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No Page curves for the de Sitter horizon. (English) Zbl 1522.83071

Summary: 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 \(\mathcal{I}^+\) 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 \(\mathcal{I}^+\) 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.

MSC:

83C45 Quantization of the gravitational field
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83F05 Relativistic cosmology

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