Testing for non-Gaussianity of the cosmic microwave background in harmonic space: an empirical process approach

Abstract

We present a new, model-independent approach for measuring non-Gaussianity of the Cosmic Microwave Background (CMB) anisotropy pattern. Our approach is based on the empirical distribution function of the normalized spherical harmonic expansion coefficients a_lm of a nearly full-sky CMB map, like the ones expected from forthcoming satellite experiments. Using a set of Kolmogorov-Smirnov type tests, we check for Gaussianity and independency of the a_lm. We test the method on two non-Gaussian toy-models of the CMB, one generated in spherical harmonic space and one in pixel (real) space. We also provide some rigorous results, possibly of independent interest, on the exact distribution of the spherical harmonic coefficients normalized by an estimated angular power spectrum.

29 pages, 7 figures, submitted to Phys. Rev. D

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Cited by in corpus (9)

• Non-Gaussianity from Inflation: Theory and Observations
• Multipole Vectors--a new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2<=l<=8
• High-Resolution Simulations of Cosmic Microwave Background non-Gaussian Maps in Spherical Coordinates
• Search for non-Gaussianity in pixel, harmonic and wavelet space: compared and combined
• Primordial non-Gaussianity: local curvature method and statistical significance of constraints on f_NL from WMAP data
• The extended empirical process test for non-Gaussianity in the CMB, with an application to non-Gaussian inflationary models
• Searching for non-Gaussianity in the VSA data
• The empirical process on Gaussian spherical harmonics
• Generation of Arbitrarily Non-Gaussian Fields with a Set Correlation Structure