  We derive covariant expressions for the one loop vacuum polarization induced
by a charged scalar on de Sitter background. Two forms are employed: one in
which two covariant derivatives act on de Sitter invariant basis tensors
multiplied by scalar structure functions, and the other in which four covariant
derivatives act on a single basis tensor times a structure function. The second
representation permits the correction to dynamical photons to be expressed as a
surface integral, which raises the important question of what sorts of effects
can be absorbed into corrections of the initial state. Results are obtained for
charged, minimally coupled scalars which are either massless or else light. The
former show de Sitter breaking whereas the latter are de Sitter invariant.
However, the de Sitter invariant formulation does not seem useful, even when it
is possible. Our work has important implications for representations of the
graviton self-energy on de Sitter.
