Dark energy and cosmic magnetic fields: electromagnetic relics from inflation

Abstract

We consider an extended electromagnetic theory in which the scalar state which is usually eliminated be means of the Lorenz condition is allowed to propagate. On super-Hubble scales, such a state is given by the temporal component of the electromagnetic potential and contributes as an effective cosmological constant to the energy-momentum tensor. Its initial amplitude is set by quantum fluctuations generated during inflation and it is shown that the predicted value for the cosmological constant agrees with observations provided inflation took place at the electroweak scale. We also consider more general theories including non-minimal couplings to the space-time curvature in the presence of the temporal electromagnetic background. We show that both in the minimal and non minimal cases, the modified Maxwell's equations include new effective current terms which can generate magnetic fields from sub-galactic scales up to the present Hubble horizon. The corresponding amplitudes could be enough to seed a galactic dynamo or even to account for observations just by collapse and differential rotation in the protogalactic cloud.