No Page curves for the de Sitter horizon

• DOI: 10.1007/jhep03(2022)040
• Publication Date: 2022-03-08T08:02:38Z
• Authors: Joshua Kames-King; Evita M. H. Verhe...; Erik P. Verlinde
• Keywords: High Energy Physics - Theory; High Energy Physics - Theory (hep-th); Nuclear and particle physics. Atomic energy. Radioactivity; 0103 physical sciences; Models of Quantum Gravity; 500; FOS: Physical sciences; QC770-798; 530; 01 natural sciences; 2D Gravity

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 $$ \mathcal{I} $$ 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 $$ \mathcal{I} $$ 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.