Testing for non-Gaussianity of the cosmic microwave background in harmonic space: An empirical process approach

We present a new, model-independent approach for measuring non-Gaussianity of the cosmic microwave background (CMB) anisotropy pattern. Our approach is based on the empirical distribution function of the normalized spherical harmonic expansion coefficients $a_{\mathcal{l}m}$ of a nearly full-sky CMB map, like the ones expected from forthcoming satellite experiments. Using a set of Kolmogorov-Smirnov type tests, we check for Gaussianity and independency of the $a_{\mathcal{l}m}.$ We test the method on two non-Gaussian toy models of the CMB, one generated in spherical harmonic space and one in pixel (real) space. We also provide some rigorous results, possibly of independent interest, on the exact distribution of the spherical harmonic coefficients normalized by an estimated angular power spectrum.