The fractal structure of the universe

We re-evaluate the experimental data concerning the large scale structure of the universe utilizing the theoretical methods of modern statistical mechanics. This allows us to test the implicit assumptions of analyticity and homogeneity present in the usual analysis. The results are quite surprising: the previous methods of analysis are mathematically inconsistent for all the cases that can be explicitly tested. In view of the untested homogeneity assumption, these methods give rise to a finite correlation length even in systems that do not possess one (i.e. those with long range power law correlations). In particular, we demonstrate that the famous galaxy correlation length r0≈5h−1 Mpc is a spurious result due to these inconsistencies. In fact it is related to the cut-off due to the finiteness of the sample and not to the correlation properties of galaxies. We can therefore predict that the value of r0 will increase with sample depth when deeper complete catalogs are available. The reanalysis of galaxy and cluster catalogs without any assumption shows long range (fractal) correlations up to the sample limits. This explains the previous contradiction between the correlation analysis and the observation of large scale structures like voids and superclusters. The correlation length, in fact, cannot be much smaller than the size of the largest structures one can observe. We also consider the angular projection of systems with long range correlations and explain why the angular distributions appear to be more homogeneous than the three dimensional ones. These studies are then generalized by an analysis of the whole distribution of visible matter (by including an estimate of the galaxy masses) which shows well defined multifractal properties. This allows one to clarify various other problems such as the so-called "luminosity segregation" phenomenon and the "richness-clustering" relation. In addition the multifractal behavior implies that the upper cut-off of the luminosity function scales with the size of the sample with a characteristic exponent which we determine. This fact has direct implications for galaxy number counts and for several other problems. One may even conjecture in this respect, that quasars may actually represent the continuation of this scaling behavior to much larger scales. In summary a new picture appears which is fundamentally different from the usual one but actually much simpler: the distribution of visible matter in the universe appears to be fractal and multifractal up to the present observational limits (200 Mpc; about one twentieth of the Hubble radius of the entire universe) without any evidence for homogenization. This implies that the nature of the distribution is strongly non-analytic and no simple average density can be defined. These results have profound consequences for our knowledge of the properties of the universe as well as for the theoretical framework that one should use to describe it.