We develop further the investigations by Narayan [de Sitter space, extremal surfaces, and time entanglement, Phys. Rev. D 107, 126004 (2023)] on de Sitter space, extremal surfaces, and time entanglement. We discuss the no-boundary de Sitter extremal surface areas as certain analytic continuations from AdS while also amounting to space-time rotations. The structure of the extremal surfaces suggests a geometric picture of the time-entanglement or pseudo-entanglement wedge. We also study some entropy relations for multiple subregions. The analytic continuation suggests a heuristic Lewkowycz-Maldacena formulation of the extremal surface areas. In the bulk, this is now a replica formulation on the Wavefunction, which suggests interpretation as pseudo-entropy. Finally, we also discuss aspects of future-past entangled states and time evolution.

• Received 9 October 2023
• Accepted 11 March 2024

DOI:https://doi.org/10.1103/PhysRevD.109.086009

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Published by the American Physical Society