Covariance of CMB anomalies

TL;DR

This paper investigates the statistical covariance of large-scale anomalies in the CMB temperature data, comparing observations with simulations to understand their significance and interrelations.

Contribution

It provides a comprehensive covariance analysis of multiple CMB anomalies using extensive simulations and principal component analysis, linking previous findings and offering a framework for future research.

Findings

Covariance structure aligns with expectations based on the angular power spectrum.

Significant differences found in quadrupole-octopole alignment covariance between Gaussian and FFP simulations.

Principal components capture 90% of variance, highlighting key anomaly combinations.

Abstract

Several unexpected features are observed at large angular scales in the CMB temperature anisotropy measurements by both WMAP and Planck. These include the lack of both variance and correlation, alignment of the lowest multipole moments with one another, hemispherical power asymmetry, and an odd-to-even parity excess. In this work, we study the statistics of eight representative large-angle CMB features in order to evaluate their covariance in LCDM. We do so using two sets of simulated CMB temperature maps; an ensemble of 100,000 simple Gaussian simulations, and 1000 Full Focal Plane (FFP) simulations provided by the Planck collaboration. In measuring feature probabilities, we pay particular attention to analysis choices, making sure that we can reproduce previous results in the literature, and explain differences where appropriate. The covariance structure we find is consistent with expectations given that many of the features studied are functions of the angular power spectrum. Notably, we find significant differences in the covariance entries associated with the quadrupole-octopole alignments derived from the Gaussian and FFP simulations. We additionally perform a principal component analysis to quantitatively gauge what combinations of features capture the most information about how simulation measurements vary, and to provide an alternative assessment of the ways in which the real sky is anomalous. The first four principal components explain about 90\% of the simulations' variance, with the first two roughly quantifying the lack of large-angle correlations, and the next two quantifying the phase-dependent anomalies (multipole alignments and power asymmetry). Though the results of this analysis are fairly unsurprising, its comprehensive approach serves to tie together a number of previous results, and will therefore provide context for future studies of large-angle anomalies.