Classification of Bianchi cosmologies in conformal flat space-times

  • Gerald E. Tauber


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.


Field Theory Elementary Particle Quantum Field Theory Arbitrary Function Line Element 


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Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

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

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