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Probability Density of the Multipole Vectors for a Gaussian Cosmic Microwave Background
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We review Maxwell's multipole vectors, and elucidate some of their mathematical properties, with emphasis on the application of this tool to the cosmic microwave background (CMB). In particular, for a completely random function on the sphere (corresponding to the statistically isotropic Gaussian model of the CMB), we derive the full probability density function of the multipole vectors. This function is used to analyze the internal configurations of the third-year Wilkinson Microwave Anisotropy Probe quadrupole and octopole, and we show the observations are consistent with the Gaussian prediction. A particular aspect is the planarity of the octopole, which we find not to be anomalous.
Forward citations
Cited by 2 Pith papers
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Multipolar structure of the local expansion rate from incomplete sky data
CF4 data yield a 3.3σ excess dipole in the local expansion-rate fluctuation field at (l,b)=(290°,-4°)±5°, sourced mainly by z∈[0.03,0.05], with quadrupole/octupole consistent with ΛCDM and no multipole-vector alignments.
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Fr\'echet Vectors as sensitive tools for blind tests of CMB anomalies
Fréchet Vectors, built from Multipole Vectors, are more sensitive to CMB anisotropies, and Planck 2018 temperature maps show small tensions with a Gaussian and statistically isotropic sky.
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