Large-scale magnetic fields, dark energy, and QCD

Cosmological magnetic fields are being observed with ever increasing correlation lengths, possibly reaching the size of superclusters, therefore disfavoring the conventional picture of generation through primordial seeds later amplified by galaxy-bound dynamo mechanisms. In this paper we put forward a fundamentally different approach that links such large-scale magnetic fields to the cosmological vacuum energy. In our scenario the dark energy is due to the Veneziano ghost (which solves the $U(1{)}_A$ problem in QCD). The Veneziano ghost couples through the triangle anomaly to the electromagnetic field with a constant which is unambiguously fixed in the standard model. While this interaction does not produce any physical effects in Minkowski space, it triggers the generation of a magnetic field in an expanding universe at every epoch. The induced energy of the magnetic field is thus proportional to cosmological vacuum energy: ${\rho }_{\mathrm{EM}}\simeq B^2\simeq (\frac{\alpha }{4\pi }{)}^2{\rho }_{\mathrm{DE}}$, ${\rho }_{\mathrm{DE}}$ hence acting as a source for the magnetic energy ${\rho }_{\mathrm{EM}}$. The corresponding numerical estimate leads to a magnitude in the nG range. There are two unique and distinctive predictions of our proposal: an uninterrupted active generation of Hubble size correlated magnetic fields throughout the evolution of the Universe; the presence of parity violation on the enormous scales $1/H$, which apparently has been already observed in CMB. These predictions are entirely rooted into the standard model of particle physics.