Debye mass in de Sitter space

We calculate the one-loop contributions to the polarization operator for scalar quantum electrodynamics in different external electromagnetic and gravitational fields. In the case of gravity, de Sitter space and its different patches were considered. It is shown that the Debye mass appears only in the case of alpha-vacuum in the Expanding Poincare Patch. It can be shown either by direct computations or by using analytical and causal properties of the de Sitter space. Also, the case of constant electric field is considered and the Debye mass is calculated.