The Apparent Fractal Conjecture

Abstract

This short communication advances the hypothesis that the observed fractal structure of large-scale distribution of galaxies is due to a geometrical effect, which arises when observational quantities relevant for the characterization of a cosmological fractal structure are calculated along the past light cone. If this hypothesis proves, even partially, correct, most, if not all, objections raised against fractals in cosmology may be solved. For instance, under this view the standard cosmology has zero average density, as predicted by an infinite fractal structure, with, at the same time, the cosmological principle remain- The issue of whether or not the large-scale distribution of matter in the Universe actually follows a fractal pattern has divided cosmologists in the last decade or so, with the debates around this thorny question leading to a split of opinions between two main, and opposing, groups.On one side, the orthodox view sustains that since a fractal structure is inhomogeneous, it cannot agree with what we know about the structure and evolution of the Universe, as this knowledge is based on the cosmological principle and the Friedmann-Lemaître-RobertsonWalker (FLRW) spacetime, with both predicting homogeneity for the universal distribution of matter. Moreover, inasmuch as the cosmic microwave background radiation (CMBR) is isotropic, a result predicted by the FLRW cosmology, this group is, understandably, not prepared to give up the standard FLRW universe model and the cosmological principle, as that would mean giving up most, if not all, of what we learned about the structure and evolution of the Universe since the dawn of cosmology

Spatial and observational homogeneities of the galaxy distribution in standard cosmologies

“…This alternative conceptual framework grew out of various works (Ribeiro 1992a(Ribeiro ,b, 1993(Ribeiro , 1994(Ribeiro , 1995(Ribeiro , 2001aAbdalla et al 2001) and was comprehensively analyzed in Ribeiro (2001b;hereafter R01b). Albani et al (2007; hereafter A07) further developed this alternative perspective in a somewhat condensed version.…”

Galaxy distributions as fractal systems

“…Early hierarchical cosmology models were proposed within the framework of Newtonian cosmology [31,74,75], as well as in more recent fractal cosmology ones [1,2]. Later on relativistic fractal cosmologies considering a fractal system embedded in a 4-dimensional spacetime along the observer's past light cone were proposed [3,56,58,[61][62][63]. Other authors have also discussed relativistic cosmological models with theoretical fractal features [7,14,36,42,[49][50][51]65,71,76] or by assuming single fractal or multifractal patterns in observational scenarios using Newtonian or relativistic models [24][25][26][27]43,47,52,54,69,70].…”