  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.
