The Apparent Fractal Conjecture

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 remaining valid. The theoretical results which suggest this conjecture are discussed, as well as possible ways of checking its validity. PACS numbers: 98.80.-k 98.65.Dx 98.80.Es 05.45.Df 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-Lemâıtre-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 (Peebles 1993; Davis 1997; Wu, Lahav and Rees 1999; Mart́ınez 1999). Communication presented as part of the talk delivered at the “South Africa Relativistic Cosmology Conference in Honour of George F. R. Ellis 60th Birthday”, University of Cape Town, February 1-5, 1999.