Islands in cosmology

TL;DR

The paper develops three general conditions for the existence of quantum extremal islands in cosmology and demonstrates their interplay through concrete spacetimes. It formulates and applies the island rule to FRW and de Sitter settings, showing islands can appear near turning points in crunching universes and in 2D JT gravity models, while analyzing how an auxiliary purifying system or tensor networks encode the island region. The work highlights the tension between the Bekenstein area bound and quantum normal region constraints, connects island physics to QNEC and maximin arguments, and provides a unifying perspective linking black hole interiors and cosmological islands through holographic encoding. Tensor-network pictures reinforce the intuition that interior regions can be holographically encoded in external degrees of freedom, offering a complementary viewpoint on cosmological and black hole information in holography.

Abstract

A quantum extremal island suggests that a region of spacetime is encoded in the quantum state of another system, like the encoding of the black hole interior in Hawking radiation. We study conditions for islands to appear in general spacetimes, with or without black holes. They must violate Bekenstein's area bound in a precise sense, and the boundary of an island must satisfy several other information-theoretic inequalities. These conditions combine to impose very strong restrictions, which we apply to cosmological models. We find several examples of islands in crunching universes. In particular, in the four-dimensional FRW cosmology with radiation and a negative cosmological constant, there is an island near the turning point when the geometry begins to recollapse. In a two-dimensional model of JT gravity in de Sitter spacetime, there are islands inside crunches that are encoded at future infinity or inside bubbles of Minkowski spacetime. Finally, we discuss simple tensor network toy models for islands in cosmology and black holes.

Figures (20)

• Figure 1: A recollapsing FRW universe, with the thermal state of matter purified by an auxiliary Minkowski spacetime. We calculate the entropy of a large region $R$ in the Minkowski spacetime and find an island $I$ near the turning point of the FRW universe.
• Figure 2: Islands inside the crunching region of a 2d de Sitter model.
• Figure 3: Islands in 2d de Sitter spacetime with a Minkowski bubble and nearby crunching regions.
• Figure 4: Island $I$ in the interior of an evaporating black hole.
• Figure 5: Regions used to regulate the Bekenstein area bound. $I$ is the island, $R$ is the non-gravitational system appearing in the island formula, and $C$ is the narrow region of width $\delta$.