Zipf's law for cosmic structures: how large are the greatest structures
  in the universe?
  The statistical characterization of the distribution of visible matter in the
universe is a central problem in modern cosmology. In this respect, a crucial
question still lacking a definitive answer concerns how large are the greatest
structures in the universe. This point is closely related to whether or not
such a distribution can be approximated as being homogeneous on large enough
scales. Here we assess this problem by considering the size distribution of
superclusters of galaxies and by leveraging on the properties of
Zipf-Mandelbrot law, providing a novel approach which complements standard
analysis based on the correlation functions. We find that galaxy superclusters
are well described by a pure Zipf's law with no deviations and this implies
that all the catalogs currently available are not sufficiently large to spot a
truncation in the power-law behavior. This finding provides evidence that
structures larger than the greatest superclusters already observed are expected
to be found when deeper redshift surveys will be completed. As a consequence
the scale beyond which galaxy distribution crossovers toward homogeneity, if
any, should increase accordingly
