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.
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Tauber, G.E. Classification of Bianchi cosmologies in conformal flat space-times. Int J Theor Phys 18, 371–396 (1979). https://doi.org/10.1007/BF00670432
- Field Theory
- Elementary Particle
- Quantum Field Theory
- Arbitrary Function
- Line Element