Characterizing the large scale inhomogeneity of the galaxy distribution
  In order to investigate whether galaxy structures are compatible with the
predictions of the standard LCDM cosmology, we focus here on the analysis of
several simple and basic statistical properties of the galaxy density field.
Namely, we test whether, on large enough scales (i.e., r>10 Mpc/h), this is
self-averaging, uniform and characterized by a Gaussian probability density
function of fluctuations. These are three different and clear predictions of
the LCDM cosmology which are fulfilled in mock galaxy catalogs generated from
cosmological N-body simulations representing this model. We consider some
simple statistical measurements able to tests these properties in a finite
sample. We discuss that the analysis of several samples of the Two Degree Field
Galaxy Redshift Survey and of the Sloan Digital Sky Survey show that galaxy
structures are non self-averaging and inhomogeneous on scales of ~100 Mpc/h,
and are thus intrinsically different from LCDM model predictions.
Correspondingly the probability density function of fluctuations shows a "fat
tail" and it is thus different from the Gaussian prediction. Finally we discuss
other recent observations which are odds with LCDM predictions and which are,
at least theoretically, compatible with the highly inhomogeneous nature of
galaxy distribution. We point out that inhomogeneous structures can be fully
compatible with statistical isotropy and homogeneity, and thus with a relaxed
version of the Cosmological Principle.
