The cut-sky cosmic microwave background is not anomalous

Abstract

The observed angular correlation function of the cosmic microwave background has previously been reported to be anomalous, particularly when measured in regions of the sky uncontaminated by Galactic emission. Recent work by Efstathiou et al. presents a Bayesian comparison of isotropic theories, casting doubt on the significance of the purported anomaly. We extend this analysis to all anisotropic Gaussian theories with vanishing mean (<delta T> = 0), using the much wider class of models to confirm that the anomaly is not likely to point to new physics. On the other hand if there is any new physics to be gleaned, it results from low-l alignments which will be better quantified by a full-sky statistic. We also consider quadratic maximum likelihood power spectrum estimators that are constructed assuming isotropy. The underlying assumptions are therefore false if the ensemble is anisotropic. Nonetheless we demonstrate that, for theories compatible with the observed sky, these estimators (while no longer optimal) remain statistically superior to pseudo-C_l power spectrum estimators.