  We study conditions for the existence of asymptotic observables in cosmology.
With the exception of de Sitter space, the thermal properties of accelerating
universes permit arbitrarily long observations, and guarantee the production of
accessible states of arbitrarily large entropy. This suggests that some
asymptotic observables may exist, despite the presence of an event horizon.
Comparison with decelerating universes shows surprising similarities: Neither
type suffers from the limitations encountered in de Sitter space, such as
thermalization and boundedness of entropy. However, we argue that no realistic
cosmology permits the global observations associated with an S-matrix.
