Multipole invariants and non-Gaussianity

Abstract

We propose a framework for separating the information contained in the CMB multipoles, $a_{\ell m}$, into its algebraically independent components. Thus we cleanly separate information pertaining to the power spectrum, non-Gaussianity and preferred axis effects. The formalism builds upon the recently proposed multipole vectors (Copi, Huterer & Starkman 2003; Schwarz & al 2004; Katz & Weeks 2004), and we elucidate a few features regarding these vectors, namely their lack of statistical independence for a Gaussian random process. In a few cases we explicitly relate our proposed invariants to components of the $n$-point correlation function (power spectrum, bispectrum). We find the invariants' distributions using a mixture of analytical and numerical methods. We also evaluate them for the co-added WMAP first year map.

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Cited by in corpus (14)

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• The non-Gaussian Cold Spot in WMAP: significance, morphology and foreground contribution
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• Global universe anisotropy probed by the alignment of structures in the cosmic microwave background
• A high-significance detection of non-Gaussianity in the WMAP 3-year data using directional spherical wavelets
• Occam's razor meets WMAP
• Non-Gaussianity detections in the Bianchi VIIh corrected WMAP 1-year data made with directional spherical wavelets
• The study of topology of the universe using multipole vectors
• Mysteries on Universe's Largest Observable Scales
• Searching for non-Gaussianity in the WMAP data
• Steerable wavelet analysis of CMB structures alignment
• Probability Density of the Multipole Vectors for a Gaussian Cosmic Microwave Background
• The impact of dipole straylight contamination on the alignment of low multipoles of CMB anisotropies
• Temperature and Polarization Patterns in Anisotropic Cosmologies