Cosmic magnetization out from the vacuum

Abstract: The large-scale magnetic fields we observe today in galaxies and galaxy clusters could be the result of a pure quantum effect taking place during inflation, to wit, the creation of particles (photons) out from the vacuum in a curved spacetime. We show that, whenever the conformal invariance of electromagnetism is broken during inflation, the actual magnetic field spectrum, in the classical limit, is given by $B_k \simeq k^2 \sqrt{n_{\mathbf{k}} }$, where $n_{\mathbf{k}} \gg 1$ is the number of created photons with wavenumber $k$. In particular, a scale-invariant magnetic field of order of $10^{12}$G can emerge in the simplest model of cosmic magnetogenesis, the one where the inflaton is kinetically coupled to the photon. Moreover, and contrarily to the general belief, we show that such a model is free from the so-called strong-coupling and backreaction problems. This conclusion follows, indirectly, from the observation that post-inflationary electric currents, which in the literature are incorrectly supposed to freeze superhorizon magnetic fields after inflation, are indeed vanishing on superhorizon scales due to causality.