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Current Trends in Mathematical Cosmology

  • Spiros Cotsakis
Part of the Astrophysics and Space Science Library book series (ASSL, volume 276)

Abstract

We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of a cosmology and focus on the issue of singularities as a theme unifying many current, seemingly unrelated trends of this subject. We discuss problems associated with the definition and asymptotic structure of the notion of cosmological solution and also problems related to the qualification of approximations and to the ranges of validity of given cosmologies.

Keywords

mathematical cosmology theories of gravity(relativistic) spacetime structure matter fields 

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References

  1. [1]
    Hawking, S.W., and G.ER. Ellis, The large-scale structure of space-time, (CUP, 1973).Google Scholar
  2. [2]
    Wheeler, J.A. Superspace and the nature of quantum geometrodynamics, in C.M. DeWitt and I.A. Wheeler (eds.), (Benjamin, 1968); see also, C.W. Misner, Minisuperspace, in J. Klauder (ed.), Magic without magic, (Freeman, 1972).Google Scholar
  3. [3]
    Ellis, G.F.R., and H. van Elst, Cosmological Models, Cargèse lectures 1998, gr-qc/9812046.Google Scholar
  4. [4]
    Cotsakis, S., Introduction to Mathematical Cosmology, (in preparation, 2001).Google Scholar
  5. [5]
    Barrow, J.D., and F.J. Tipler, The Anthopic Cosmological Principle, (OUP, 1986).Google Scholar
  6. [6]
    Belinski, V.A., E.M. Lifshitzand I.M. Khalatnikov, Sov. Phys. Usp. 13, 745 (1971).ADSCrossRefGoogle Scholar
  7. [7]
    Belinski, V.A., I.M. Khalatnikov and E.M. Lifshitz, Adv. Phys. 13, 639 (1982).ADSCrossRefGoogle Scholar
  8. [8]
    Barrow, J.D. Phys. Rep. 85, 97 (1982).MathSciNetCrossRefGoogle Scholar
  9. [9]
    Misner, C.W., in D. Hobill et al. (Eds.), Deterministic chaos in general relativity, (Plenum, 1994) pp. 317–328.Google Scholar
  10. [10]
    Barrow, J.D., and A. Ottewill, J. Phys. A. 16 2757 (1983).MathSciNetADSCrossRefGoogle Scholar
  11. [11]
    Barrow, J.D., and D.H. Sonoda, Phys. Rep. 139, 1 (1986).MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    Cotsakis, S., and G.P. Flessas, Phys. Rev. D48, 3577 (1993).ADSGoogle Scholar
  13. [13]
    Wainwright, I., and G.F.R. Ellis, Dynamical systems in cosmology, (CUP, 1997).Google Scholar
  14. [14]
    Hale, J., and H. Koçak, Dynamics and bifurcations, (Springer-Verlag, 1991).Google Scholar
  15. [15]
    Belinski, V.A., and I.M. Khalatnikov, Sov. Phys. JETP. 36, 591 (1972).ADSGoogle Scholar
  16. [16]
    Berger, B.K. Phys. Rev. D61, 023508 (2000).MathSciNetADSGoogle Scholar
  17. [17]
    Bogoyavlenski, O.I., and S.P. Novikov, JETP. 64, 1475 (1973).Google Scholar
  18. [18]
    Bogoyavlenski, O.I. Dynamical systems in Astrophysics, (Springer-Verlag, 1986).Google Scholar
  19. [19]
    Barrow, J.D., and S. Cotsakis, Phys. Lett. B258, 299 (1991).Google Scholar
  20. [20]
    Demaret, J., M. Henneaux, and P. Spindel, Phys. Lett. B164, 27 (1986); see also, A. Hosoya, L.G. Jensen,and J.A. Stein-Shabes, Nucl. Phys. B283, 657 (1987).MathSciNetGoogle Scholar
  21. [21]
    Barrow, J.D., and M.P. Dabrowski, String cosmology and chaos, gr-qc/9806023.Google Scholar
  22. [22]
    Damour, T., and M. Henneaux, Phys. Rev. Lett. 85, 920 (2000); see also, T. Damourand M. Henneaux, Phys.Lett. B488, 108 (2000).MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. [23]
    Barrow, J.D., and S. Cotsakis, Phys. Lett. B214, 515 (1988).MathSciNetGoogle Scholar
  24. [24]
    Faraoni, V., E. Gunzig and P. Nardone, Fund. Cosm. Phys. 20, 121 (1999).ADSGoogle Scholar
  25. [25]
    Berger, B.K., et al., Mod. Phys. Lett. A13, 1565 (1998); see also,B. K. Berger, Approach to the Singularity in Spatially Inhomogeneous Cosmologies, gr-qc/Ol06009.ADSCrossRefGoogle Scholar
  26. [26]
    Ellis, G.F.R., et al, Phys. Rep. 124, 316 (1985).ADSCrossRefGoogle Scholar
  27. [27]
    Ellis, G.F.R., and W. Stoeger, Class. Quant. Grav. 4, 1697 (1987).MathSciNetADSzbMATHCrossRefGoogle Scholar
  28. [28]
    Christodoulou, D. Class. Quant. Grav. 16, A23 (1999).MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Spiros Cotsakis
    • 1
  1. 1.GEODYSYC, Department of MathematicsUniversity of the AegeanKarlovassiGreece

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