Zipf's law for cosmic structures: how large are the greatest structures in the universe?

TL;DR

This paper uses Zipf's law to analyze the size distribution of galaxy superclusters, suggesting that larger structures exist beyond current observations and informing the scale of cosmic homogeneity.

Contribution

It introduces a novel Zipf's law-based method to characterize cosmic structures, providing new insights into the size distribution of superclusters and the universe's large-scale structure.

Findings

Galaxy superclusters follow a pure Zipf's law with no deviations.

Current catalogs are too small to detect a truncation in the power-law behavior.

Larger structures are expected to be discovered in future surveys.

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 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