Zipf’s law for cosmic structures: How large are the greatest structures in the universe?

¹ Centro Ricerche Enrico Fermi, Via Panisperna 89 A, 00184 Rome, Italy
e-mail: sylos@cref.it
² Sapienza School for Advanced Studies, “Sapienza”, P.le A. Moro, 2, 00185 Rome, Italy
³ Istituto dei Sistemi Complessi (ISC) – CNR, UoS Sapienza, P.le A. Moro, 2, 00185 Rome, Italy
⁴ Dipartimento di Fisica Università “Sapienza”, P.le A. Moro, 2, 00185 Rome, Italy

Received: 14 April 2021
Accepted: 12 May 2021

Abstract

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 the greatest structures in the universe are. 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 the properties of Zipf–Mandelbrot law, providing a novel approach which complements the 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.