A Test for the Zero Mean Hypothesis in Cosmology

Abstract

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 $2.5\sigma$ and $3.1\sigma$ in the multipole ranges of $\ell \approx 61$-$86$ 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.

arXiv comment12 pages, 8 figures, accepted version

References in corpus (26)

• Planck 2013 results. XVI. Cosmological parameters
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results
• Planck 2013 results. XXII. Constraints on inflation
• Asymmetries in the CMB anisotropy field
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps
• Increasing evidence for hemispherical power asymmetry in the five-year WMAP data
• Non-Gaussian Signatures in the Temperature Fluctuation Observed by the Wilkinson Microwave Anisotropy Probe
• Power Asymmetry in Cosmic Microwave Background Fluctuations from Full Sky to Sub-degree Scales: Is the Universe Isotropic?
• A Test of the Copernican Principle
• Power asymmetry in WMAP and Planck temperature sky maps as measured by a local variance estimator
• Geocentrism reexamined
• Is the Universe homogeneous?
• Planck 2013 results. V. LFI calibration
• Inhomogeneities in the universe
• Non-detection of a statistically anisotropic power spectrum in large-scale structure
• Anomalous CMB north-south asymmetry
• The isotropic blackbody CMB as evidence for a homogeneous universe
• Directional dependence of LCDM cosmological parameters
• Testing homogeneity with the fossil record of galaxies
• A method for testing the cosmic homogeneity with Shannon entropy
• The effect of asymmetric beams in the Wilkinson Microwave Anisotropy Probe experiment
• Testing Homogeneity with Galaxy Star Formation Histories
• Do Cosmological Perturbations Have Zero Mean?
• Test for anisotropy in the mean of the CMB temperature fluctuation in spherical harmonic space

Cited by in corpus (1)

• Cosmological consequences of statistical inhomogeneity