Islands in de Sitter space

TL;DR

This paper investigates how entanglement entropy in 2D de Sitter JT gravity with black holes is stabilized by island surfaces, reconciling entropy growth with monogamy constraints and providing insights into the de Sitter horizon.

Contribution

It introduces a novel island formula in de Sitter space that accounts for horizon contributions and stabilizes entropy growth, extending the understanding of entanglement in cosmological settings.

Findings

Island surfaces stabilize entropy growth in de Sitter black holes.

Both black hole and cosmological horizons contribute to island formation.

The results support a Page curve-like behavior in de Sitter space.

Abstract

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.