Seeing patterns in noise: gigaparsec-scale ‘structures’ that do not violate homogeneity

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 Data Release 7 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 130h−1 Mpc, which is much less than the upper limit for ΛCDM. 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.