On the Average Density of Galaxies

The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a crossover to an homogeneous one at large scale. However up to now, the quantitative determination of this presumed homogeneity scale is still lacking. Contrary to such expectations, observational results show, in fact, a very inhomogeneous galaxy distribution. Some years ago we criticise the standard statistical approach and proposed a new one based on the concepts and methods of modern statistical analysis. The main result of new analysis is that, contrary to the conclusion of standard methods, the distribution of galaxies in the available samples, does not show any crossover to homogeneity, but has fractal correlations (with dimension $D \approx 2$) up to the limits of present three dimensional catalogs ($\approx 1000 h^{-1} Mpc$). The very first consequence of this result is that the standard approach is incorrect for all the length scale probed until now; moreover it calls for fascinating conceptual implication for the theoretical challenge in this field.