Classical and Quantum Chaos in Robertson-Walker Cosmologies

  • Roman Tomaschitz
Part of the NATO ASI Series book series (NSSB, volume 332)


An elementary review of my work on the physical impact of the topological structure of space-time is given. An account on classical chaos in an open, multiply connected universe is presented. The uniformity of the galactic background is related to the erratic behavior of the classical world lines around the chaotic nucleus of the universe. On the quantum level we discuss particle creation, backscattering, anisotropy in the microwave background, parity violation and how all this relates to the multiple connectivity of the open spacelike slices.


Expansion Factor Covering Space Covering Group Solid Torus Deformation 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Infeld, L. and Schild, A., (1945), Phys. Rev., 68, 250.MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    Schrödinger, E., (1956), Expanding Universe, Camb. Univ. Press, Cambridge.Google Scholar
  3. [3]
    Jordan, P., (1955), Schwerkraft und Weltall, 2nd ed., p. 113, Vieweg, Braunschweig.zbMATHGoogle Scholar
  4. [4]
    Tomaschitz, R., (1991), J. Math. Phys., 32, 2571.MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. [5]
    Tomaschitz, R., (1992), Complex Systems, 6, 137.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Tomaschitz, R., (1993), in Proceedings of the XIX International Colloquium on Group Theoretical Methods in Physics, (J. Mateos, ed.), CIEMAT, Madrid.Google Scholar
  7. [7]
    Tomaschitz, R., (1993), J. Math. Phys., 34, 1022.MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. [8]
    Tomaschitz, R., (1993), J. Math. Phys., 34, 3133.MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. [9]
    Tomaschitz, R., (1993), “Cosmological CP violation”, preprint.Google Scholar
  10. [10]
    Wheeler, J. A., (1973), in The Physicist’s Conception of Nature, (J. Mehra, ed.), D. Reidel, Dordrecht.Google Scholar
  11. [11]
    Poincaré, H., (1985), Papers on Fuchsian Functions (J. Stillwell, ed.), Springer, New York.CrossRefGoogle Scholar
  12. [12]
    Fenchel, W., (1989), Elementary Geometry in Hyperbolic Space, de Gruyter, Berlin.zbMATHCrossRefGoogle Scholar
  13. [13]
    Marden, A., (1980), Bull. Am. Math. Soc. (New Series) 3, 1001.MathSciNetzbMATHCrossRefGoogle Scholar
  14. [14]
    Maskit, B., (1986), Kleinian Groups, Springer, Berlin.Google Scholar
  15. [15]
    Tomaschitz, R., (1992), in Chaotic Dynamics: Theory and Practice, (T. Bountis, ed.), Plenum, New York.Google Scholar
  16. [16]
    Tomaschitz, R., (1994), to appear in Intern. J. Theoret. Phys. Google Scholar
  17. [17]
    Tomaschitz, R., (1994), in Fractals in the Natural and Applied Sciences, (M. Novak, ed.), to appear (Elsevier, Amsterdam).Google Scholar
  18. [18]
    Akaza, T., (1964), Nagoya Math. J., 24, 43.MathSciNetzbMATHGoogle Scholar
  19. [19]
    Tomaschitz, R., (1992), in Quantum Chaos-Quantum Measurement, (P. Cvitanovic, ed.), Kluwer, Dordrecht.Google Scholar
  20. [20]
    Dyson, F. J., (1979), Rev. Mod. Phys., 51, 447.ADSCrossRefGoogle Scholar
  21. [21]
    Misner, C. W., Thorne, K. S. and Wheeler, J. A., (1973), Gravitation, Freeman, San Francisco.Google Scholar
  22. [22]
    Schrödinger, E., (1939), Physica, 6, 899.MathSciNetADSCrossRefGoogle Scholar
  23. [23]
    Birrell, N. D. and Davies, D. C. W., (1982), Quantum Fields in Curved Space, Camb. Univ. Press, Cambridge, UK.zbMATHCrossRefGoogle Scholar
  24. [24]
    Parker, L., (1972), Phys. Rev., D5, 2905.ADSGoogle Scholar
  25. [25]
    Sachs R. K. and Wolfe, A. M., (1967), Astrophys. J., 147, 73.ADSCrossRefGoogle Scholar
  26. [26]
    Israel, W., (1972), in General Relativity, (L. O’Raifeartaigh, ed.), Clarendon Press, Oxford.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Roman Tomaschitz
    • 1
  1. 1.Physics DepartmentUniversity of the WitwatersrandJohannesburg, WITSSouth Africa

Personalised recommendations