A global picture of quantum de Sitter space

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 Poincar\'e recurrences are briefly discussed.