No Page Curves for the de Sitter Horizon

Abstract

We investigate the fine-grained entropy of the de Sitter cosmological horizon. Starting from three-dimensional pure de Sitter space, we consider a partial reduction approach, which supplies an auxiliary system acting as a heat bath both at future infinity and inside the static patch. This allows us to study the time-dependent entropy of radiation collected for both observers in the out-of-equilibrium Unruh-de Sitter state, analogous to black hole evaporation for a cosmological horizon. Central to our analysis in the static patch is the identification of a weakly gravitating region close to the past cosmological horizon; this is suggestive of a relation between observables at future infinity and inside the static patch. We find that in principle, while the meta-observer at future infinity naturally observes a pure state, the static patch observer requires the use of the island formula to reproduce a unitary Page curve. However, in practice, catastrophic backreaction occurs at the Page time, and neither observer will see unitary evaporation.

33 pages, 8 figures. v2: references added, minor edits. v3: as published in JHEP. Minor edits. Comments and clarifications added, regarding e.g. the static patch backreacted dilaton, and the weakly-coupled radiation region

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• Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands
• BCFT in a Black Hole Background: An Analytical Holographic Model
• Planar Black Holes in Holographic Axion Gravity: Islands, Page Times, and Scrambling Times
• An Outsider's Perspective on Information Recovery in de Sitter Space
• Defect extremal surfaces for entanglement negativity
• Island formula in Planck brane
• JT Gravity in de Sitter Space and the Problem of Time
• Bridging the static patches: de Sitter holography and entanglement
• Black Hole and de Sitter Microstructures from a Semiclassical Perspective
• Islands in Kerr-de Sitter spacetime and their flat limit
• Evolution of thermodynamic quantities on cosmological horizon in $\Lambda (t)$ model
• Entropy of Radiation with Dynamical Gravity
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• Implication of island for inflation and primordial perturbations
• Reflected Entropy and Entanglement Negativity for Holographic Moving Mirrors
• Islands in Proliferating de Sitter Spaces
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• Horizon thermodynamics and cosmological equations: A holographic-like connection between thermostatistical quantities on a cosmological horizon and in the bulk
• On the Quantum Bousso Bound in JT gravity
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• Supersymmetric $d{S}_n$ solutions for $n\ge 5$ in $D=11$ supergravity
• The quantum de Sitter root of quasi de Sitter observables: a pedagogical review
• Holography for de Sitter bubble geometries
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model