Inhomogeneities in the universe
  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.
