Spherical Mexican hat wavelet: an application to detect non-Gaussianity inthe COBE-DMR maps

The spherical Mexican hat wavelet is introduced in this paper, with the aim of testing the Gaussianity of the cosmic microwave background temperature fluctuations. Using the information given by the wavelet coefficients at se veral scales, we have performed several statistical tests on the COBE-DMR m aps to search for evidence of non-Gaussianity. Skewness, kurtosis, scale-sc ale correlations (for two and three scales) and Kolmogorov-Smirnov tests in dicate that the COBE-DMR data are consistent with a Gaussian distribution. We have extended the analysis to compare temperature values provided by COB E-DMR data with distributions (obtained from Gaussian simulations) at each pixel and at each scale. The number of pixels with temperature values outsi de the 95 and 99 per cent limits is consistent with that obtained from Gaus sian simulations, at all scales. Moreover, the extrema values for COBE-DMR data (maximum and minimum temperatures in the map) are also consistent with those obtained from Gaussian simulations.