Re-Examining the Evidence of the Hercules-Corona-Borealis Great Wall

TL;DR

This paper critically re-examines the evidence for the Hercules-Corona-Borealis Great Wall, showing that previous statistical claims of its existence are likely overestimated and that the anisotropies can be explained by isotropic models and sky-exposure effects.

Contribution

It demonstrates that the statistical significance of the HCB's anisotropy is overestimated and that the evidence for its existence is doubtful when considering updated data and simulations.

Findings

Monte-Carlo simulations can reproduce observed anisotropies under isotropy.

Updated samples increase the probability of isotropic origin for the anisotropies.

Previous significance levels are overestimated due to statistical considerations.

Abstract

In the {\Lambda}-CDM paradigm of cosmology, anisotropies larger than 260 Mpc shouldn't exist. However, the existence of the Hercules-Corona Borealis Great Wall (HCB) is purported to challenge this principle by some with an estimated size exceeding 2000 Mpc. Recently, some have challenged the assertion of the existence of the HCB, attributing the anisotropy to sky exposure effects. It has never been explained why the original methods purporting the existence of the HCB produce anisotropies, even if sky-exposure effects are taken into account. In this paper, I apply the methods of the original papers purporting the existence of the HCB in various Monte-Carlo simulations that assume isotropy to analyze the empirical meaning of the significance levels of the original tests used. I find that, although the statistical tests at first glance show significant anisotropies present in the suspect sample, Monte-Carlo simulations can easily reproduce the sample in most cases, and if not, the differences can be accounted for by other statistical considerations. An updated sample raises the probability of drawing the observed clustering from an isotropic sample ten-fold in some cases. Thus the statistical tests used in prior studies overestimate the significance of the observed anisotropy, and an updated sample returns even less significant probabilities. Given the ability to reproduce the observed anisotropy in Monte-Carlo simulations, the new, higher probabilities of being drawn from isotropy for an updated sample, and the work of previous papers attributing anisotropies to sky-selection effects, the existence of the HCB must be treated as doubtful at best.