Scalar current of created pairs by Schwinger mechanism in de Sitter spacetime

We consider a charged scalar field in a \(D\)-dimensional de Sitter spacetime and investigate pair creation by a Schwinger mechanism in a constant electric field background. Using a semiclassical approximation the current of the created pairs has been estimated. We find that the semiclassical current of the created pairs in the strong electric field limit responds as \(E^{\frac{D}{2}}\). Going further but restricting to \(D=3\) dimensional de Sitter spacetime, the quantum expectation value of the spacelike component of the induced current has been computed in the in-vacuum state by applying an adiabatic subtraction scheme. We find that, in the strong electric field limit, the current responds as \(E^{\frac{3}{2}}\). In the weak electric field limit the current has a linear response in \(E\) and an inverse dependence on the mass of the scalar field. In the case of a massless scalar field, the current varies with \(E^{-1}\) which leads to a phenomenon of infrared hyperconductivity. A new relation between infrared hyperconductivity, tachyons, and conformality is discussed, and a scheme to avoid an infrared hyperconductivity regime is proposed. In \(D\) dimension, we eventually presented some first estimates of the backreaction of the Schwinger pairs to the gravitational field, and we find a decrease of the Hubble constant due to the pair creation.