de Sitter QED in Coulomb gauge: First order transition amplitudes

We construct the de Sitter QED in Coulomb gauge assuming that the quantum modes are prepared by a global apparatus which is able to determine a stable and invariant vacuum state, independent of the local coordinates. Then we proceed in a traditional manner, postulating the appropriate equal-time commutators and anticommutators of the interacting fields and deriving the perturbation expansion of the scattering operator. In this approach, we consider the in-out transitions amplitudes of the QED on the de Sitter expanding universe. We define the in and out fields as asymptotic-free fields, without electromagnetic interaction but remaining coupled to the de Sitter gravity, assuming that these are measured by the same global apparatus. Then the transition amplitudes can be calculated exactly by using the reduction formalism and the perturbation procedure as in the flat case but with significant differences due to the de Sitter gravity. A specific feature is that this eliminates the constraints due to the simultaneous momentum-energy conservation giving rise to QED transitions with nonvanishing amplitudes even in the first order of perturbations. Of a special interest could be the first order amplitudes of the electromagnetic particle creation allowed by the expansion of the de Sitter universe. We show that this effect is significant only in the very strong gravity of the early universe. DOI: 10.1103/PhysRevD.87.044016