Scaling Regimes as obtained from the DR5 Sloan Digital Sky Survey

Standard cosmology is based on the assumption that the universe is spatially homogeneous. However the consensus on a homogeneous matter structure, even on very large scales, has never been complete. The advantage of correlation dimension calculations is that they enable one to obtain the transition scale to a homogeneous distribution, whereas other methods, such as those using the two-point correlation function, make it hard to exhibit the possible fractal properties of the Universe matter content. Our purpose is to calculate the correlation dimension $D_2$, looking for a possible transition to homogeneity, which would imply $D_2 = 3$. We apply the correlation integral method to the three dimensional sample composed of 332,876 galaxies which we extract from the Fifth Data Release of the Sloan Digital Sky Survey. We analyze the raw data up to the scale $d_{max} = 160$ Mpc, assuming $H_0 = 70$ km s$^{-1}$ Mpc$^{-1}$ and considering three cosmological models in order to test the model dependence of our method. Using volume limited samples for this range leaves us with about 20,000 galaxies. Applying our method to random maps helps us to calibrate our results. We obtain a correlation dimension of the galaxy distribution which seems to increase with scales up to $D_2=3$ reached around 70 Mpc. The results of our analysis, performed on the largest volume limited sample which can be extracted from the SDSS catalog, are compatible with those formerly obtained by other authors. However, to get a more reliable description of the structures at various scales, we think it will be mandatory to use still larger catalogs than those which are currently available.