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Wavelets and WMAP non-Gaussianity

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posted on 2023-06-08, 09:30 authored by Pia Mukherjee, Yun Wang
We study the statistical properties of the first-year Wilkinson Microwave Anisotropy Probe (WMAP) data on different scales using the spherical Mexican hat wavelet transform. Consistent with the 2004 results of Vielva et al., we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on 3-4 scales in the southern Galactic hemisphere. This paper extends the work of Vielva et al. as follows: We find that the non-Gaussian signal shows up more strongly in the form of a larger than expected number of cold pixels and also in the form of scale-scale correlations among wavelet coefficients. We establish the robustness of the non-Gaussian signal under more wide-ranging assumptions regarding the Galactic mask applied to the data and the noise statistics. This signal is unlikely to be due to the usual quadratic term parameterized by the nonlinearity parameter fNL. We use the skewness of the spherical Mexican hat wavelet coefficients to constrain fNL with the first-year WMAP data. Our results constrain fNL to be 50+/-80 at 68% confidence and less than 280 at 99% confidence.


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One of the first applications of wavelets as powerful non-Gaussianity estimators was my 2000 work on COBE data. Here an extended technique is applied to much better data from WMAP. I also extend the method to constrain a specific form of non-Gaussianity. This paper has over 50 citations.

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