The seed magnetic field generated during recombination

Nonlinear dynamics creates vortical currents when the tight-coupling approximation between photons and baryons breaks down around the time of recombination. This generates a magnetic field at second order in cosmological perturbations, whose power spectrum is fixed by standard physics, without the need for any ad hoc assumptions. We present the fully relativistic calculation of the magnetic power spectrum, including the effects of metric perturbations, second-order velocity and the photon anisotropic stress, thus generalizing and correcting previous results. We also show that significant magnetogenesis continues to occur after recombination. The power spectrum $\sqrt{k^3 P_B} $ behaves as $ \propto k^4$ on large scales, and $\propto k^{0.5}$ on small scales, down to $\sim 1\,$Mpc. On cluster scales, the created field has strength $\sim 3\times 10^{-29}$ Gauss.