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

Abstract

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order ᐉ is represented by ᐉ unit vectors pointing in directions on 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 rotation group SO(3). However, they are related to the familiar spherical harmonic coefficients a ᐉm in a nonlinear way and are therefore sensitive to different aspects of the cosmic microwave background ͑CMB͒ anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. A code implementing this algorithm is available at http://www.phys.cwru.edu/projects/mpvectors/. Using the Wilkinson Microwave Anisotropy Probe ͑WMAP͒ full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs 2рᐉ 1 ᐉ 2 р8 is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the internal linear combination map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the ᐉϭ3 and ᐉϭ8 multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

Asymmetries in the angular distribution of the cosmic microwave background

“…Other anomalies were found in the WMAP data that were not expected according to the ΛCDM model either, such as the alignment between the quadrupole and octopole (e.g. Bielewicz et al 2004;Schwarz et al 2004;Copi et al 2004;de Oliveira-Costa et al 2004;Bielewicz et al 2005;Land & Magueijo 2005;Copi et al 2006;Abramo et al 2006;Frommert & Ensslin 2010;Gruppuso & Burigana 2010), the low quadrupole and octopole amplitudes (e.g., Mukherjee & Wang 2003;Ayata et al 2010;Cayon 2010;Cruz et al 2011), the north-south asymmetry (e.g., Eriksen et al 2004a;Hansen et al 2004a;Eriksen et al 2004b;Hansen et al 2004b;Donoghue et al 2005;Hoftuft et al 2009;Paci et al 2010;Pietrobon et al 2010;Vielva & Sanz 2010), the anomalous alignment of the CMB features toward the Ecliptic poles (e.g., Wiaux et al 2006;Vielva et al 2007), and the cold spot (e.g., Vielva et al 2004;Cruz et al 2005Cruz et al , 2007Vielva 2010).…”

BeyondΛCDM: Problems, solutions, and the road ahead

“…It has long been noticed that the large-angle fluctuations of the microwave background temperature are uncooperative with "the program" -they exhibit several statistically significant anomalies that have persisted from WMAP to Planck [476,477,478,479,480,481,16,482,483,484,485,486,487,488,489] (see also Ref. [490] for a recent critical review).…”

Testing for Non‐Gaussianity in theWilkinson Microwave Anisotropy ProbeData: Minkowski Functionals and the Length of the Skeleton

“…Tests for nonGaussianity afford possible methods for detecting, characterizing, and subsequently removing such effects. Further impetus for the study of such signatures has arisen in recent months from putative detections of non-Gaussian features in the Wilkinson Microwave Anisotropy Probe (WMAP; Bennett et al 2003a) first-year sky maps (Coles et al 2004;Naselsky et al 2003;Vielva et al 2004;Copi et al 2004;Park 2004;Eriksen et al 2004).…”