Symmetry of the CMB sky as a new test of its statistical isotropy. Non Cosmological Octupole?

TL;DR

This paper introduces a new method to test the statistical isotropy of the CMB by exploiting symmetries of Galactic foregrounds, revealing anomalies and correlations in the octupole component that suggest residual foreground contamination or systematic effects.

Contribution

The paper proposes a novel symmetry-based test for CMB isotropy, applied to the octupole, revealing significant anomalies and phase correlations not previously identified.

Findings

Detected abnormal symmetry in the octupole at 0.58% significance.

Found strong phase correlations between the kinematic dipole and octupole.

Observed broad multipole range deviations from isotropy and homogeneity.

Abstract

In this article we propose a novel test for statistical anisotropy of the CMB. The test is based on the fact, that the Galactic foregrounds have a remarcably strong symmetry with respect to their antipodal points and with respect to the Galactic plane, while the cosmological signal should not be symmetric or asymmetric under these transitions. We have applied the test for the octupole component of the WMAP ILC 7 map, by looking at a_3,1 and a_3,3, and their ratio to a_3,2 both for real and imaginary values. We find abnormal symmetry of the octupole component at the level of 0.58%, compared to Monte Carlo simulations. By using the analysis of the phases of the octupole we found remarkably strong cross-correlations between the phases of kinematic dipole and ILC 7 octupole, in full agreement with previous results. We further test the multipole range 2<l<100, by investigating the ratio between the l+m=even and l+m=odd parts of power spectra. We compare the results to simulations of a Gaussian random sky, and find significant departure from the statistically isotropic and homogeneous case, for a very broad range of multipoles. We found that for the most prominent peaks of our estimator, the phases of the corresponding harmonics are coherent with phases of the octupole. We believe, our test would be very useful for detections of various types of residuals of the foreground and systematic effects at very a broad range of multipoles 2 < l < 1500-3000 for the forthcoming PLANCK CMB map, before any conclusions about primordial non-Gaussianity and statistical anisotropy of the CMB.