Energy spectrum of magnetic fields from electroweak symmetry breaking

We study the magnetic fields produced in the early Universe during the electroweak symmetry breaking by considering random configurations of an inhomogeneous Higgs field. By exploiting the inherent randomness of the initial configurations the spectrum of the produced magnetic field is essentially analytic, which bypasses the need for costly lattice simulations. On the numerical side, we devise a simulation framework which results in continuous fields capable of resolving the small-scale structure of the fields that was inaccessible for the lattice-based calculation. Finally, by revisiting the effects of statistical isotropy and causality on the spectrum, we define general correlation functions that are then fitted to the simulation data and compared to the analytic results.