A 6σ detection of non-Gaussianity in the WMAP 1-year data using directional spherical wavelets

A directional spherical wavelet analysis is performed to examine the Gaussianity of the WMAP 1-year data. Such an analysis is facilitated by the introduction of a fast directional continuous spherical wavelet transform. The directional nature of the analysis allows one 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 foreground removed maps. In particular, the skewness of spherical real Morlet wavelet coefficients on wavelet scale 550 (corresponding to an effective size on the sky of ∼ 26) and at an azimuthal orientation of 72, deviates by 5.88 standard deviations for the WMAP map and by 6.72 standard deviations for the Tegmark map. These detections are made at the 99% significance level. Furthermore, the wavelet analysis allows one to localise on the sky the most pronounced deviations from Gaussianity. When these regions are removed from the analysis the data are consistent with Gaussianity, suggesting these localised regions are the source of the detected non-Gaussianity. Further analysis is required to ascertain whether these regions correspond to foreground or instrumental effects, or whether the non-Gaussianity detected is due to intrinsic primordial fluctuations in the cosmic microwave backround.