Class. Quantum Grav. 28 (2011) 164003.
Standard models of galaxy formation predict that matter distribution is statistically homogeneous and isotropic and characterized by (i) spatial homogeneity for r<10 Mpc/h, (ii) small-amplitude structures of relatively limited size (i.e., r<100) Mpc/h and (iii) anti-correlations for r > r_c ~ 150 Mpc/h (i.e., no structures of size larger than r_c). Whether or not the observed galaxy distribution is interpreted to be compatible with these predictions depend on the a-priori assumptions encoded in the statistical methods employed to characterize the data and on the a-posteriori hypotheses made to interpret the results. We present strategies to test the most common assumptions and we find evidences that, in the available samples, galaxy distribution is spatially inhomogeneous for r<100 Mpc/h but statistically homogeneous and isotropic. We conclude that the observed inhomogeneities pose a fundamental challenge to the standard picture of cosmology but they also represent an important opportunity which may open new directions for many cosmological puzzles.