Relativistic corrections to fractal analyses of the galaxy distribution

Abstract

The effect of curvature on the results of fractal analyses of the galaxy distribution is investigated. We show that, if the universe satisfies the criteria of a wide class of parabolic homogeneous models, the observers measuring the fractal index with the integrated conditional density procedure may use the Hubble formula, without having to allow for curvature, out to distances of 600 Mpc, and possibly far beyond. This contradicts a previous claim by Ribeiro (1995) that, in the Einstein-de Sitter case, relativistic corrections should be taken into account at much smaller scales. We state for the class of cosmological models under study, and give grounds for conjecture for others, that the averaging procedure has a smoothing effect and that, therefore, the redshift-distance relation provides an upper limit to the relativistic corrections involved in such analyses.