  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 casual properties of the
de-Sitter space. Also, the case of constant electric field is considered and
the Debye mass is calculated.
