Classification of Bianchi cosmologies in conformal flat space-times

  • Gerald E. Tauber
Article

Abstract

There exist nine types of Bianchi cosmologies classified according to the structure constants of the corresponding Lie groups. Each of these types gives rise to a particular form of the line element, the Friedmann universe corresponding to the simplest type I. It is also known that there exists a simple correspondence (transformation) between the Robertson-Walker line element and the conformal line element but restricting the arbitrary function of that line element. This suggests that a classification of conformai flat line elements according to their parameters should yield a classification similar to that of Bianchi. The conformal group has 15 parameters, corresponding to the pure conformal group, Lorentz group, translation, and dilation. A classification of the line element according to these has been carried out, singly and combining several of them. It has been found that the Friedmann universe is a subclass, as expected, with other cosmologies resulting as wider subclasses. Comparison with the Bianchi classification is also made.

Keywords

Field Theory Elementary Particle Quantum Field Theory Arbitrary Function Line Element 

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References

  1. Bianchi, L. (1897).Sugli Spazi a tre dimensioni che ammettono un gruppo continuo di movimenti. Accademia dei Lincei.Google Scholar
  2. Eisenhart, L. P. (1935).Continuous Groups of Transformations. Princeton University Press, Princeton, New Jersey.Google Scholar
  3. Eisenhart, L. P. (1964).Riemannian Geometry. Princeton University Press, Princeton, New Jersey.Google Scholar
  4. Infeld, L. and Schild, A. (1945).Physical Review,68, 250.Google Scholar
  5. Taub, A. (1951).Annals of Mathematics,53, 472.Google Scholar
  6. Tauber, G. E. (1967).Journal of Mathematical Physics,8, 118.Google Scholar
  7. Wess, J. (1960).Nuovo Cimento,18, 1086.Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • Gerald E. Tauber
    • 1
  1. 1.Tel Aviv UniversityTel AvivIsrael

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