The electromagnetic dark sector

Abstract

We consider electromagnetic field quantization in an expanding universe. We find that the covariant (Gupta–Bleuler) method exhibits certain difficulties when trying to impose the quantum Lorenz condition on cosmological scales. We thus explore the possibility of consistently quantizing without imposing such a condition. In this case there are three physical states, which are the two transverse polarizations of the massless photon and a new massless scalar mode coming from the temporal and longitudinal components of the electromagnetic field. An explicit example in de Sitter space–time shows that it is still possible to eliminate the negative norm state and to ensure the positivity of the energy in this theory. The new state is decoupled from the conserved electromagnetic currents, but is non-conformally coupled to gravity and therefore can be excited from vacuum fluctuations by the expanding background. The cosmological evolution ensures that the new state modifies Maxwell's equations in a totally negligible way on sub-Hubble scales. However, on cosmological scales it can give rise to a non-negligible energy density which could explain in a natural way the present phase of accelerated expansion of the universe.