Journal Article

On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity

A. Curto, E. Martínez-González and R. B. Barreiro

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 412, issue 2, pages 1038-1046
Published in print April 2011 | ISSN: 0035-8711
Published online March 2011 | e-ISSN: 1365-2966 | DOI:
On the optimality of the spherical Mexican hat wavelet estimator for the primordial non-Gaussianity

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We study the spherical Mexican hat wavelet as a detector of primordial non-Gaussianity of the local type on the cosmic microwave background (CMB) anisotropies. For this purpose, we define third-order statistics based on the wavelet coefficient maps and the original map. We find the dependence of these statistics in terms of the non-linear coupling parameter fnl and the bispectrum of this type of non-Gaussianity. We compare the analytical values for these statistics with the results obtained with non-Gaussian simulations for an ideal full-sky CMB experiment without noise. We study the power of this method to detect fnl, that is, the variance of this parameter σ2(fnl), and compare it with the variance obtained from the primary bispectrum for the same experiment. Finally, we apply our wavelet-based estimator on Wilkinson Microwave Anisotropy Probe like maps with incomplete sky and inhomogeneous noise, and compare with the optimal bispectrum estimator. The results show that the wavelet cubic statistics are as efficient as the bispectrum as optimal detectors of this type of primordial non-Gaussianity.

Keywords: methods: data analysis; cosmic background radiation; cosmology: observations

Journal Article.  5539 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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