  In this article we prove a family of local (in time) weighted Strichartz
estimates with derivative losses for the Klein-Gordon equation on
asymptotically de Sitter spaces and provide a heuristic argument for the
non-existence of a global dispersive estimate on these spaces. The weights in
the estimates depend on the mass parameter and disappear in the "large mass"
regime. We also provide an application of these estimates to establish
small-data global existence for a class of semilinear equations on these
spaces.
