A high-significance detection of non-Gaussianity in theWilkinson Microwave Anisotropy Probe1-yr data using directional spherical wavelets

Abstract

A directional spherical wavelet analysis is performed to examine the Gaussianity of the Wilkinson Microwave Anisotropy Probe (WMAP) 1-yr data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows us to probe orientated structure in the data. Significant deviations from Gaussianity are detected in the skewness and kurtosis of spherical elliptical Mexican hat and real Morlet wavelet coefficients for both the WMAP and Tegmark, de Oliveira-Costa & Hamilton foreground-removed maps. The previous non-Gaussianity detection made by Vielva et al. using the spherical symmetric Mexican hat wavelet is confirmed, although their detection at the 99.9 per cent significance level is only made at the 95.3 per cent significance level using our most conservative statistical test. Furthermore, deviations from Gaussianity in the skewness of spherical real Morlet wavelet coefficients on a wavelet scale of 550 arcmin (corresponding to an effective global size on the sky of ∼26° and an internal size of ∼3°) at an azimuthal orientation of 72°, are made at the 98.3 per cent significance level, using the same conservative method. The wavelet analysis inherently allows us to localize on the sky those regions that introduce skewness and those that introduce kurtosis. Preliminary noise analysis indicates that these detected deviation regions are not atypical and have average noise dispersion. Further analysis is required to ascertain whether these detected regions correspond to secondary or instrumental effects, or whether in fact the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave background.