The discriminating power of wavelets to detect non-Gaussianity in the cosmic microwave background

We investigate the power of wavelets in detecting non-Gaussianity in the cosmic microwave background (CMB). We use a wavelet-based method on small simulated patches of the sky to discriminate between a pure inflationary model and inflationary models that also contain a contribution from cosmic strings. We show the importance of the choice of a good test statistic in order to optimize the discriminating power of the wavelet technique. In particular, we construct the Fisher discriminant function, which combines all the information available in the different wavelet scales. We also compare the performance of different decomposition schemes and wavelet bases. For our case, we find that the Mallat and a ` trous algorithms are superior to the 2D-tensor wavelets. Using this technique, the inflationary and strings models are clearly distinguished even in the presence of a superposed Gaussian component with twice the rms amplitude of the original cosmic string map.