Seeing patterns in noise: Gigaparsec-scale `structures' that do not violate homogeneity (1306.1700v2)

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.

• The paper evaluates claims of gigaparsec-scale structures like the Huge-LQG, demonstrating they do not necessarily violate the principle of cosmic homogeneity on large scales.
• Statistical analysis, including fractal dimension, shows the quasar distribution is homogeneous above ~130 h^-1 Mpc, and the clustering algorithm used to find the Huge-LQG routinely finds similar structures in simulated homogeneous data.
• The analysis emphasizes that assessing cosmic homogeneity relies on statistical averages, not isolated structures, and highlights the critical need for null tests to distinguish real structures from statistical artifacts.

Evaluating Gigaparsec-Scale Structures and Cosmological Homogeneity

The paper by Seshadri Nadathur critically evaluates the claim of discovering a large quasar group (LQG), termed the Huge-LQG, within the Sloan Digital Sky Survey (SDSS) Data Release 7 quasar catalogue. The Huge-LQG's reported extent, with a characteristic size of approximately 500 Mpc and a length exceeding 1 Gpc, raised questions about its compatibility with the principle of cosmic homogeneity and thus challenged the standard cosmological model, specifically the $\Lambda$ Cold Dark Matter ($\Lambda$CDM) paradigm. Nadathur's analysis aims to reconcile this claim with the notion of statistical homogeneity expected on cosmic scales.

Nadathur addresses the point that the assessment of cosmic homogeneity should not rely on isolated large structures, as they do not negate the average homogeneous nature of the Universe on large scales. A crucial element of the paper is a fractal dimension analysis, which applies standard statistical methods to examine the DR7 quasar catalogue. The results demonstrate that the quasar distribution remains homogeneous above scales of around 130 $h^{-1}$ Mpc, which is well within the theoretical limits for a $\Lambda$CDM Universe.

A significant part of the investigation inspects the clustering algorithm employed to identify the Huge-LQG. It was found that this algorithm, when applied to simulated homogeneously-distributed point samples mimicking the quasar catalogue, can routinely discover even larger assemblies than the Huge-LQG. These findings suggest the algorithm's results are statistical anomalies or artifacts rather than genuine astronomical structures. Nadathur emphasizes that the null test—comparing catalogue data against homogeneously distributed point processes—serves as a critical control step to quantify the probability of such clusters occurring by chance.

The paper asserts that the existence of individual structures like LQGs should not be confused with violations of cosmic homogeneity. Such structures, even if extensive, do not imply the breakdown of large-scale homogeneity because the homogeneity metric refers to statistical averages rather than individual instances. This distinction is important for interpreting cosmological datasets correctly.

Practically, this analysis illustrates the robustness of the standard cosmological model against assertions based on singular extreme objects. Theoretically, it affirms the distinction between structural identification and statistical homogeneity, advocating for comprehensive methodologies that rule out clustering artifacts.

The exploration underscores future research avenues, including refining structure-finding algorithms to better discern between actual cosmological features and statistical artifacts. Additionally, it prompts further investigations into the scale-dependent definition of homogeneity and the characterization of cosmic structures within a probabilistic framework. Nadathur's work stands as a crucial reminder of the importance of null tests and statistical rigor in cosmological research, offering insights into both methodological consistency and the interpretation of cosmic-scale data.