Primordial Magnetic Field and Non-Gaussianity of the One-Year Wilkinson Microwave Anisotropy Probe Data

Alfvén turbulence caused by statistically isotropic and homogeneous primordial magnetic field induces correlations in the cosmic microwave background (CMB) anisotropies. The correlations are specifically between the spherical harmonic modes al-1,m and al+1,m. In this paper we approach this issue from phase analysis of the CMB maps derived from the WMAP data sets. Using circular statistics and return phase mapping, we examine phase correlation of Δl = 2 for the primordial non-Gaussianity caused by the Alfvén turbulence at the epoch of recombination. Our analyses show that such specific features from the power-law Alfvén turbulence do not contribute significantly in the phases of the maps and could not be a source of primordial non-Gaussianity of the CMB.