Wavelets and WMAP non-Gaussianity
Pia Mukherjee, Yun Wang
TL;DR
This paper tests Gaussianity in the WMAP 1-year CMB data using the spherical Mexican hat wavelet across multiple scales. It reinforces prior evidence of a non-Gaussian signal in the southern hemisphere, manifested as excess kurtosis and more cold pixels, and demonstrates robustness to mask choice and noise modeling through extensive simulations. In addition to kurtosis, it uncovers scale-scale correlations consistent with the detected non-Gaussianity and places quantitative constraints on primordial non-Gaussianity via $f_{NL}$, finding $f_{NL}=50\pm80$ (68% CL). The results align with prior analyses (bispectrum and Minkowski functionals) and highlight the utility of scale-localized wavelet methods for probing early-universe physics.
Abstract
We study the statistical properties of the 1st year WMAP data on different scales using the spherical mexican hat wavelet transform. Consistent with the results of Vielva et al. (2003) we find a deviation from Gaussianity in the form of kurtosis of wavelet coefficients on $3-4^\circ$ 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 amongst 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 parametrized by the non-linearity parameter $f_{NL}$. We use the skewness of the spherical mexican hat wavelet coefficients to constrain $f_{NL}$ with the 1st year WMAP data. Our results constrain $f_{NL}$ to be $50\pm 80$ at 68% confidence, and less than 280 at 99% confidence.