Statistical power, the bispectrum, and the search for non-Gaussianity in the cosmic microwave background anisotropy

We use simulated maps of the cosmic microwave background (CMB) anisotropy t o quantify the ability of different statistical tests to discriminate betwe en Gaussian and non-Gaussian models. Despite the central limit theorem on l arge angular scales, both the genus and extrema correlations are able to di scriminate between Gaussian models and a semianalytic texture model selecte d as a physically motivated non-Gaussian model. When run on the COBE 4 year CMB maps, both tests prefer the Gaussian model. Although the bispectrum ha s comparable statistical power when computed on the full sky, once a Galact ic cut is imposed on the data, the bispectrum loses the ability to discrimi nate between models. Off-diagonal elements of the bispectrum are comparable to the diagonal elements for the non-Gaussian texture model and must be in cluded to obtain maximum statistical power.