Extended empirical process test for non-Gaussianity in the CMB, with an application to non-Gaussian inflationary models

In a previous paper, we presented a new approach for measuring the non-Gaussianity of the cosmic microwave background (CMB) anisotropy pattern, based on the multivariate empirical distribution function of the spherical harmonics $a_{\mathcal{l}m}$ of a CMB map. The present paper builds upon the same ideas and proposes several improvements and extensions. More precisely, we exploit the additional information on the random phases of the $a_{\mathcal{l}m}$ to provide further tests based on the empirical distribution function. Also we take advantage of the effect of rotation on improving the power of our procedures. The suggested tests are implemented on physically motivated models of non-Gaussian fields; Monte Carlo simulations suggest that this approach may be very promising in the analysis of non-Gaussianity generated by nonstandard models of inflation. We address also some experimentally meaningful situations, such as the presence of instrumental noise and a galactic cut in the map.