Symmetry breaking

Quantum mechanics

Replica trick

Theoretical physics

de Sitter–Schwarzschild metric

Mathematical physics

De Sitter space

Entropy (arrow of time)

de Sitter invariant special relativity

Classical mechanics

Black hole thermodynamics

Physics

Quantum entanglement

Mathematics

Wormhole

Geometry

Quantum

Anti-de Sitter space

De Sitter universe

Universe

Journal of High Energy Physics

We consider black holes in 2d de Sitter JT gravity coupled to a CFT, and entangled with matter in a disjoint non-gravitating universe. Tracing out the entangling matter leaves the CFT in a density matrix whose stress tensor backreacts on the de Sitter geometry, lengthening the wormhole behind the black hole horizon. Naively, the entropy of the entangling matter increases without bound as the strength of the entanglement increases, but the monogamy property predicts that this growth must level off. We compute the entropy via the replica trick, including wormholes between the replica copies of the de Sitter geometry, and find a competition between conventional field theory entanglement entropy and the surface area of extremal "islands" in the de Sitter geometry. The black hole and cosmological horizons both play a role in generating such islands in the back-reacted geometry, and have the effect of stabilizing the entropy growth as required by monogamy. We first show this in a scenario in which the de Sitter spatial section has been decompactified to an interval. Then we consider the compact geometry, and argue for a novel interpretation of the island formula in the context of closed universes that recovers the Page curve. Finally, we comment on the application of our construction to the cosmological horizon in empty de Sitter space.

Islands in de Sitter space