Cosmological distances and fractal statistics of galaxy distribution

• Published in: Astronomy and astrophysics (Berlin) 2005-01, Vol.429 (1), p.65-74
• Main Author: Ribeiro, M. B.
• Format: Article
• Language: English
• Subjects: cosmology: large-scale structure of the Universe; cosmology: observation; cosmology: theory; galaxies: distances and redshifts; galaxies: statistics
• ISSN: 0004-6361; 1432-0746
• DOI: 10.1051/0004-6361:20041469

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 $\gamma^\ast$ 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 $\gamma^\ast$ 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 $\gamma^\ast$ constant for all redshifts; (4) a possible galaxy fractal system at scales larger than 100 Mpc ($z \approx 0.03$) may only be found if those statistics are calculated with the luminosity or redshift distances, as they are the ones where γ and $\gamma^\ast$ 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.