Probing CMB Non-Gaussianity Using Local Curvature

Abstract

It is possible to classify pixels of a smoothed cosmic microwave background (CMB) fluctuation map according to their local curvature in ``hill'', ``lake'' and ``saddle'' regions. In the Gaussian case, fractional areas occupied by pixels of each kind can be computed analytically for families of excursion sets as functions of threshold and moments of the fluctuation power spectrum. We show how the shape of these functions can be used to constrain accurately the level of non-Gaussianity in the data by applying these new statistics to an hypothetical mixed model suggested by Bouchet et al. (2001). According to our simple test, with only one 12.5x12.5 deg^2 map, Planck should be able to detect with a high significance a non-Gaussian level as weak as 10% in temperature standard deviation (rms) (5% in C_l), whereas a marginal detection would be possible for MAP with a non-Gaussian level around 30% in temperature (15% in C_l).

11 pages, 13 figures, submitted to MNRAS

References in corpus (11)

• Generating the curvature perturbation without an inflaton
• A measurement by BOOMERANG of multiple peaks in the angular power spectrum of the cosmic microwave background
• DASI First Results: A Measurement of the Cosmic Microwave Background Angular Power Spectrum
• A High Spatial Resolution Analysis of the MAXIMA-1 Cosmic Microwave Background Anisotropy Data
• Measurement of the cosmic microwave background bispectrum on the COBE DMR sky maps
• Estimate of the Cosmological Bispectrum from the MAXIMA-1 Cosmic Microwave Background Map
• On the trispectrum as a gaussian test for cosmology
• Search for non-gaussian signals in the BOOMERanG maps: pixel-space analysis
• The Trispectrum of the 4 Year COBE-DMR data
• The discriminating power of wavelets to detect non-Gaussianity in the CMB
• Lensing-induced Non-Gaussian Signatures in the Cosmic Microwave Background

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