The Multipole Vectors of WMAP, and their frames and invariants

Abstract

We investigate the Statistical Isotropy and Gaussianity of the CMB fluctuations, using a set of multipole vector functions capable of separating these two issues. In general a multipole is broken into a frame and $2\ell -3$ ordered invariants. The multipole frame is found to be suitably sensitive to galactic cuts. We then apply our method to real WMAP datasets; a coadded masked map, the Internal Linear Combinations map, and Wiener filtered and cleaned maps. Taken as a whole, multipoles in the range $\ell =2-10$ or $\ell =2-20$ show consistency with statistical isotropy, as proved by the Kolmogorov test applied to the frame's Euler angles. This result in {\it not} inconsistent with previous claims for a preferred direction in the sky for $\ell =2,...5$. The multipole invariants also show overall consistency with Gaussianity apart from a few anomalies of limited significance (98%), listed at the end of this paper.

arXiv comment9 pages. Submitted to MNRAS

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• Large scale anomalies in the CMB and non-Gaussianity in bouncing cosmologies
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• Measuring Statistical Isotropy of CMB Anisotropy
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• Large scale directional anomalies in the WMAP 5yr ILC map
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• Bias in low-multipole CMB reconstructions
• Steerable wavelet analysis of CMB structures alignment
• Topological signatures in CMB temperature anisotropy maps
• Statistical Characterization of Temperature Patterns in Anisotropic Cosmologies
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• Angular-planar CMB power spectrum
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• Correlation of supernova redshifts with temperature fluctuations of the Cosmic Microwave Background
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• On the Coherence of WMAP and Planck Temperature Maps
• Temperature and Polarization Patterns in Anisotropic Cosmologies
• Cosmic Acceleration Driven by Mirage Inhomogeneities
• A search for concentric rings with unusual variance in the 7-year WMAP temperature maps using a fast convolution approach
• Testing cosmological models with large-scale power modulation using microwave background polarization observations
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