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 inmodern cosmology. In this respect, a crucial question still lacking a definitive answer concerns how large are the greateststructures in the universe. This point is closely related to whether or not such a distribution can be approximated as beinghomogeneous on large enough scales. Here we assess this problem by considering the size distribution of superclustersof galaxies and by leveraging on the properties of Zipf-Mandelbrot law, providing a novel approach which complementsstandard analysis based on the correlation functions. We find that galaxy superclusters are well described by a pureZipf’s law with no deviations and this implies that all the catalogs currently available are not sufficiently large to spot atruncation in the power-law behavior. This finding provides evidence that structures larger than the greatest superclustersalready observed are expected to be found when deeper redshift surveys will be completed. As a consequence the scalebeyond which galaxy distribution crossovers toward homogeneity, if any, should increase accordingly

Link to the paper

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