Friedmann equations (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Friedmann equations" in English language version.

Last modified: 07:34:47, 24 June 2026 (UTC)

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Friedman, A (29 May 1922). "Über die Krümmung des Raumes" (PDF). Z. Phys. (in German). 10 (1). Petrograd: Springer-Verlag GmbH & Co. KG: 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902 – via Michael Kachelrieß: Norges Teknisk-Naturvitenskapelige Universitet. (English translation: Friedman, A (1999). "On the Curvature of Space". General Relativity and Gravitation. 31 (12). Translated by F.R. Ellis; H. van Elst. Springer-Verlag GmbH & Co. KG: 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.)
Scolnic, Daniel; Riess, Adam G.; Murakami, Yukei S.; Peterson, Erik R.; Brout, Dillon; Acevedo, Maria; Carreres, Bastien; Jones, David O.; Said, Khaled; Howlett, Cullan; Anand, Gagandeep S. (2025-01-15). "The Hubble Tension in Our Own Backyard: DESI and the Nearness of the Coma Cluster". The Astrophysical Journal Letters. 979 (1): L9. arXiv:2409.14546. Bibcode:2025ApJ...979L...9S. doi:10.3847/2041-8213/ada0bd. ISSN 2041-8205.
Nemiroff, Robert J.; Patla, Bijunath (2008). "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations". American Journal of Physics. 76 (3): 265–276. arXiv:astro-ph/0703739. Bibcode:2008AmJPh..76..265N. doi:10.1119/1.2830536. S2CID 51782808.
Rosu, H. C.; Ojeda-May, P. (June 2006). "Supersymmetry of FRW Barotropic Cosmologies". International Journal of Theoretical Physics. 45 (6): 1152–1157. arXiv:gr-qc/0510004. Bibcode:2006IJTP...45.1152R. doi:10.1007/s10773-006-9123-2. ISSN 0020-7748. S2CID 119496918.
McCrea, W. H.; Milne, E. A. (1934). "Newtonian universes and the curvature of space". Quarterly Journal of Mathematics. 5: 73–80. Bibcode:1934QJMat...5...73M. doi:10.1093/qmath/os-5.1.73.
Belenkiy, Ari (2012-10-01). "Alexander Friedmann and the origins of modern cosmology". Physics Today. 65 (10): 38–43. Bibcode:2012PhT....65j..38B. doi:10.1063/PT.3.1750. ISSN 0031-9228. It's clear that in adumbrating Big Bang cosmology, Friedmann went much further than his predecessors or early successors like Lemaître.

aip.org (Global: 2,273^rd place; English: 1,697^th place)

pubs.aip.org

Belenkiy, Ari (2012-10-01). "Alexander Friedmann and the origins of modern cosmology". Physics Today. 65 (10): 38–43. Bibcode:2012PhT....65j..38B. doi:10.1063/PT.3.1750. ISSN 0031-9228. It's clear that in adumbrating Big Bang cosmology, Friedmann went much further than his predecessors or early successors like Lemaître.

arxiv.org (Global: 49^th place; English: 31^st place)

Scolnic, Daniel; Riess, Adam G.; Murakami, Yukei S.; Peterson, Erik R.; Brout, Dillon; Acevedo, Maria; Carreres, Bastien; Jones, David O.; Said, Khaled; Howlett, Cullan; Anand, Gagandeep S. (2025-01-15). "The Hubble Tension in Our Own Backyard: DESI and the Nearness of the Coma Cluster". The Astrophysical Journal Letters. 979 (1): L9. arXiv:2409.14546. Bibcode:2025ApJ...979L...9S. doi:10.3847/2041-8213/ada0bd. ISSN 2041-8205.
Nemiroff, Robert J.; Patla, Bijunath (2008). "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations". American Journal of Physics. 76 (3): 265–276. arXiv:astro-ph/0703739. Bibcode:2008AmJPh..76..265N. doi:10.1119/1.2830536. S2CID 51782808.
Rosu, H. C.; Ojeda-May, P. (June 2006). "Supersymmetry of FRW Barotropic Cosmologies". International Journal of Theoretical Physics. 45 (6): 1152–1157. arXiv:gr-qc/0510004. Bibcode:2006IJTP...45.1152R. doi:10.1007/s10773-006-9123-2. ISSN 0020-7748. S2CID 119496918.

bbc.com (Global: 26^th place; English: 23^rd place)

Murphy, Matt (November 28, 2022). "China's protests: Blank paper becomes the symbol of rare demonstrations". BBC News.

books.google.com (Global: 3^rd place; English: 3^rd place)

Bergström, Lars; Goobar, Ariel (2008). Cosmology and particle astrophysics. Springer Praxis books in astronomy and planetary science (2. ed., reprinted ed.). Chichester, UK: Praxis Publ. p. 61. ISBN 978-3-540-32924-4.

caltech.edu (Global: 240^th place; English: 473^rd place)

ned.ipac.caltech.edu

John. A. Peacock (1999). "3. THE ISOTROPIC UNIVERSE 3.1 The Robertson-Walker Metric". Cosmological Physics. Cambridge University Press: NASA/IPAC Extragalactic Database - California Institute of Technology. Archived 8 September 2025 at the Wayback Machine

cambridge.org (Global: 209^th place; English: 151^st place)

Peacock, J. A. (1998-12-28). Cosmological Physics (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511804533. ISBN 978-0-521-41072-4.
Tropp, Eduard A.; Frenkel, Viktor Ya.; Chernin, Artur D. (1993-06-03). Alexander A Friedmann: The Man who Made the Universe Expand. Translated by Dron, Alexander; Burov, Michael (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511608131. ISBN 978-0-521-38470-4.

doi.org (Global: 2^nd place; English: 2^nd place)

Friedman, A (29 May 1922). "Über die Krümmung des Raumes" (PDF). Z. Phys. (in German). 10 (1). Petrograd: Springer-Verlag GmbH & Co. KG: 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902 – via Michael Kachelrieß: Norges Teknisk-Naturvitenskapelige Universitet. (English translation: Friedman, A (1999). "On the Curvature of Space". General Relativity and Gravitation. 31 (12). Translated by F.R. Ellis; H. van Elst. Springer-Verlag GmbH & Co. KG: 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.)
Navas, S.; et al. (Particle Data Group) (2024). "Review of Particle Physics". Physical Review D. 110 (3): 1–708. doi:10.1103/PhysRevD.110.030001. hdl:20.500.11850/695340. 22.1.3 The Friedmann equations of motion
Peacock, J. A. (1998-12-28). Cosmological Physics (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511804533. ISBN 978-0-521-41072-4.
Scolnic, Daniel; Riess, Adam G.; Murakami, Yukei S.; Peterson, Erik R.; Brout, Dillon; Acevedo, Maria; Carreres, Bastien; Jones, David O.; Said, Khaled; Howlett, Cullan; Anand, Gagandeep S. (2025-01-15). "The Hubble Tension in Our Own Backyard: DESI and the Nearness of the Coma Cluster". The Astrophysical Journal Letters. 979 (1): L9. arXiv:2409.14546. Bibcode:2025ApJ...979L...9S. doi:10.3847/2041-8213/ada0bd. ISSN 2041-8205.
Nemiroff, Robert J.; Patla, Bijunath (2008). "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations". American Journal of Physics. 76 (3): 265–276. arXiv:astro-ph/0703739. Bibcode:2008AmJPh..76..265N. doi:10.1119/1.2830536. S2CID 51782808.
Rosu, H. C.; Ojeda-May, P. (June 2006). "Supersymmetry of FRW Barotropic Cosmologies". International Journal of Theoretical Physics. 45 (6): 1152–1157. arXiv:gr-qc/0510004. Bibcode:2006IJTP...45.1152R. doi:10.1007/s10773-006-9123-2. ISSN 0020-7748. S2CID 119496918.
Longair, Malcolm S. (2023). Galaxy Formation. Astronomy and Astrophysics Library. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-662-65891-8. ISBN 978-3-662-65890-1.
McCrea, W. H.; Milne, E. A. (1934). "Newtonian universes and the curvature of space". Quarterly Journal of Mathematics. 5: 73–80. Bibcode:1934QJMat...5...73M. doi:10.1093/qmath/os-5.1.73.
Tropp, Eduard A.; Frenkel, Viktor Ya.; Chernin, Artur D. (1993-06-03). Alexander A Friedmann: The Man who Made the Universe Expand. Translated by Dron, Alexander; Burov, Michael (1 ed.). Cambridge University Press. doi:10.1017/cbo9780511608131. ISBN 978-0-521-38470-4.
Belenkiy, Ari (2012-10-01). "Alexander Friedmann and the origins of modern cosmology". Physics Today. 65 (10): 38–43. Bibcode:2012PhT....65j..38B. doi:10.1063/PT.3.1750. ISSN 0031-9228. It's clear that in adumbrating Big Bang cosmology, Friedmann went much further than his predecessors or early successors like Lemaître.

hdl.handle.net (Global: 66^th place; English: 34^th place)

Navas, S.; et al. (Particle Data Group) (2024). "Review of Particle Physics". Physical Review D. 110 (3): 1–708. doi:10.1103/PhysRevD.110.030001. hdl:20.500.11850/695340. 22.1.3 The Friedmann equations of motion

ilorentz.org (Global: low place; English: low place)

Friedman, A (29 May 1922). "Über die Krümmung des Raumes" (PDF). Z. Phys. (in German). 10 (1). Petrograd: Springer-Verlag GmbH & Co. KG: 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902 – via Michael Kachelrieß: Norges Teknisk-Naturvitenskapelige Universitet. (English translation: Friedman, A (1999). "On the Curvature of Space". General Relativity and Gravitation. 31 (12). Translated by F.R. Ellis; H. van Elst. Springer-Verlag GmbH & Co. KG: 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.

nasa.gov (Global: 12^th place; English: 73^rd place)

map.gsfc.nasa.gov

"Universe 101". NASA. Retrieved September 9, 2015. The actual density of atoms is equivalent to roughly 1 proton per 4 cubic meters.

ntnu.no (Global: 6,459^th place; English: 6,427^th place)

web.phys.ntnu.no

Friedman, A (29 May 1922). "Über die Krümmung des Raumes" (PDF). Z. Phys. (in German). 10 (1). Petrograd: Springer-Verlag GmbH & Co. KG: 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902 – via Michael Kachelrieß: Norges Teknisk-Naturvitenskapelige Universitet. (English translation: Friedman, A (1999). "On the Curvature of Space". General Relativity and Gravitation. 31 (12). Translated by F.R. Ellis; H. van Elst. Springer-Verlag GmbH & Co. KG: 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.

semanticscholar.org (Global: 15^th place; English: 8^th place)

api.semanticscholar.org

Friedman, A (29 May 1922). "Über die Krümmung des Raumes" (PDF). Z. Phys. (in German). 10 (1). Petrograd: Springer-Verlag GmbH & Co. KG: 377–386. Bibcode:1922ZPhy...10..377F. doi:10.1007/BF01332580. S2CID 125190902 – via Michael Kachelrieß: Norges Teknisk-Naturvitenskapelige Universitet. (English translation: Friedman, A (1999). "On the Curvature of Space". General Relativity and Gravitation. 31 (12). Translated by F.R. Ellis; H. van Elst. Springer-Verlag GmbH & Co. KG: 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.)
Nemiroff, Robert J.; Patla, Bijunath (2008). "Adventures in Friedmann cosmology: A detailed expansion of the cosmological Friedmann equations". American Journal of Physics. 76 (3): 265–276. arXiv:astro-ph/0703739. Bibcode:2008AmJPh..76..265N. doi:10.1119/1.2830536. S2CID 51782808.
Rosu, H. C.; Ojeda-May, P. (June 2006). "Supersymmetry of FRW Barotropic Cosmologies". International Journal of Theoretical Physics. 45 (6): 1152–1157. arXiv:gr-qc/0510004. Bibcode:2006IJTP...45.1152R. doi:10.1007/s10773-006-9123-2. ISSN 0020-7748. S2CID 119496918.

springer.com (Global: 182^nd place; English: 172^nd place)

link.springer.com

Longair, Malcolm S. (2023). Galaxy Formation. Astronomy and Astrophysics Library. Berlin, Heidelberg: Springer Berlin Heidelberg. doi:10.1007/978-3-662-65891-8. ISBN 978-3-662-65890-1.

theguardian.com (Global: 16^th place; English: 11^th place)

Sullivan, Helen (2022-11-29). "Blank paper, equations and alpacas: the symbols of China's zero-Covid protests". The Guardian. ISSN 0261-3077. Retrieved 2026-04-24.

web.archive.org (Global: 1^st place; English: 1^st place)

John. A. Peacock (1999). "3. THE ISOTROPIC UNIVERSE 3.1 The Robertson-Walker Metric". Cosmological Physics. Cambridge University Press: NASA/IPAC Extragalactic Database - California Institute of Technology. Archived 8 September 2025 at the Wayback Machine

worldcat.org (Global: 4^th place; English: 4^th place)

search.worldcat.org

Scolnic, Daniel; Riess, Adam G.; Murakami, Yukei S.; Peterson, Erik R.; Brout, Dillon; Acevedo, Maria; Carreres, Bastien; Jones, David O.; Said, Khaled; Howlett, Cullan; Anand, Gagandeep S. (2025-01-15). "The Hubble Tension in Our Own Backyard: DESI and the Nearness of the Coma Cluster". The Astrophysical Journal Letters. 979 (1): L9. arXiv:2409.14546. Bibcode:2025ApJ...979L...9S. doi:10.3847/2041-8213/ada0bd. ISSN 2041-8205.
Rosu, H. C.; Ojeda-May, P. (June 2006). "Supersymmetry of FRW Barotropic Cosmologies". International Journal of Theoretical Physics. 45 (6): 1152–1157. arXiv:gr-qc/0510004. Bibcode:2006IJTP...45.1152R. doi:10.1007/s10773-006-9123-2. ISSN 0020-7748. S2CID 119496918.
Belenkiy, Ari (2012-10-01). "Alexander Friedmann and the origins of modern cosmology". Physics Today. 65 (10): 38–43. Bibcode:2012PhT....65j..38B. doi:10.1063/PT.3.1750. ISSN 0031-9228. It's clear that in adumbrating Big Bang cosmology, Friedmann went much further than his predecessors or early successors like Lemaître.
Sullivan, Helen (2022-11-29). "Blank paper, equations and alpacas: the symbols of China's zero-Covid protests". The Guardian. ISSN 0261-3077. Retrieved 2026-04-24.

Friedmann equations (English Wikipedia)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

aip.org (Global: 2,273rd place; English: 1,697th place)

pubs.aip.org

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caltech.edu (Global: 240th place; English: 473rd place)

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cambridge.org (Global: 209th place; English: 151st place)

doi.org (Global: 2nd place; English: 2nd place)

hdl.handle.net (Global: 66th place; English: 34th place)