[Paper Review] Testing the Cosmological Principle with CatWISE Quasars: A Bayesian Analysis of the Number-Count Dipole

Lawrence Dam, Geraint F. Lewis+1 more|arXiv (Cornell University)|Dec 15, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This Bayesian analysis of 1.36 million CatWISE quasars confirms a dipole in their number counts with direction consistent with the CMB dipole, but finds an amplitude 2.7 times larger than expected from kinematic motion, yielding a 5.7σ discrepancy with ΛCDM predictions. The study attributes part of the tension to Galactic plane masking, which leaks power into higher multipoles and suppresses the expected dipole amplitude.

ABSTRACT

The Cosmological Principle, that the Universe is homogeneous and isotropic on sufficiently large scales, underpins the standard model of cosmology. However, a recent analysis of 1.36 million infrared-selected quasars has identified a significant tension in the amplitude of the number-count dipole compared to that derived from the CMB, thus challenging the Cosmological Principle. Here we present a Bayesian analysis of the same quasar sample, testing various hypotheses using the Bayesian evidence. We find unambiguous evidence for the presence of a dipole in the distribution of quasars with a direction that is consistent with the dipole identified in the CMB. However, the amplitude of the dipole is found to be 2.7 times larger than that expected from the conventional kinematic explanation of the CMB dipole, with a statistical significance of $5.7σ$. To compare these results with theoretical expectations, we sharpen the $Λ$CDM predictions for the probability distribution of the amplitude, taking into account a number of observational and theoretical systematics. In particular, we show that the presence of the Galactic plane mask causes a considerable loss of dipole signal due to a leakage of power into higher multipoles, exacerbating the discrepancy in the amplitude. By contrast, we show using probabilistic arguments that the source evolution of quasars improves the discrepancy, but only mildly so. These results support the original findings of an anomalously large quasar dipole, independent of the statistical methodology used.

Motivation & Objective

• To test the Cosmological Principle using number-count dipole anisotropies in a large sample of infrared-selected quasars.
• To determine whether the observed dipole in quasar counts is consistent with the kinematic dipole expected from our motion relative to the CMB rest frame.
• To quantify the statistical significance of the dipole amplitude discrepancy using Bayesian evidence and model comparison.
• To assess the impact of observational systematics—particularly Galactic plane masking and source evolution—on the predicted dipole amplitude in ΛCDM.
• To evaluate whether the observed anomaly could be explained by theoretical uncertainties or if it indicates a fundamental challenge to the standard cosmological model.

Proposed method

• Applied a Bayesian hierarchical model to the CatWISE quasar catalog to infer the dipole amplitude and direction from number-count fluctuations across the sky.
• Used the likelihood function for Poisson-distributed number counts to model the observed dipole, incorporating a dipole term proportional to the cosine of the angle from the dipole direction.
• Calculated Bayesian evidence for multiple models (e.g., dipole vs. isotropic) to compare their relative plausibility given the data.
• Simulated full-sky dipole distributions under ΛCDM using HEALPix and Monte Carlo methods, including the effects of the Galactic plane mask and redshift-dependent spectral index.
• Accounted for systematics such as magnification bias and source evolution by incorporating redshift-dependent spectral indices into the kinematic dipole model.
• Compared the posterior distribution of the observed dipole amplitude with the theoretical prediction distribution, marginalizing over all other parameters to assess statistical significance.

Experimental results

Research questions

• RQ1 Is the observed number-count dipole in CatWISE quasars statistically consistent with the kinematic dipole expected from our motion relative to the CMB rest frame?
• RQ2 What is the statistical significance of the amplitude discrepancy between the observed quasar dipole and the ΛCDM-predicted kinematic dipole?
• RQ3 How do observational systematics—particularly the Galactic plane mask—alter the expected dipole amplitude distribution in ΛCDM?
• RQ4 To what extent does the redshift evolution of quasar spectral indices affect the predicted dipole amplitude and the observed tension?
• RQ5 Can the observed anomaly be reconciled with ΛCDM through known theoretical or observational uncertainties?

Key findings

• The data show unambiguous evidence for a dipole in the quasar number counts with amplitude $ D = (19 \pm 2) \times 10^{-3} $, direction $ (l,b) = (237.2^{+7.9}_{-8.0}, 41.8 \pm 5.0)^\circ $, consistent with the CMB dipole direction.
• The observed dipole amplitude is 2.7 times larger than the kinematically expected value of $ 5 \times 10^{-3} $, corresponding to a velocity of $ 1002\,\mathrm{km\,s^{-1}} $, a discrepancy at the $ 5.7\sigma $ level.
• The Galactic plane mask significantly suppresses the expected dipole amplitude in full-sky ΛCDM simulations, worsening the observed tension by leaking power into higher multipoles.
• Including redshift-dependent spectral indices for quasars slightly reduces the tension, but not enough to resolve the discrepancy, due to uncertainty in the magnification bias and redshift distribution.
• The dipole amplitude remains anomalously large even after accounting for systematics, indicating a robust tension with the standard model.
• A concurrent Bayesian analysis of RACS and NVSS radio surveys found a similar dipole amplitude excess of ~3× the expected value at 4.8σ, supporting the robustness of the result.