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 Poincaré recurrences are briefly discussed.

Figure 1

De Sitter space with boost Killing field $B=H_S-H_N$ and horizons. The dashed line is the neck, the smallest $S^{D-1}$ in this frame. The dot is the $S^{D-2}$ left fixed by $B$. The worldline of the south (north) pole observer is the right (left) edge of the diagram.