On the electromagnetic nature of dark energy and the origin of cosmic magnetic fields

Abstract: In this work we consider quantum electromagnetic fields in an expanding universe. We start by reviewing the difficulties found when trying to impose the Lorenz condition in a time-dependent geometry. Motivated by this fact, we explore the possibility of extending the electromagnetic theory by allowing the scalar state which is usually eliminated by means of the Lorenz condition to propagate, preserving at the same time the dynamics of ordinary transverse photons. We show that the new state cannot be generated by charged currents, but it breaks conformal invariance and can be excited gravitationally. In fact, primordial quantum fluctuations produced during inflation can give rise to super-Hubble temporal electromagnetic modes whose energy density behaves as a cosmological constant. The value of the effective cosmological constant is shown to agree with observations provided inflation took place at the electroweak scale. The theory is compatible with all the local gravity tests and is free from classical or quantum instabilities. Thus we see that, not only the true nature of dark energy can be established without resorting to new physics, but also the value of the cosmological constant finds a natural explanation in the context of standard inflationary cosmology. On sub-Hubble scales, the new state generates an effective charge density which, due to the high electric conductivity of the cosmic plasma after inflation, gives rise to both vorticity and magnetic fields. Present upper limits on vorticity coming from CMB anisotropies are translated into lower limits on the present value of cosmic magnetic fields. We find that magnetic fields $B_{\lambda}> 10^{-12}$ G can be typically generated with coherence lengths ranging from sub-galactic scales up to the present Hubble radius.