Statistics of phase correlations as a test for non-Gaussianity of the CMB maps

Abstract

Gaussianity is the very basis for derivation of the cosmological parameters from the cosmic microwave background (CMB) angular power spectrum. Non-Gaussian signal, whether originated from experimental error or primordial source, could mimic extra power in the power spectrum, thereby leading to a wrong set of parameters. In this paper we present a new Gaussianity analysis of the derived CMB signals. It is based on the trigonometric moments of phases, which can be concluded with a ``mean angle,'' allowing us to see the global trend of non-Gaussianity of the signals. These moments are also closely related to the Pearson's random walks. We apply these analyses on the derived CMB maps and their different morphologies manifest themselves through these functions. We also comment on rotational invariance of the trigonometric moments of phases as a non-Gaussianity test.