Effective field theory of magnetogenesis: Identifying the necessary and sufficient conditions

Abstract

At all Universe scales, there is a detectable amount of magnetic field. There are several probable origins for this observed magnetic field, including the possibility of its origin in the early Universe. There are several models for primordial magnetogenesis, and if the inflationary background is taken into account, breaking conformal symmetry is required to generate a sufficient amount of magnetic field. The conformal symmetry breaking is introduced either by new couplings between electromagnetic field and inflaton field or including higher derivative terms to the theory. To unify these different approaches in the literature, we propose an Effective Field Theory (EFT) approach, where EFT parameters describe the magnetogenesis scenario in the early Universe, and different choices of parameters correspond to different models. We show that the vector perturbations do not have temporal evolution; hence, only the gauge field is the relevant gauge-invariant variable for the EFT. We explicitly show that the generation of primordial magnetic fields requires two necessary conditions -- conformal invariance breaking and causal propagation. Hence, conformal invariance breaking is only a necessary condition, \emph{not} a sufficient condition. We confirm this by considering a specific model of primordial magnetogenesis.Comment: 37 pages, 2 figure