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We propose a novel representation of cosmic microwave anisotropy maps, whereeach multipole order l is represented by l unit vectors pointing in directionson the sky and an overall magnitude. These "multipole vectors and scalars"transform as vectors under rotations. Like the usual spherical harmonics,multipole vectors form an irreducible representation of the proper rotationgroup SO(3). However, they are related to the familiar spherical harmoniccoefficients, alm, in a nonlinear way, and are therefore sensitive to differentaspects of the CMB anisotropy. Nevertheless, it is straightforward to determinethe multipole vectors for a given CMB map and we present an algorithm tocompute them. Using the WMAP full-sky maps, we perform several tests of thehypothesis that the CMB anisotropy is statistically isotropic and Gaussianrandom. We find that the result from comparing the oriented area of planesdefined by these vectors between multipole pairs 2<=l1!=l2<=8 is inconsistentwith the isotropic Gaussian hypothesis at the 99.4% level for the ILC map andat 98.9% level for the cleaned map of Tegmark et al. A particular correlationis suggested between the l=3 and l=8 multipoles, as well as several otherpairs. This effect is entirely different from the now familiar planarity andalignment of the quadrupole and octupole: while the aforementioned is fairlyunlikely, the multipole vectors indicate correlations not expected in Gaussianrandom skies that make them unusually likely. The result persists afteraccounting for pixel noise and after assuming a residual 10% dust contaminationin the cleaned WMAP map. While the definitive analysis of these results willrequire more work, we hope that multipole vectors will become a valuable toolfor various cosmological tests, in particular those of cosmic isotropy.

Multipole vectors: A new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2⩽l⩽8