Seeing patterns in noise: Gigaparsec-scale `structures' that do not violate homogeneity

TL;DR

This paper argues that large quasar groups do not violate cosmic homogeneity, demonstrating that apparent Gpc-scale structures can arise in random distributions and clarifying the true scale of homogeneity in the universe.

Contribution

It provides the first fractal dimension analysis of the quasar catalogue and shows that large structures are consistent with homogeneity, challenging claims of violations of the cosmological principle.

Findings

Quasar catalogue is homogeneous above 130 Mpc/h.

Large Gpc-scale clusters can appear in random homogeneous simulations.

The method used to identify large structures can find larger clusters in random data.

Abstract

Clowes et al. (2013) have recently reported the discovery of a Large Quasar Group (LQG), dubbed the Huge-LQG, at redshift z~1.3 in the DR7 quasar catalogue of the Sloan Digital Sky Survey. On the basis of its characteristic size ~500 Mpc and longest dimension >1 Gpc, it is claimed that this structure is incompatible with large-scale homogeneity and the cosmological principle. If true, this would represent a serious challenge to the standard cosmological model. However, the homogeneity scale is an average property which is not necessarily affected by the discovery of a single large structure. I clarify this point and provide the first fractal dimension analysis of the DR7 quasar catalogue to demonstrate that it is in fact homogeneous above scales of at most 130 Mpc/h, which is much less than the upper limit for \Lambda CDM. In addition, I show that the algorithm used to identify the Huge-LQG regularly finds even larger clusters of points, extending over Gpc scales, in explicitly homogeneous simulations of a Poisson point process with the same density as the quasar catalogue. This provides a simple null test to be applied to any cluster thus found in a real catalogue, and suggests that the interpretation of LQGs as `structures' is misleading.