The European Physical Journal H

, Volume 42, Issue 3, pp 431–474 | Cite as

Einstein’s 1917 static model of the universe: a centennial review

  • Cormac O’Raifeartaigh
  • Michael O’Keeffe
  • Werner Nahm
  • Simon Mitton


We present a historical review of Einstein’s 1917 paper ‘Cosmological Considerations in the General Theory of Relativity’ to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein’s development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy and cosmology. Our review includes a description of the observational and theoretical background to the paper; a paragraph-by-paragraph guided tour of the work; a discussion of Einstein’s views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to little-known aspects of the paper such as Einstein’s failure to test his model against observation, his failure to consider the stability of the model and a mathematical oversight concerning his interpretation of the role of the cosmological constant. We recall the response of theorists and astronomers to Einstein’s cosmology in the context of the alternate models of the universe proposed by Willem de Sitter, Alexander Friedman and Georges Lemaître. Finally, we consider the relevance of the Einstein World in today’s ‘emergent’ cosmologies.


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  1. 1.
    Associated Press Report. 1931a. Prof. Einstein begins his work at Mt. Wilson. New York Times, Jan 3, p. 1Google Scholar
  2. 2.
    Associated Press Report. 1931b. Red shift of nebulae a puzzle, says Einstein. New York Times, Feb 12, p. 2Google Scholar
  3. 3.
    Atazadeh, K. 2014. Stability of the Einstein universe in Einstein-Cartan theory. JCAP 06: 020-033ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Ball, R.S. 1881. The distances of stars. Nature 24: 91-92CrossRefGoogle Scholar
  5. 5.
    Barbour, J. 1990. The part played by Mach’s Principle in the genesis of relativistic cosmology. In Modern Cosmology in Retrospect. B. Bertotti et al. (eds.), pp. 47-66Google Scholar
  6. 6.
    Barrow, J., G.F.R. Ellis, R. Maartens and C.G. Tsagas. 2003. On the stability of the Einstein static universe. Class. Quant. Gravity. 20 (11): L155-161ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bartusiak, M. 2009. The Day We Found the Universe. Vintage Books, New YorkGoogle Scholar
  8. 8.
    Belenkiy, A. 2012. Alexander Friedmann and the origins of modern cosmology. Physics Today 65 (10): 38-43CrossRefGoogle Scholar
  9. 9.
    Belenkiy, A. 2013. The waters I am entering no one yet has crossed: Alexander Friedman and the origins of modern cosmology. In Origins of the Expanding Universe. M. Way and D. Hunter (eds.), Astron. Soc. Pacific. Conf. Series 471: 71-96ADSGoogle Scholar
  10. 10.
    Bondi, H. 1952. Cosmology. Cambridge University Press, Cambridge.Google Scholar
  11. 11.
    Charlier, C. 1908. Wie eine unendliche Welt aufgebaut sein kann. Arkiv Mat. Ast. Fysik 4: 1-15zbMATHGoogle Scholar
  12. 12.
    Clark, R.W. 1973. Einstein: The Life and Times. Hodder and Stoughton, LondonGoogle Scholar
  13. 13.
    Coles, P. and F. Lucchin. 2002. Cosmology: The Origin and Evolution of Cosmic Structure. Wiley & Sons, ChichesterGoogle Scholar
  14. 14.
    Crelinsten, J. 2006. Einstein’s Jury: The Race To Test Relativity. Princeton University Press, New JerseyGoogle Scholar
  15. 15.
    de Sitter, W. 1916a. On Einstein’s theory of gravitation and its astronomical consequences. Second Paper. MNRAS 77: 155-184ADSCrossRefGoogle Scholar
  16. 16.
    de Sitter, W. 1916b. De relativiteit der rotatie in de theorie van Einstein. Kon. Akad. van Wetensch. Amsterdam 25: 499-504. Or ‘On the relativity of rotation in Einstein’s theory.’ Proc. Roy. Neth. Acad. Art. Sci. 19 (1): 527-532 (1917)zbMATHGoogle Scholar
  17. 17.
    de Sitter, W. 1916c. Letter to Albert Einstein, November 1st. CPAE 8 (Doc. 272).
  18. 18.
    de Sitter, W. 1916d. Notebook S12 on Relativity. Willem de Sitter Archive. AFA-FC-Wds 132. Leiden University Library, Leiden. Excerpts in eng. transl. (Peruzzi and Realdi 2011).Google Scholar
  19. 19.
    de Sitter, W. 1917a. On Einstein’s theory of gravitation and its astronomical consequences. Third paper. MNRAS 78: 3-28ADSCrossRefGoogle Scholar
  20. 20.
    de Sitter, W. 1917b. On the relativity of inertia. Remarks concerning Einstein’s latest hypothesis. Proc. Roy. Neth. Acad. Arts and Sci. 19 (11): 1217-1225Google Scholar
  21. 21.
    de Sitter, W. 1917c. Letter to Albert Einstein, March 15th. CPAE 8 (Doc. 312).
  22. 22.
    de Sitter, W. 1917d. Letter to Albert Einstein, March 20th. CPAE 8 (Doc. 313).
  23. 23.
    de Sitter, W. 1917e. Letter to Albert Einstein, April 1st. CPAE 8 (Doc. 321).
  24. 24.
    de Sitter, W. 1930a. On the distances and radial velocities of the extragalactic nebulae, and the explanation of the latter by the relativity theory of inertia. PNAS. 16: 474-488ADSCrossRefzbMATHGoogle Scholar
  25. 25.
    de Sitter, W. 1930b. The expanding universe. Discussion of Lemaître’s solution of the equations of the inertial field. Bull. Astron. Inst. Neth. 5 (193): 211-218ADSGoogle Scholar
  26. 26.
    Duerbeck, H.W. and W.C. Seitter. 2000. In Edwin Hubble’s shadow: Early investigations on the expansion of the Universe. Act. Hist. Ast. 10: 120-147.Google Scholar
  27. 27.
    Earman, J. 2001. Lambda: the constant that refuses to die. Arch. Hist. Exact. Sci. 55 (3): 189-220MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Eddington, A.S. 1914. Stellar Movements and the Structure of the Universe. MacMillan, LondonGoogle Scholar
  29. 29.
    Eddington, A.S. 1923. The Mathematical Theory of Relativity. Cambridge University Press, CambridgeGoogle Scholar
  30. 30.
    Eddington, A.S. 1930. On the instability of Einstein’s spherical world. MNRAS 90: 668-678ADSCrossRefzbMATHGoogle Scholar
  31. 31.
    Eddington A.S. 1931. The recession of the extra-galactic nebulae. MNRAS 92: 3-6ADSCrossRefGoogle Scholar
  32. 32.
    Eddington A.S. 1933. The Expanding Universe. Cambridge University Press, Cambridge.Google Scholar
  33. 33.
    Einstein, A. 1905a. Zur Elektrodynamik bewegter Körper. Annal. Physik 17: 891-921. Or ‘On the electrodynamics of moving bodies’. CPAE 2 (Doc. 23).ADSCrossRefzbMATHGoogle Scholar
  34. 34.
    Einstein, A. 1915a. Die Feldgleichungen der Gravitation. Sitz. König. Preuss. Akad. 844-847. Or ‘The field equations of gravitation’. CPAE 6(Doc. 25).
  35. 35.
    Einstein, A. 1915b. Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie. Sitz. König. Preuss. Akad. 831-839. Or ‘Explanation of the perhelion motion of Mercury from the general theory of relativity’. CPAE 6 (Doc. 24).
  36. 36.
    Einstein, A. 1916a. Die Grundlage der allgemeinen Relativitätstheorie. Ann. Physik. 49: 769-822. Or ‘The foundation of the general theory of relativity’. CPAE 6(Doc. 30).ADSCrossRefzbMATHGoogle Scholar
  37. 37.
    Einstein, A. 1916b. Strahlungs-Emission und -Absorption nach der Quantentheorie. Verh. Deutsch. Physik. Gesell. 18: 318-332. Or ‘Emission and absorption of radiation in quantum theory’. CPAE 6(Doc. 34).ADSGoogle Scholar
  38. 38.
    Einstein, A. 1916c. Zur Quantentheorie der Strahlung. Physik. Gesell. Zürich. 18: 47-62. Or ‘On the quantum theory of radiation’. CPAE 6 (Doc. 38) ADSGoogle Scholar
  39. 39.
    Einstein, A. 1916d. Näherungsweise Integration der Feldgleichungen der Gravitation. Sitz. König. Preuss. Akad. 688-696. Or ‘Approximative integration of the field equations of gravitation’. CPAE 6(Doc. 32)
  40. 40.
    Einstein, A. 1916e. Hamiltonsches und allgemeine Relativitätstheorie. Sitz. König. Preuss. Akad. 1111-1116. Or ‘Hamilton’s Principle and the general theory of relativity’. CPAE 6(Doc.41)
  41. 41.
    Einstein, A. 1916f. Letter to Karl Schwarzschild, January 9th. CPAE 8(Doc. 181).
  42. 42.
    Einstein, A. 1916g. Letter to Michele Besso, May 14th. CPAE 8 (Doc. 219).
  43. 43.
    Einstein, A. 1916h. Letter to Michele Besso, October 31st. CPAE 8(Doc. 270).
  44. 44.
    Einstein, A. 1916i. Letter to Willem de Sitter, November 4th. CPAE 8(Doc. 273).
  45. 45.
    Einstein, A. 1916j. Letter to Karl Schwarzschild, February 19th. CPAE 8(Doc. 194).
  46. 46.
    Einstein, A. 1917a. Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie. Sitz. König. Preuss. Akad. 142-152. Or ‘Cosmological considerations in the general theory of relativity’ in (Lorentz et al. 1952): 175-188. CPAE 6(Doc. 43).
  47. 47.
    Einstein, A. 1917b. Über die Spezielle und die Allgemeine Relativitätstheorie (Gemeinverständlich). Vieweg (Braunschweig). Or ‘Relativity: The Special and General Theory’ (Metheun 1920). CPAE 6 (Doc.42).
  48. 48.
    Einstein, A. 1917c. Letter to Paul Ehrenfest, February14th. CPAE 8(Doc. 298).
  49. 49.
    Einstein, A. 1917d. Letter to Michele Besso, March 9th. CPAE 8(Doc. 306).
  50. 50.
    Einstein, A. 1917e. Letter to Heinrich Zangger, March 10th. CPAE 8(Doc. 309).
  51. 51.
    Einstein, A. 1917f. Letter to Willem de Sitter, March 12th. CPAE 8(Doc. 311).
  52. 52.
    Einstein, A. 1917g. Letter to Willem de Sitter, February 2nd. CPAE 8(Doc. 293).
  53. 53.
    Einstein, A. 1917h. Letter to Paul Ehrenfest, February 4th. CPAE 8(Doc. 294).
  54. 54.
    Einstein, A. 1917i. Letter to Rudolf Förster, November 16th. CPAE 8(Doc. 400).
  55. 55.
    Einstein, A. 1917j. Letter to Erwin Freundlich, February 18th. CPAE 8(Doc. 300).
  56. 56.
    Einstein, A. 1917k. Letter to Felix Klein, March 26th. CPAE 8(Doc. 319).
  57. 57.
    Einstein, A. 1917l. Letter to de Sitter, June 28th. CPAE 8(Doc. 359).
  58. 58.
    Einstein, A. 1917m. Letter to de Sitter, April 14th. CPAE 8(Doc. 325).
  59. 59.
    Einstein, A. 1918a. Prinzipelles zur allgemeinen Relativitätstheorie. Annal. Physik 55: 241-244. Or ‘On the foundations of the general theory of relativity’. CPAE 7(Doc. 4).ADSCrossRefzbMATHGoogle Scholar
  60. 60.
    Einstein 1918b. Über die Spezielle und die Allgemeine Relativitätstheorie. Vieweg (Braunschweig). 3rd edn. CPAE 6(Doc.42).
  61. 61.
    Einstein, A. 1918c. Bemerkung zu Herrn Schrödingers Notiz “Über ein Lösungssystem der allgemein kovarianten Gravitationsgleichungen”. Phys. Zeit. 19: 165-166. Or ‘Comment on Schrödinger’s Note “On a system of solutions for the generally covariant gravitational field equations” ’. CPAE 7(Doc. 3).zbMATHGoogle Scholar
  62. 62.
    Einstein 1918d. Letter to Michele Besso, July 29th. CPAE 8(Doc. 591).
  63. 63.
    Einstein 1918e. Letter to Michele Besso, August 20th. CPAE 8(Doc. 604).
  64. 64.
    Einstein, A. 1918f. Kritisches zu einer von Hrn. De Sitter gegebenen Lösung der Gravitationsgleichungen. Sitz. König. Preuss. Akad. 270-272. Or ‘Critical comment on a solution of the gravitational field equations given by Mr. de Sitter’. CPAE 7 (Doc. 5).
  65. 65.
    Einstein 1918g. Letter to Felix Klein, June 20th. CPAE 8(Doc. 567).
  66. 66.
    Einstein, A. 1919a. Bermerkung über periodischen Schwankungen der Mondlänge, welche bisher nach der Newtonschen Mechanik nicht erklärbar schienen. Sitz. König. Preuss. Akad. 433-436. Or ‘Comment about periodical fluctuations of lunar longitude, which so far appeared to be inexplicable in Newtonian mechanics’. CPAE 7(Doc. 18).
  67. 67.
    Einstein, A. 1919b. Spielen Gravitationsfelder im Aufbau der materiellen Elementarteilchen eine wesentliche Rolle? Sitz. König. Preuss. Akad. 349-356. Or ‘Do gravitation fields play an essential part in the structure of the elementary particles of matter?’. CPAE 7(Doc. 17).
  68. 68.
    Einstein, A. 1921a. Geometrie und Erfahrung. Springer, Berlin. Or ‘Geometry and Experience’ (Einstein 1954b). CPAE 7(Doc. 52).
  69. 69.
    Einstein, A. 1921b. Eine einfache Anwendung des Newtonschen Gravitationsgesetzes auf die kugelförmigen Sternhaufen. In Festschrift der Kaiser-Wilhelm-Gesellschaft zur Förderung der Wissenschaften. Springer, Berlin 50-52. Or ‘A simple application of the Newtonian law of gravitation to globular star clusters’. CPAE 7 (Doc. 56)
  70. 70.
    Einstein, A. 1922a. Bemerkung zu der Arbeit von A. Friedmann “Über die Krümmung des Raumes” Zeit. Phys. 11: 326. Or ‘Comment on A. Friedmann’s paper “On The Curvature of Space” ’. CPAE 13(Doc. 340).ADSCrossRefzbMATHGoogle Scholar
  71. 71.
    Einstein, A.1922b. Bemerkung zu der Franz Seletyschen Arbeit “Beiträge zum kosmologischen System”. Ann. Physik 69: 436–438. Or ‘Comment on Franz Selety’s paper “Contributions to the Cosmological System” ’. CPAE 13(Doc. 370).ADSCrossRefzbMATHGoogle Scholar
  72. 72.
    Einstein, A.1922c. Letter to Franz Selety, September 25th. CPAE 13(Doc. 371).
  73. 73.
    Einstein, A. 1922d. Vier Vorlesungen über Relativitätstheorie. Vieweg, Berlin. Or The Meaning of Relativity. Methuen, London 1922 (Transl. E. Adams). CPAE 7 (Doc. 71)
  74. 74.
    Einstein, A. 1923a. Notiz zu der Arbeit von A. Friedmann “Über die Krümmung des Raumes”. Zeit. Phys. 16: 228. Or ‘Note to the paper by A. Friedmann “On the Curvature of Space”’. CPAE 14(Doc. 51).ADSCrossRefzbMATHGoogle Scholar
  75. 75.
    Einstein, A. 1923b. Notiz zu der Arbeit von A. Friedmann “Über die Krümmung des Raumes” . The Albert Einstein Archives. Doc. 1: 26.
  76. 76.
    Einstein, A. 1923c. Postcard to Hermann Weyl, May 23rd. CPAE 14(Doc. 40).
  77. 77.
    Einstein, A. 1931. Zum kosmologischen Problem der allgemeinen Relativitätstheorie. Sitz. König. Preuss. Akad. 235-237. Eng. transl. (O’Raifeartaigh and McCann 2014)Google Scholar
  78. 78.
    Einstein, A. 1933. Sur la structure cosmologique de l’espace (transl. M. Solovine). In ‘La Théorie de la Relativité’, Hermann, Paris. Eng. transl. (O’Raifeartaigh et al. 2015)Google Scholar
  79. 79.
    Einstein, A. 1945. On the ‘cosmologic problem’. Appendix I to The Meaning of Relativity. Princeton University Press, Princeton (3rd Ed.) 112-135.Google Scholar
  80. 80.
    Einstein, A. and W. de Sitter. 1932. On the relation between the expansion and the mean density of the universe. PNAS 18 (3): 213-214ADSCrossRefzbMATHGoogle Scholar
  81. 81.
    Eisinger, J. 2011. Einstein on the Road. Prometheus Books, New YorkGoogle Scholar
  82. 82.
    Ellis, G.F.R. 1986. The Expanding Universe: A History of Cosmology from 1917 to 1960. In Einstein and the History of General Relativity, Einstein Studies Volume 1. D. Howard and J. Stachel (eds.): 367-431Google Scholar
  83. 83.
    Ellis, G.F.R. and R. Maartens. 2004. The emergent universe: inflationary cosmology with no singularity. Class. Quant. Gravity 21: 223-239ADSMathSciNetCrossRefzbMATHGoogle Scholar
  84. 84.
    Ellis, G.F.R., J. Murugan and C.G.T. Tsagas. 2004. The emergent universe: an explicit construction. Class. Quant. Gravity 21: 233-242ADSMathSciNetCrossRefzbMATHGoogle Scholar
  85. 85.
    Fölsing, 1993. Albert Einstein: Eine Biographie. Suhrkamp Verlag, Frankfurt.Google Scholar
  86. 86.
    Fölsing, A. 1997. Albert Einstein: A Biography. (Transl. E. Osers). Viking Penguin, USA.Google Scholar
  87. 87.
    Friedman, A. 1922. Über die Krümmung des Raumes. Zeit. Physik. 10: 377-386. Or ‘On the curvature of space’ Gen. Rel. Grav. 31(12): 1991 (1999)CrossRefGoogle Scholar
  88. 88.
    Gamow, G. 1956. The evolutionary universe. Sci. Am. 192: 136-154CrossRefGoogle Scholar
  89. 89.
    Gamow, G. 1970. My World Line: An Informal Autobiography. Viking Press, New YorkGoogle Scholar
  90. 90.
    Gibbons, G. 1987. The entropy and stability of the universe. Nuc. Phys. B 292: 784-792ADSMathSciNetCrossRefGoogle Scholar
  91. 91.
    Gutfreund H. and J. Renn. 2015. The Road to Relativity: The History and Meaning of Einstein’s “The Foundation of General Relativity”. Princeton University Press.Google Scholar
  92. 92.
    Harrison, E. 1967. Classification of uniform cosmological models. MNRAS 137: 69-79ADSCrossRefGoogle Scholar
  93. 93.
    Harrison, E. 2000. Cosmology. 2nd edn. Cambridge University Press, Cambridge.Google Scholar
  94. 94.
    Harvey, A. 2012. How Einstein discovered dark energy. Physics ArXiv preprint 1211.6338
  95. 95.
    Harvey, A. and E. Schucking. 2000. Einstein’s mistake and the cosmological constant. Am. J. Phys. 68(8): 723-727ADSMathSciNetCrossRefzbMATHGoogle Scholar
  96. 96.
    Harzer, P. 1908. Die Sterne und der Raum. Jahresbericht der Deutschen Mathematiker-Vereinigung 17: 237-267zbMATHGoogle Scholar
  97. 97.
    Hawley J.F. and K.A. Holcomb. 2005. Foundations of Modern Cosmology. 2nd edn. Oxford University Press, Oxford.Google Scholar
  98. 98.
    Heckmann, O. 1931. Über die Metrik des sich ausdehnenden Universums. Nach. Gesell. Wiss. Göttingen, Math.-Phys. Klasse 2: 126-131zbMATHGoogle Scholar
  99. 99.
    Heckmann, O. 1932. Die Ausdehnung der Welt in ihrer Abhängigkeit von der Zeit. Nach. Gesell. Wiss. Göttingen, Math.-Phys. Klasse 2: 181-190zbMATHGoogle Scholar
  100. 100.
    Herschel, J. 1848. Kosmos. The Edinburgh Review. January Issue. Also available in Essays from the Edinburgh and Quarterly Reviews. Longmans and Roberts (London 1857), pp. 257-364Google Scholar
  101. 101.
    Hoefer, C. 1994. Einstein’s struggle for a Machian gravitation theory. Stud. His. Phil. Sci. 25 (3): 287-335MathSciNetCrossRefGoogle Scholar
  102. 102.
    Huang, H., P. Wu and H. Yu. 2014. Stability of the Einstein static universe in the Jordan-Brans-Dicke theory. Phys. Rev. D 89: 103521-103560ADSCrossRefGoogle Scholar
  103. 103.
    Hubble, E. 1925. Cepheids in spiral nebulae. The Observatory 48: 139-142ADSGoogle Scholar
  104. 104.
    Hubble, E. 1926. Extragalactic nebulae. Astro. J. 64: 321-369ADSCrossRefGoogle Scholar
  105. 105.
    Hubble, E. 1929. A relation between distance and radial velocity among extra-galactic nebulae. PNAS. 15: 168-173ADSCrossRefzbMATHGoogle Scholar
  106. 106.
    Illy, J. 2006. Albert Meets America: How Journalists Treated Genius During Einstein’s 1921 Travels. John Hopkins University Press, MarylandGoogle Scholar
  107. 107.
    Isaacson, W. 2007. Einstein: His Life and Universe. Simon & Schuster, London.Google Scholar
  108. 108.
    Janssen, M. 2005. Of pots and holes: Einstein’s bumpy road to general relativity. Ann. Physik 14(Suppl S1): 58-85ADSMathSciNetCrossRefGoogle Scholar
  109. 109.
    Janssen, M. 2016. The Einstein-de Sitter debate and its aftermath. HSci/Phys 4121.Google Scholar
  110. 110.
    Janssen M. and J. Renn. 2007. Untying the knot: how Einstein found his way back to field equations discarded in the Zurich notebook. In The Genesis of General Relativity Vol 2. M. Janssen et al. (eds). Boston Studies in the Philosophy of Science 250: 839-925. Springer, Berlin.Google Scholar
  111. 111.
    Janssen, M. and J. Renn. 2015. Arch and Scaffold: How Einstein found his field equations. Physics Today 68(11): 30-36.CrossRefGoogle Scholar
  112. 112.
    Janssen M., R. Schulmann, J. Illy, C. Lehner and D. Kormos-Buchwald. 2002. The Collected Papers of Albert Einstein Volume 7. The Berlin Years: Writings 1918-1921 (Transl. A. Engel). Princeton University Press, PrincetonGoogle Scholar
  113. 113.
    Jung, T. 2005. Franz Selety: Seine kosmologische Arbeiten und der Briefwechsel mit Einstein. In Einsteins Kosmos H. Duerbeck and W. Dick (eds) Deutsch, Frankfurt, pp. 125-142Google Scholar
  114. 114.
    Kahn, C. and F. Kahn. 1975. Letters from Einstein to de Sitter on the nature of the universe. Nature 257: 451-454ADSCrossRefGoogle Scholar
  115. 115.
    Kapteyn, J. 1908. Recent researches in the structure of the universe. The Observatory 31: 346-348.ADSGoogle Scholar
  116. 116.
    Kerzberg, P. 1989a. The Einstein-de Sitter controversy of 1916–1917 and the rise of relativistic cosmology. In Einstein and the History of General Relativity, Einstein Studies Volume 1. Howard and J. Stachel (eds.): 325-366Google Scholar
  117. 117.
    Kerzberg, P. 1989b. The Invented Universe: The Einstein-de Sitter Controversy (1916–1917) and the Rise of Relativistic Cosmology. Clarendon Press, OxfordGoogle Scholar
  118. 118.
    Khodadi, M., Y. Heydarzade, K. Nozari and F. Darabi. 2015. On the stability of the Einstein static universe in doubly general relativity scenario. Eur. Phys. J. C 75: 590-595ADSCrossRefGoogle Scholar
  119. 119.
    Klein, F. 1918. Letter to Albert Einstein, June 16th. CPAE 8(Doc. 566).
  120. 120.
    Kox, A.J., M.J. Klein and R. Schulmann. 1996. The Collected Papers of Albert Einstein Volume 6. The Berlin Years: Writings 1914–1917 (Transl. A. Engel). Princeton University Press, PrincetonGoogle Scholar
  121. 121.
    Kragh, H. 1996. Cosmology and Controversy. Princeton University Press, Princeton, New JerseyGoogle Scholar
  122. 122.
    Kragh, H. 2007. Conceptions of Cosmos. Oxford University Press, OxfordGoogle Scholar
  123. 123.
    Kragh, H. 2012a. Is space flat? Nineteenth-century astronomy and non-Euclidean geometry. J Ast. Hist. Herit. 15(3): 149-158ADSGoogle Scholar
  124. 124.
    Kragh, H. 2012b. Geometry and astronomy: pre-Einstein speculations of non-Euclidean space. ArXiv preprint 1205.4909
  125. 125.
    Kragh, H. 2015. Masters of the Universe: Conversations with Cosmologists of the Past. Oxford University Press, Oxford.Google Scholar
  126. 126.
    Kragh, H. and J. Overduin. 2014. The Weight of the Vacuum: A Scientific History of Dark Energy. Springer, New York.Google Scholar
  127. 127.
    Lambourne, R. 2010. Relativity, Gravitation and Cosmology. Cambridge University Press, CambridgeGoogle Scholar
  128. 128.
    Lanczos, K. 1922. Bemerkung zur de Sitterschen Welt. Phys. Zeit. 23: 539-543.zbMATHGoogle Scholar
  129. 129.
    Lemaître, G. 1925. Note on de Sitter’s universe. J. Math. Phys. 4: 188-192CrossRefzbMATHGoogle Scholar
  130. 130.
    Lemaître, G. 1927. Un univers homogène de masse constante et de rayon croissant, rendant compte de la vitesse radiale des nébuleuses extra-galactiques. Annal. Soc. Sci. Brux. Série A. 47: 49-59zbMATHGoogle Scholar
  131. 131.
    Lemaître, G. 1931a. The beginning of the world from the point of view of quantum theory. Nature 1 27: 706CrossRefzbMATHGoogle Scholar
  132. 132.
    Lemaître, G. 1931b. A homogeneous universe of constant mass and increasing radius, accounting for the radial velocity of the extra-galactic nebulae. MNRAS 91: 483-490ADSCrossRefzbMATHGoogle Scholar
  133. 133.
    Lemaître, G. 1933. L’univers en expansion. Ann. Soc. Sci. Brux A53: 51-85. Or ‘The expanding universe’ Gen. Rel. Grav. 29(5): 641-680 (1997)zbMATHGoogle Scholar
  134. 134.
    Lemaître, G. 1958. Recontres avec Einstein. Rev. Quest. Sci. 129: 129-132Google Scholar
  135. 135.
    Livio, M. 2013. Brilliant Blunders: from Darwin to Einstein. Simon & Schuster, New YorkGoogle Scholar
  136. 136.
    Lobachevsky, N.I. 2010. Pangeometry. In Source Book of Mathematics (D.E. Smith ed.). McGraw Hill. Dover (1984): 360-371. European Mathematical SocietyGoogle Scholar
  137. 137.
    Lorentz H.A., A. Einstein, H. Minkowski and H. Weyl. 1923. ‘The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity.’ Metheun and Co., New York. Reprinted by Dover in 1952.Google Scholar
  138. 138.
    Lundmark, K. 1924. The determination of the curvature of space-time in de Sitter’s world. MNRAS 84: 747-764ADSCrossRefGoogle Scholar
  139. 139.
    Mamone-Capria, M. 2005. The rebirth of cosmology; from the static to the expanding universe. In Physics Before and After Einstein. (M. Mamone-Capria ed.), IOS Press, Amsterdam.Google Scholar
  140. 140.
    Milne, E.A. 1933. World-Structure and the Expansion of the Universe. Zeit. Astrophys. 6: 1-95ADSzbMATHGoogle Scholar
  141. 141.
    Milne, E.A. 1935. Relativity, Gravitation and World Structure. Clarendon Press, Oxford.Google Scholar
  142. 142.
    Minkowski, H. 1908. Raum und Zeit. Address at the 80th Assembly of German Natural Scientists and Physicians at Cologne, September 21st. Or ‘Space and Time’ in (Lorentz et al. 1952): 73-91Google Scholar
  143. 143.
    Neumann, C. 1896. Allgemeine Untersuchungen über das Newtonsche Prinzip der Fernwirkungen. Teubner, Leipzig.Google Scholar
  144. 144.
    Newcomb, S. 1898. The philosophy of hyperspace. Science 7: 1-7. Reprinted in Popular. Astronomy 6(1898): 380-389ADSMathSciNetCrossRefzbMATHGoogle Scholar
  145. 145.
    Newcomb, S. 1906. The structure of the universe. In Sidelights on Astronomy and Kindred Fields of Popular Science. Harper & Bros, New YorkGoogle Scholar
  146. 146.
    North, J.D. 1965. The Measure of the Universe: A History of Modern Cosmology. Oxford University Press, Oxford. Republished by Dover in 1990.Google Scholar
  147. 147.
    Norton J. 1984. How Einstein found his field equations: 1912–1915. Hist. Stud. Phys. Sci. 14: 253-316Google Scholar
  148. 148.
    Norton J. 1999. The cosmological woes of Newtonian gravitation theory. In The Expanding Worlds of General Relativity, Einstein Studies Vol. 7. H. Goenner, et al. (eds.): 271-322.Google Scholar
  149. 149.
    Nussbaumer, H. 2014a. Einstein’s conversion from his static to an expanding universe. Eur. Phys. J. H 39 (1): 37-62CrossRefGoogle Scholar
  150. 150.
    Nussbaumer, H. 2014b. Einstein’s aborted attempt at a dynamic steady-state universe. Physics ArXiv preprint 1402.4099
  151. 151.
    Nussbaumer, H. and L. Bieri. 2009. Discovering the Expanding Universe, Cambridge University Press, CambridgeGoogle Scholar
  152. 152.
    Ohanian, H.C. 2008. Einstein’s Mistakes: The Human Failings of a Genius. Norton & Co., New YorkGoogle Scholar
  153. 153.
    Olbers, H. 1826. Über die Durchsichtigkeit des Weltraums. Astron. Jahrbuch 51: 110-121Google Scholar
  154. 154.
    O’Raifeartaigh, C. 2013. The contribution of V.M. Slipher to the discovery of the expanding universe. In ‘Origins of the Expanding Universe: 1912–1932’. M. Way and D. Hunter (eds.), Astron. Soc. Pacific. Conf. Series 471: 49-61Google Scholar
  155. 155.
    O’Raifeartaigh, C. and B. McCann. 2014. Einstein’s cosmic model of 1931 revisited; an analysis and translation of a forgotten model of the universe. Eur. Phys. J H 39(1): 63-85Google Scholar
  156. 156.
    O’Raifeartaigh, C., B. McCann, W. Nahm and S. Mitton. 2014. Einstein’s steady-state theory: an abandoned model of the cosmos. Eur. Phys. J H 39 (3): 353-367CrossRefGoogle Scholar
  157. 157.
    O’Raifeartaigh, C., M. O’Keeffe, W. Nahm and S. Mitton. 2015. Einstein’s cosmology review of 1933: a new perspective on the Einstein-de Sitter model of the cosmos. Eur. Phys. J H 40(3): 301-336CrossRefGoogle Scholar
  158. 158.
    Pais, A. 1982. The Life and Science of Albert Einstein. Clarendon Press, OxfordGoogle Scholar
  159. 159.
    Pais, A. 1994. Einstein Lived Here. Clarendon Press, OxfordGoogle Scholar
  160. 160.
    Parisi, L., N. Radicella and G. Vilasi. 2012. Stability of the static Einstein universe in massive gravity. Phys. Rev. D 86: 024035-024045ADSCrossRefzbMATHGoogle Scholar
  161. 161.
    Parisi L., M. Bruni, R. Maartens and K. Vandersloot. 2007. The Einstein static universe in loop quantum cosmology. Class. Quant. Grav. 24: 6243-6251ADSMathSciNetCrossRefzbMATHGoogle Scholar
  162. 162.
    Peebles, P. J.E. 1993. Principles of Physical Cosmology. Princeton University Press, Princeton.Google Scholar
  163. 163.
    Peebles, P.J.E. and B. Ratra. 2003. The cosmological constant and dark energy. Rev. Mod. Phys. 75(2): 559-606ADSMathSciNetCrossRefzbMATHGoogle Scholar
  164. 164.
    Peirce, C.S. 1891. The architecture of theories. The Monist 1: 161-176CrossRefGoogle Scholar
  165. 165.
    Peruzzi, G. and M. Realdi. 2011. The quest for the size of the universe in early relativistic cosmology. Arch. Hist. Exact. Sci. 65: 659-689MathSciNetCrossRefzbMATHGoogle Scholar
  166. 166.
    Realdi, M. and G. Peruzzi. 2009. Einstein, de Sitter and the beginning of relativistic cosmology in 1917. Gen. Rel. Grav. 41(2): 225-247ADSMathSciNetCrossRefzbMATHGoogle Scholar
  167. 167.
    Renn, J. 2007. The Third Way to General Relativity: Einstein and Mach in Context. In The Genesis of General Relativity. J. Renn, et al. (eds.): pp. 945-1000.
  168. 168.
    Rindler, W. 1969. Essential Relativity: Special, General, and Cosmological. Van Nostrand, New York.Google Scholar
  169. 169.
    Robertson, H.P. 1928. On relativistic cosmology. Phil Mag 5(Suppl): 835-848CrossRefzbMATHGoogle Scholar
  170. 170.
    Robertson, H.P. 1929. On the foundations of relativistic cosmology. PNAS 15: 822-829ADSCrossRefzbMATHGoogle Scholar
  171. 171.
    Robertson, H.P. 1932. The expanding universe. Science 76: 221-226ADSCrossRefzbMATHGoogle Scholar
  172. 172.
    Robertson, H.P. 1933. Relativistic cosmology. Rev. Mod. Phys. 5(1): 62-90ADSCrossRefzbMATHGoogle Scholar
  173. 173.
    Robinson, A. 2005. Einstein: A Hundred Years of Relativity. Palazzo Editions, BathGoogle Scholar
  174. 174.
    Schrödinger, E. 1918. Über ein Lösungssystem der allgemein kovarianten Gravitationsgleichungen. Phys. Zeit. 19: 20-22. Excerpts in eng. transl. (Harvey [2012a]).zbMATHGoogle Scholar
  175. 175.
    Schulmann R., A.J. Kox, M. Janssen and J. Illy. 1998. The Collected Papers of Albert Einstein Volume 8. The Berlin Years: Correspondence 1914-1918 (Transl. A.M. Hentschel). Princeton University Press, Princeton.Google Scholar
  176. 176.
    Schwarzschild, K. 1900. Über das zulässige Krümmungsmass des Raumes. Vierteljahrschrift Ast. Gesell. 35: 337-347. Or ‘On the permissible curvature of space’. Class. Quant. Grav. 15: 2539-2544 (1998).zbMATHGoogle Scholar
  177. 177.
    Schwarzschild, K. 1916a. Über das Gravitationsfeld eines Massenpunktes nach der Einsteinischen Theorie. Sitz. König. Preuss. Akad. Wiss. 189-196. Or ‘On the gravitational field of a mass point according to Einstein’s theory’. Gen. Rel. Grav. 35(5): 951-959 (2003).Google Scholar
  178. 178.
    Schwarzschild, K. 1916b. Letter to Albert Einstein, February 6th. CPAE 8 (Doc. 188)
  179. 179.
    Seahra, S.S. and C.G. Bohmer. 2009. Einstein static universes are unstable in generic f(R) models. Phys. Rev. D 79: 064009-064019ADSMathSciNetCrossRefGoogle Scholar
  180. 180.
    Seeliger, H. von. 1895. Über das Newtonische Gravitationsgesetz. Astron. Nach. 137: 129-136.ADSCrossRefzbMATHGoogle Scholar
  181. 181.
    Seeliger, H. von. 1896. Über das Newtonische Gravitationsgesetz Sitz. König. Bayer. Akad. Wiss. 126: 373-400Google Scholar
  182. 182.
    Seeliger, H. von. 1898a. Betrachtungen über die räumliche Verteilung der Fixsterne. Sitz. König. Bayer. Akad. Wiss Google Scholar
  183. 183.
    Seeliger, H. von. 1898b. On Newton’s law of gravitation. Pop. Astron. 5: 544-551.ADSGoogle Scholar
  184. 184.
    Seeliger, H. von. 1909. Über die Anwendung der Naturgesetze auf das Universum. Sitz. König. Bayer. Akad. Wiss: 3-25Google Scholar
  185. 185.
    Selety, F. 1922. Beitrage zum kosmologischen Problem. Ann. Physik 68: 281-334ADSCrossRefzbMATHGoogle Scholar
  186. 186.
    Selety, F. 1923. Erwiderung auf die Bermerkungen Einsteins über meine Arbeit ‘Beitrage zum kosmologischen Problem’. Ann. Physik 72: 58-66ADSCrossRefzbMATHGoogle Scholar
  187. 187.
    Selety, F. 1924. Unendlichkeit des Raumes und allgemeine Relativitätstheorie. Ann. Physik 73: 291-325ADSCrossRefzbMATHGoogle Scholar
  188. 188.
    Shabani H. and A.H. Ziaie. 2017. Stability of the Einstein universe in f(R,T) gravity. Eur. Phys. J. C 77(31): 1-15.ADSGoogle Scholar
  189. 189.
    Shapley, H. 1915. Studies based on the colours and magnitudes in stellar clusters. Second paper. Contrib. Mt Wilson Solar Observatory. No. 116Google Scholar
  190. 190.
    Shapley, H. 1918. Globular clusters and the structure of the galactic system. Pub. Ast. Soc. Pac. 30: 42-54ADSCrossRefGoogle Scholar
  191. 191.
    Silberstein, L. 1922. The curvature of de Sitter’s spacetime derived from globular clusters. MNRAS 84: 363-366ADSCrossRefGoogle Scholar
  192. 192.
    Slipher, V.M. 1915. Spectrographic observations of nebulae. Pop. Ast. 23: 21-24ADSGoogle Scholar
  193. 193.
    Slipher, V.M. 1917. Nebulae, Proc. Am. Phil. Soc. 56: 403-409ADSGoogle Scholar
  194. 194.
    Smeenk, Christopher. 2014. Einstein’s role in the creation of relativistic cosmology. In The Cambridge Companion to Einstein. M. Janssen and C. Lehner (eds). Cambridge University Press, Cambridge: pp. 228-269Google Scholar
  195. 195.
    Smith, R. 1982. The Expanding Universe: Astronomy’s Great Debate 1900-1931. Cambridge University Press, CambridgeGoogle Scholar
  196. 196.
    Speziali, P. 1972. Albert Einstein, Michele Besso: Correspondance 1903-1955. Hermann, ParisGoogle Scholar
  197. 197.
    Stachel, J. 1977. Notes on the Andover Conference. In Foundations of Space-Time Theories, J.S. Earman et al. (eds). Minnesota Studies in the Philosophy of Science VIII pp viii–xiiGoogle Scholar
  198. 198.
    Straumann N. 2002. The history of the cosmological constant problem. In On the Nature of Dark Energy: Proceedings of the 18th IAP Astrophysics Colloquium. P. Brax et al., Frontier Group (Paris). Physics ArXiv preprint 0208027.
  199. 199.
    Strömberg, G. 1925. Analysis of radial velocities of globular clusters and non-galactic nebulae. Astrophys. J 61: 353-388ADSCrossRefGoogle Scholar
  200. 200.
    Taylor E.F. and J.A. Wheeler. 2000. Exploring Black Holes: Introduction to General Relativity. Addison Wesley, San Francisco.Google Scholar
  201. 201.
    Thomson, W. 1901. On ether and gravitational matter through infinite space. Phil. Mag. 2: 160-177CrossRefGoogle Scholar
  202. 202.
    Tolman, R. 1930a. The effect of the annihilation of matter on the wave-length of light from the nebulae. PNAS. 16: 320-337ADSCrossRefzbMATHGoogle Scholar
  203. 203.
    Tolman, R.C. 1930b. More complete discussion of the time-dependence of the non-static line element for the universe. PNAS. 16: 409-420ADSCrossRefzbMATHGoogle Scholar
  204. 204.
    Tolman, R.C. 1931a. On the theoretical requirements for a periodic behaviour of the universe. Phys. Rev. 38: 1758-1771ADSCrossRefzbMATHGoogle Scholar
  205. 205.
    Tolman, R.C. 1931b. Letter to Albert Einstein. September 14th. Albert Einstein Archive. 23-31Google Scholar
  206. 206.
    Tolman, R.C. 1932. On the behaviour of non-static models of the universe when the cosmological term is omitted. Phys. Rev. 39: 835-843ADSCrossRefzbMATHGoogle Scholar
  207. 207.
    Tolman, R.C. 1934. Relativity, Thermodynamics and Cosmology. Oxford University Press, Oxford. Reprinted by Dover in 1987.Google Scholar
  208. 208.
    Topper, D.R. 2013. How Einstein Created Relativity out of Physics and Astronomy. Springer, New York.Google Scholar
  209. 209.
    Trautman, A. 1965. Foundations and current problems in general relativity. In Lectures on General Relativity. A. Trautman et al. (eds). Prentice Hall, New Jersey: 1-248.Google Scholar
  210. 210.
    Weinstein, G. 2013. The mythical snake which swallows its tail: Einstein’s matter world. Physics ArXiv preprint 1309.6590
  211. 211.
    Weyl, H. 1923a. Raum, Zeit, Materie. Springer, Berlin. Or Space, Time, Matter (Dover, 1952)Google Scholar
  212. 212.
    Weyl, H. 1923b. Zur allgemeinen Relativitätstheorie. Phys. Zeit. 24: 230-232zbMATHGoogle Scholar
  213. 213.
    Wirtz, C. 1922. Einiges zur Stastik der Radialbewegungen der Spiralnebelen und Kugelsternhaufen. Ast. Nach. 215: 350-354ADSGoogle Scholar
  214. 214.
    Young, C. 1889. A Texbook of General Astronomy for Colleges and Scientific Schools. Ginn and Company. BostonGoogle Scholar
  215. 215.
    Zöllner, J.C.F. 1872. Über die Natur der Cometen. Engelmann, LeipzigGoogle Scholar

Copyright information

© EDP Sciences and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Cormac O’Raifeartaigh
    • 1
  • Michael O’Keeffe
    • 1
  • Werner Nahm
    • 2
  • Simon Mitton
    • 3
  1. 1.School of Science and Computing, Waterford Institute of TechnologyWaterfordIreland
  2. 2.School of Theoretical Physics, Dublin Institute for Advanced StudiesDublin 2Ireland
  3. 3.St Edmund’s College, University of CambridgeCambridgeUK

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