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Topology of the Universe: Theory and Observation

  • Jean-Pierre Luminet
  • Boudewijn F. Roukema
Part of the NATO Science Series book series (ASIC, volume 541)

Abstract

“One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an exactly identical copy of our Milky Way. Would we really cling on to the assumption of infinitely many identical repetitions of the same world?… We would be much happier with the view that these repetitions are illusory, that in reality space has peculiar connection properties so that if we leave any one cube through a side, then we immediately reenter it through the opposite side.” (Schwarzschild 1900 translation 1998)

Developments in the theoretical and observational sides of cosmic topology were slow for most of the century, but are now progressing rapidly at a scale of most interest, with the hope of detecting the topological parameters of the universe within the next ten years.

The historical, mathematical and observational aspects of the subject are briefly reviewed in this course.

Keywords

Fundamental Domain Holonomy Group Klein Bottle Spherical Space Universal Covering Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Atkatz, D., Pagels, H., 1982, Phys. Rv. D 25, 2065ADSCrossRefGoogle Scholar
  2. 2.
    Barbour J. & Pfister H., 1995, (Eds.), Mach’s Principle: From Newton’s Bucket to Quantum Gravity (Einstein Studies, Vol 6), BirkhauserGoogle Scholar
  3. 3.
    Beardon, A.F. 1983, The Geometry of Discrete Groups (GTM91), New York:SpringerCrossRefGoogle Scholar
  4. 4.
    Bieberbach, L., 1911, Mathematische Annalen, 70,297. 1912; Ibid, 72, 400.Google Scholar
  5. 5.
    Bond J. R., Pogosyan D., Souradeep T., 1998, Class.Quant.Gray., 15, 2573 (astroph/9804041)ADSzbMATHCrossRefGoogle Scholar
  6. 6.
    Briel U. G., Henry J. P., Böhringer H., 1992, A&A, 259, L31ADSGoogle Scholar
  7. 7.
    Carlip S., 1998, Class.Quant.Gray., 15, 2629 (gr-qc/9710114)MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    Cornish N. J., Spergel D. N., Starkman G. D., 1996, Phys.Rev.Lett., 77, 215ADSCrossRefGoogle Scholar
  9. 9.
    Cornish N. J., Spergel D. N., Starkman G. D., 1998a, astro-ph/9708225Google Scholar
  10. 10.
    Cornish N. J., Spergel D. N., Starkman G. D., 1998b, Class.Quant.Gray., 15, 2657 (astro-ph/9801212)MathSciNetADSzbMATHCrossRefGoogle Scholar
  11. 11.
    da Costa L. N., in Cosmic Velocity Fields, ed. Bouchet F., Lachièze-Rey M., (Gif-sur-Yvette, France: Editions Frontières), p.475Google Scholar
  12. 12.
    Dekel, A., Burnstein, D., White, S., 1996, in Critical Dialogues in Cosmology, ed. N. Turok, World Scientific.Google Scholar
  13. 13.
    de Oliveira Costa A., Smoot G. F., 1995, Ap.J., 448, 477ADSCrossRefGoogle Scholar
  14. 14.
    de Sitter W., 1917, MNRAS, 78, 3ADSGoogle Scholar
  15. 15.
    Dowker H. F., Garcia R. S., 1998, gr-qc/9711042Google Scholar
  16. 16.
    e Costa S. S., Fagundes H. V., 1998, gr-qc/9801066Google Scholar
  17. 17.
    Einstein, A., Postcard to Hermann Weyl, June 1918, from Einstein Archives, Princeton (freely translated from German by J.-P. Luminet).Google Scholar
  18. 18.
    Einstein, A., 1919, Postcard to Kelix Klein, April 16th, ibid.Google Scholar
  19. 19.
    Einstein, A., de Sitter W., 1932, Proc. Nat. Acad. Sci18213.ADSCrossRefGoogle Scholar
  20. 20.
    Ellis, G.F.R. 1971, Gen.Rel.Gray.27ADSzbMATHCrossRefGoogle Scholar
  21. 21.
    Ellis G.F.R., Schreiber, G., 1986, PhysLettA, 115, 97MathSciNetADSGoogle Scholar
  22. 22.
    Fagundes H. V., 1985, Ap.J., 291, 450MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Fagundes H. V., 1989, Ap.J., 338, 618ADSCrossRefGoogle Scholar
  24. 24.
    H.V. Fagundes, 1993, Phys. Rev. Lett.701579ADSCrossRefGoogle Scholar
  25. 25.
    Fagundes H. V., 1996, Ap.J., 470, 43ADSCrossRefGoogle Scholar
  26. 26.
    Fagundes H. V., Wichoski U. F., 1987, Ap.J., 322, L5ADSCrossRefGoogle Scholar
  27. 27.
    Fagundes, H.&Gausmann, E., 1997,On Closed Einstein-de Sitter Universes, astroph/9704259.Google Scholar
  28. 28.
    Fagundes, H. & Gausmann, E., 1999, astro-ph/9811368Google Scholar
  29. 29.
    Feodoroff, E., 1885, Russian journal for crystallography and mineralogy, St Petersburg21. Google Scholar
  30. 30.
    Ferreira, Pedro G., Magueijo, Joao, Gorski, Krzysztof M., 1998, Ap.J., 503, LIGoogle Scholar
  31. 31.
    Friedmann, A., 1922, Zeitschrift für Physik1037.CrossRefGoogle Scholar
  32. 32.
    Friedmann, A., 1923Mir kak prostranstvo ivremya (The Universe as Space and Time), Leningrad, Akademiya (French translation in Essais de Cosmologie, Le Seuil/Sources du Savoir, Paris, 1997.)Google Scholar
  33. 33.
    Friedmann A., 1924, Zeitschr.für Phys., 21, 326MathSciNetADSzbMATHCrossRefGoogle Scholar
  34. 34.
    Gabai, D., Meyerhoff, R., Thurston, N., 1996Homotopy Hyperbolic 3-manifoldsAre Hyperbolic, preprint available at http://www.msri.org Google Scholar
  35. 35.
    Gomero, G. I., Teixeira, A. F. F., Reboucas, M. J., Bernui, A., 1999, gr-qc/9811038Google Scholar
  36. 36.
    Gott J. R., 1980, MNRAS, 193, 153 1986, in Inner Space/OuterGoogle Scholar
  37. 37.
    Harrison, E., 1987Darkness at nightHarvard University Press.Google Scholar
  38. 38.
    Hawking S., 1984, NuclPhysB, 239, 257MathSciNetADSGoogle Scholar
  39. 39.
    Inoue, K.T., astro-ph/9810034.Google Scholar
  40. 40.
    Ionicioiu R., 1998, gr-qc/9711069Google Scholar
  41. 41.
    Jing Y.-P., Fang L.-Z., 1994, PhysRevLett, 73, 1882 (astro-ph/9409072)ADSGoogle Scholar
  42. 42.
    Klein, F., 1890, Mathematisches Annalen37544.zbMATHCrossRefGoogle Scholar
  43. 43.
    Killing, W., 1891, Mathematisches Annalen39257.MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Lachièze-Rey M., Luminet J.-P., 1995, PhysRep, 254, 136ADSGoogle Scholar
  45. 45.
    Lehoucq R., Luminet J.-P., Lachièze-Rey M., 1996, ALA, 313, 339Google Scholar
  46. 46.
    Lehoucq R., Luminet J.-P., Uzan J.-P., 1999, A&A, to be published (astroph/9811107)Google Scholar
  47. 47.
    Lemaître, G., 1927, Ann. Soc. Sci. Bruxelles, ser. A4729.Google Scholar
  48. 48.
    Lemaître, G., 1931, MNRAS90490.Google Scholar
  49. 49.
    Lemaître G., 1958, in LaStructure et l’Evolutiondel’Univers, Onzième Conseil de Physique Solvay, ed. Stoops R., (Brussels: Stoops), p.1Google Scholar
  50. 50.
    Lemaître, G., 1978 (posth.) inL’Univers problème accessible àla science humaine, Revue d’Histoire Scientifique,31 pp. 345–359.Google Scholar
  51. 51.
    Levin J., Scannapieco E., Silk J., 1998, Class.Quant.Gray., 15, 2689MathSciNetADSzbMATHCrossRefGoogle Scholar
  52. 52.
    Levin J., Scannapieco E., de Gasperis, G., Silk J., Barrow, J.D., 1998, astroph/9807206Google Scholar
  53. 53.
    Luminet, J.-P., 1997L’inventiondubig bang, suivi de A. Friedmann, G. Lemaître Essais de Cosmologie (Le Seuil/Sources du Savoir, Paris).Google Scholar
  54. 54.
    Luminet, J.-P., 1998, Acta Cosmologica24(gr-qc/9804006)Google Scholar
  55. 55.
    Luminet, J.-P. & Lachièze-Rey, M., 1994, La physique et l’infini (Flammarion/Dominos, Paris).Google Scholar
  56. 56.
    Madore J., Saeger L. A., 1998, Class.Quant.Gray., 15, 811 (gr-qc/9708053)MathSciNetADSzbMATHCrossRefGoogle Scholar
  57. 57.
    Matveev S.V., Fomenko A.T., 1988, Russian Math. Surveys433.MathSciNetADSzbMATHCrossRefGoogle Scholar
  58. 58.
    Novacki, W., 1934, Commentarii Mathematici Helvetici, 7, 81. rig. Pando, J., Valls-Gabaud, D., Fang, L.-7,h., 1998, PhysRevLett, accepted, (ast.ro1h/9810165) GO. Peebles, P.J.E., 1993, Principles of Physical Cosmology, Princeton, U.S.A.: Princeton Univ. Press (;1. Pierre, M., 1999, Proceedings of the workshopCosmological Topology in Paris 1998Obs. Paris/IAP, Paris 14 December 1998 (“http://www.iap.fr/users/roukema/CTP98/resumes.html”) G2. Rainer M., 1996, gr-gc/9602059.
  59. 63.
    Rosales J.-L., 1998, gr-gc/9712059Google Scholar
  60. 64.
    Roukema B. F., 1996, MNRAS, 283, 1147ADSGoogle Scholar
  61. 65.
    Roukema B. F., 1999, submittedGoogle Scholar
  62. 66.
    Roukema, B.F., et al., 1999, Proceedings of the workshopCosmological TopologyObs. Paris/IAP, Paris 14 December 1998 (http://www.iap.fr/users/roukema/CTP98/resumes.html ) Google Scholar
  63. 67.
    Roukema B. F., Bajtlik, S., 1999, submitted to MNRASGoogle Scholar
  64. 68.
    Roukema B. F., Blanloeil V., 1998, Class.Quant.Gray., 15, 2645 (astro-ph/9802083)MathSciNetADSzbMATHCrossRefGoogle Scholar
  65. 69.
    Roukema B. F., Edge A. C., 1997. MNRAS, 292, 105ADSGoogle Scholar
  66. 70.
    Roukema B. F., Luminet, I.-P., 1999, submittedGoogle Scholar
  67. 71.
    Schwarzschild, N. Vierteljahrschrift der Ast.. Ges. 35 67, 1900Google Scholar
  68. 72.
    Schwarzschild, K., 1998, Class.Quant.Gray., 15, 2539 [english translation of Schwarzschild (1900)]MathSciNetADSzbMATHCrossRefGoogle Scholar
  69. 73.
    Spaans, M., 1999, gr-gc/9901025Google Scholar
  70. 74.
    Starkman G. D., 1998, Class.Quant.Gray., 15, 2529ADSCrossRefGoogle Scholar
  71. 75.
    Starkman, G. et. al., 1998, Invited papers from the workshop Cosmology and topology (CWRU, Cleveland, 25–27 October 1997), Class. Quant. Gray. 15, 2529 7G. St.arobinskv A. A.. 1993, JETPLett., 57, 622Google Scholar
  72. 77.
    Stevens D.. Scott, Silk J., 1993, PhysRevLett, 71, 20ADSGoogle Scholar
  73. 78.
    Thurston, W. P.. 1979The geometryand topology of three manifolds, (Princeton Lecture Notes)Google Scholar
  74. 79.
    Thurston, W. P., 1997, Three-Dimensional Geometry and Topology, ed. Levy, S., Princeton, U.S.A.: Princeton University PressGoogle Scholar
  75. 80.
    J-P. Uzan, 1998, Phys. Rev. D58, 087301MathSciNetADSGoogle Scholar
  76. 81.
    Lass. Quant. Gray. 15, 2711 Uzan J.-P.. Lehoucq R., Luminet. J.-P., 1999, in preparationGoogle Scholar
  77. 83.
    Uzan, J.-P., Peter P., 1997, Phys.Lett. B 406, 20MathSciNetADSCrossRefGoogle Scholar
  78. 84.
    Weeks I., 1985, PhD thesis, Princeton University.Google Scholar
  79. 85.
    Weeks J. R., 1998, Class.Quant.Gray., 15, 2599 (astro-ph/9802012)MathSciNetADSzbMATHCrossRefGoogle Scholar
  80. 86.
    Wolf, J.A., 1960, C. R. Acad. Si. Paris,250, 3443.zbMATHGoogle Scholar
  81. 87.
    Zel’dovich Y. B., Grishchuk L. P., 1984, MNRAS, 207, 23PADSGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Jean-Pierre Luminet
    • 1
  • Boudewijn F. Roukema
    • 2
    • 3
  1. 1.DARC, Observatoire de Paris-MeudonMeudon CedexFrance
  2. 2.Institut d’Astrophysique de ParisParisFrance
  3. 3.Inter-University Centre for Astronomy and AstrophysicsPuneIndia

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