Cosmic electromagnetic fields due to perturbations in the gravitational field

Abstract

We use non-linear gauge-invariant perturbation theory to study the interaction of an inflation produced seed magnetic field with density and gravitational wave perturbations in an almost Friedmann-Lemaˆıtre-Robertson-Walker (FLRW) spacetime with zero spatial curvature. We compare the effects of this coupling under the assumptions of poor conductivity, perfect conductivity and the case where the electric field is sourced via the coupling of velocity perturbations to the seed field in the ideal magnetohydrodynamic (MHD) regime, thus generalizing, improving on and correcting previous results. We solve our equations for long wavelength limits and numerically integrate the resulting equations to generate power spectra for the electromagnetic field variables, showing where the modes cross the horizon. We find that the interaction can seed Electric fields with non-zero curl and that the curl of the electric field dominates the power spectrum on small scales, in agreement with previous arguments.