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 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.Comment: 9 pages, 6 figures. MNRAS published online. v2: minor typo corrected, added one missing referenc

Tracing the gravitational potential using cosmic voids

The properties of large underdensities in the distribution of galaxies in the Universe, known as cosmic voids, are potentially sensitive probes of fundamental physics. We use data from the MultiDark suite of N-body simulations and multiple halo occupation distribution mocks to study the relationship between galaxy voids, identified using a watershed void-finding algorithm, and the gravitational potential $\Phi$. We find that the majority of galaxy voids correspond to local density minima in larger-scale overdensities, and thus lie in potential wells. However, a subset of voids can be identified that closely trace maxima of the gravitational potential and thus stationary points of the velocity field. We identify a new void observable, $\lambda_v$, which depends on a combination of the void size and the average galaxy density contrast within the void, and show that it provides a good proxy indicator of the potential at the void location. A simple linear scaling of $\Phi$ as a function of $\lambda_v$ is found to hold, independent of the redshift and properties of the galaxies used as tracers of voids. We provide an accurate fitting formula to describe the spherically averaged potential profile $\Phi(r)$ about void centre locations. We discuss the importance of these results for the understanding of the evolution history of voids, and for their use in precision measurements of the integrated Sachs-Wolfe effect, gravitational lensing and peculiar velocity distortions in redshift space.Comment: 14 pages, 9 figures. Minor changes to match version accepted for publication in MNRA