CMB and matter power spectra from cross correlations of primordial curvature and magnetic fields

A complete numerical calculation of the temperature anisotropies and the polarization of the cosmic microwave background is presented for a nonzero cross correlation of a stochastic magnetic field with the primordial curvature perturbation. Such a cross correlation results, for example, if the magnetic field is generated during inflation by coupling electrodynamics to a scalar field that is identified with the curvaton. For a nearly scale-invariant magnetic field of 1 nG it is found that the contribution due to the cross correlation dominates over that of the pure magnetic mode. A similar behavior on large scales is found for the linear matter power spectrum.