The large scale distribution of galaxies in the universe displays a complex
pattern of clusters, super-clusters, filaments and voids with sizes limited
only by the boundaries of the available samples. A quantitative statistical
characterization of these structures shows that galaxy distribution is
inhomogeneous in these samples, being characterized by large-amplitude
fluctuations of large spatial extension. Over a large range of scales, both the
average conditional density and its variance show a nontrivial scaling
behavior: at small scales, r<20 Mpc/h, the average (conditional) density scales
as 1/r. At larger scales, the density depends only weakly (logarithmically) on
the system size and density fluctuations follow the Gumbel distribution of
extreme value statistics. These complex behaviors are different from what is
expected in a homogeneous distribution with Gaussian fluctuations. The observed
density inhomogeneities pose a fundamental challenge to the standard picture of
cosmology but it also represent an important opportunity which points to new
directions with respect to many cosmological puzzles. Indeed, the fact that
matter distribution is not uniform, in the limited range of scales sampled by
observations, rises the question of understanding how inhomogeneities affect
the large-scale dynamics of the universe. We discuss several attempts which try
to model inhomogeneities in cosmology, considering their effects with respect
to the role and abundance of dark energy and dark matter.Comment: 30 pages, 10 figure
