Islands in Closed and Open Universes

TL;DR

This paper investigates how spatial curvature influences the formation of entanglement islands in cosmological models, revealing that positive curvature ensures the entire universe is an island, while negative cosmological constant enables certain subsets to be islands.

Contribution

It demonstrates the critical role of spatial curvature in entanglement island existence within cosmology, extending understanding beyond flat models.

Findings

Positive curvature guarantees the entire universe is an island.

Subsets of a universe can be islands if the cosmological constant is sufficiently negative.

Curvature significantly affects entanglement structures in cosmological settings.

Abstract

We show that spatial curvature has a significant effect on the existence of entanglement islands in cosmology. We consider a homogeneous, isotropic universe with thermal radiation purified by a reference spacetime. Arbitrarily small positive curvature guarantees that the entire universe is an island. Proper subsets of the time-symmetric slice of a closed or open universe can be islands, but only if the cosmological constant is negative and sufficiently large in magnitude.