Abstract
Recent works have revealed that quantum extremal islands can contribute to the fine-grained entropy of black hole radiation reproducing the unitary Page curve. In this paper, we use these results to assess if an observer in de Sitter space can decode information hidden behind their cosmological horizon. By computing the fine-grained entropy of the Gibbons-Hawking radiation in a region where gravity is weak we find that this is possible, but the observer’s curiosity comes at a price. At the same time the island appears, which happens much earlier than the Page time, a singularity forms which the observer will eventually hit. We arrive at this conclusion by studying de Sitter space in Jackiw-Teitelboim gravity. We emphasize the role of the observer collecting radiation, breaking the thermal equilibrium studied so far in the literature. By analytically solving for the backreacted geometry we show how an island appears in this out-of-equilibrium state.
Highlights
Tension between unitarity and the thermal nature of Hawking radiation is known as the information paradox
We showed that the fine-grained entropy of radiation collected in a static patch follows a Page curve which is consistent with the idea that a static observer in de Sitter space should be able to recover information that has fallen through their cosmological horizon
We studied information recovery in the static patch of de Sitter space by employing the island formula in two different two-dimensional JT gravity models with a known higher dimensional pedigree
Summary
Jackiw-Teitelboim (JT) gravity is a two-dimensional dilaton theory of gravity that can be obtained as a dimensional reduction of a higher-dimensional theory. We review some known aspects of JT gravity on a de Sitter background and consider two different models that have a distinct higher-dimensional origin. By coupling to a twodimensional conformal matter sector we construct solutions in different vacuum states and study their corresponding backreacted geometry in detail
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