The luminosity function of galaxies and clusters as well as their correlations can be calculated assuming that the many-body correlation functions are scale invariant. The same hypothesis leads to predictions on the fractal dimension of the galaxy distribution. The latter is found to be bifractal, characterized by two dimensions D = 3 - γ in the cluster region, and D = (3 - γ)(2+α) in the nearly empty regions, α being the index introduced by Schechter for the galaxy luminosity function. Finally, the same models lead to predictions for the evolution of the cluster and X-ray luminosity functions, as well as for the Sunyaev-Zeldovich effect due to all virialized clusters, which is found to be large and to produce fluctuations of order 10-5 at sub-arc minute scalar in the microwave background.
Large Scale Structures of the Universe
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