  Consideration of vacuum polarization in quantum electrodynamics may affect
the momentum dispersion relation for photons for a non-trivial background, due
to appearance of curvature dependent terms in the effective action. We
investigate the effect of a positive cosmological constant $\Lambda$ on this at
one loop order for stationary $\Lambda$-vacuum spacetimes. To the best of our
knowledge, so far it has been shown that $\Lambda$ affects the propagation in a
time dependent black hole spacetime. Here we consider the static de Sitter
cosmic string and the Kerr-de Sitter spacetime to show that there can be some
non-vanishing effect due to $\Lambda$ for physical polarizations. Consistency
of these results with the polarization sum rule is discussed.
