS, SDSS, DESI, and simulations like those run at Argonne National Laboratory and Princeton Plasma Physics Laboratory.
Extensions incorporate anisotropic models such as Bianchi classification explored by Luca Amendola and John Barrow, inhomogeneous solutions like the Lemaître–Tolman metric studied by George Lemaître and Hermann Bondi, modified gravity theories proposed by Clifton, Ferreira, Padilla, and Skordis and researchers at Imperial College London, and quantum cosmology approaches advanced by Stephen Hawking, James Hartle, and Bryce DeWitt. Inflationary generalizations involve mechanisms by Alan Guth, Andrei Linde, Alexei Starobinsky, and Andrzej Linde (note: Linde listed earlier), while dark energy models link to works by Padmanabhan and R. R. Caldwell.
Friedmann's 1922 papers preceded observational confirmation by Edwin Hubble in 1929 and theoretical debate with Albert Einstein who initially rejected and later accepted expanding solutions. The models influenced later developments by Georges Lemaître, George Gamow, Robert Dicke, and led to Nobel-recognized observations by Adam Riess, Saul Perlmutter, and Brian Schmidt. Institutions such as Kavli Institute for Cosmology, Harvard–Smithsonian Center for Astrophysics, Max Planck Society, and NASA helped translate Friedmann models into quantitative cosmology used in missions like COBE and Planck. The paradigm reshaped research at universities including Princeton University, Harvard University, University of Cambridge, University of California, Berkeley, and Moscow State University and influenced awardees of Nobel Prize in Physics and Wolf Prize in Physics.