2014/06/30 by Kiyotomo Ichiki · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Anisotropy #Astrophysics #Cosmic microwave background #Cosmology #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Homogeneity (statistics) #Mathematics #Multipole expansion #Observational cosmology #Physics #Planck #Quantum mechanics #Sigma #Spherical harmonics #Statistical hypothesis testing #Statistical physics #Statistics #Zero (linguistics) #astro-ph.CO
paper · pdf · doi:10.1103/physrevd.90.123008
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 90(12) (American Physical Society) · 12 pages, 8 figures, accepted version
arxiv created 2014/12/08 · openalex publication_date 2014/12/17 · arxiv updated 2014/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
One working hypothesis on which analyses of cosmological data are based is the zero ensemble mean hypothesis, which is related to the statistical homogeneity of cosmological perturbations. This hypothesis, however, should be tested by observational data in the current era of precision cosmology. Herein, we test the hypothesis by analyzing recent, foreground-reduced cosmic microwave background (CMB) maps, combining the spherical harmonic coefficients of the masked CMB temperature anisotropies in such a way that the combined variables can be treated as statistically independent samples. We find evidence against the zero mean hypothesis in two particular ranges of multipoles, with significance levels of 2.5\ensuremathσ and 3.1\ensuremathσ in the multipole ranges of \ensuremathℓ\ensuremath≈61--86 and 213--256, respectively, for both the Planck and Wilkinson Microwave Anisotropy Probe maps. The latter signal is consistent with our previous result found by using brute-force Monte Carlo simulations. However, within the method employed in this paper we conclude that the zero mean hypothesis is consistent with the current CMB data on the basis of Stouffer's weighted Z statistics, which takes multiple testing into account.