Further remarks on de Sitter space, extremal surfaces, and time entanglement

We develop further the investigations by Narayan de Sitter space, extremal surfaces, and time entanglement, 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. Published by the American Physical Society 2024