  Super-homogeneity is a property that is supposed to be satisfied by matter
fluctuations in all standard theoretical models of structure formation, such as
LCDM and its variants. This is a global condition on the correlation properties
of the matter density field, which can be understood as a consistency
constraint in the framework of FRW cosmology, and it corresponds to a very fine
tuned balance between negative and positive correlations of density
fluctuations and to the fastest possible decay of the normalized mass variance
on large scales. By considering several galaxy samples, we discuss that these
are characterized by the presence of large amplitude fluctuations with spatial
extension limited only the size of the current samples. There is therefore a
tension between the standard prediction of super-homogeneity and the detection
of large scale inhomogeneities in the matter distribution at scales of the
order of 100 Mpc/h. We discuss the theoretical implications of these results
with respect to models of structure formation and to future galaxy and CMBR
data, emphasizing the central role of the super-homogeneity property in the
current description of fluctuations in FRW models.
