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The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies
This paper presents an analysis of the smoothness problem in cosmology by
focussing on the ambiguities originated in the simplifying hypotheses aimed at
observationally verifying if the large-scale distribution of galaxies is
homogeneous, and conjecturing that this distribution should follow a fractal
pattern in perturbed standard cosmologies. This is due to a geometrical effect,
appearing when certain types of average densities are calculated along the past
light cone. The paper starts reviewing the argument concerning the possibility
that the galaxy distribution follows such a scaling pattern, and the premises
behind the assumption that the spatial homogeneity of standard cosmology can be
observable. Next, it is argued that to discuss observable homogeneity one needs
to make a clear distinction between local and average relativistic densities,
and showing how the different distance definitions strongly affect them,
leading the various average densities to display asymptotically opposite
behaviours. Then the paper revisits Ribeiro's (1995: astro-ph/9910145) results,
showing that in a fully relativistic treatment some observational average
densities of the flat Friedmann model are not well defined at z ~ 0.1, implying
that at this range average densities behave in a fundamentally different manner
as compared to the linearity of the Hubble law, well valid for z < 1. This
conclusion brings into question the widespread assumption that relativistic
corrections can always be neglected at low z. It is also shown how some key
features of fractal cosmologies can be found in the Friedmann models. In view
of those findings, it is suggested that the so-called contradiction between the
cosmological principle, and the galaxy distribution forming an unlimited
fractal structure, may not exist.Comment: 30 pages, 2 figures, LaTeX. This paper is a follow-up to
gr-qc/9909093. Accepted for publication in "General Relativity and
Gravitation
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