Magnetic Field Generation from Cosmological Perturbations

In this Letter, we discuss the generation of magnetic field from cosmological perturbations. We consider the evolution of three component plasma (electron, proton, and photon) evaluating the collision term between electrons and photons up to the second order. The collision term is shown to induce electric current, which then generates magnetic field. There are three contributions, two of which can be evaluated from the first-order quantities, while the other one is fluid vorticity, which is purely second order. We estimate the magnitudes of the former contributions and show that the amplitude of the produced magnetic field is about ∼10^-19  G at 10 Mpc comoving scale at the decoupling. Compared to astrophysical and inflationary mechanisms for seed-field generation, our study suffers from much less ambiguities concerning unknown physics and/or processes.