  Perturbative gravity about a de Sitter background motivates a global picture
of quantum dynamics in `eternal de Sitter space,' the theory of states which
are asymptotically de Sitter to both future and past. Eternal de Sitter physics
is described by a finite dimensional Hilbert space in which each state is
precisely invariant under the full de Sitter group. This resolves a
previously-noted tension between de Sitter symmetry and finite entropy.
Observables, implications for Boltzmann brains, and Poincare recurrences are
briefly discussed.
