Cosmological distances and fractal statistics of galaxy distribution

This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various distance definitions are used to calculate the differential density γ and the integral differential density of the dust distribution in the Einstein-de Sitter cosmology. The main results are as follows: (1) the choice of distance plays a crucial role in determining the scale where relativistic corrections must be taken into account, as both γ and are strongly affected by such a choice; (2) inappropriate distance choices may lead to failure to find evidence of a galaxy fractal structure when one calculates those quantities, even if such a structure does occur in the galaxy distribution; (3) the comoving distance and the distance given by Mattig's formula are unsuitable to probe for a possible fractal pattern as they render γ and constant for all redshifts; (4) a possible galaxy fractal system at scales larger than 100 Mpc () may only be found if those statistics are calculated with the luminosity or redshift distances, as they are the ones where γ and decrease at higher redshifts; (5) Célérier & Thieberger's (CITE) critique of Ribeiro's (CITE) earlier study are rendered impaired as their objections were based on misconceptions regarding relativistic distance definitions.