Entanglement and Chaos in De Sitter Holography: An SYK Example

TL;DR

The paper builds a framework for de Sitter holography via static-patch holography with horizon degrees of freedom acting as the fundamental holographic substrate. It reformulates entanglement and complexity concepts for dS, showing how hyperfast scrambling and hyperfast complexity growth naturally arise from horizon dynamics and the exponential interior, and provides a concrete, computable SYK-based limit that mirrors these de Sitter features. By linking scrambling, quasinormal modes, maximal slices, and inflation to a unified holographic picture, the work suggests that a high-temperature, non-k-local limit of SYK may realize a de Sitter dual and offers a path to simulate cosmological spacetimes with quantum information tools.

Abstract

Entanglement, chaos, and complexity are as important for de Sitter space as for AdS and for black holes. There are similarities and great differences between AdS and dS in how these concepts are manifested in the space-time geometry. In the first part of this paper the Ryu-Takayanagi prescription, the theory of fast scrambling, and the holographic complexity correspondence are reformulated for de Sitter space. Criteria are proposed for a holographic model to describe de Sitter space. The criteria can be summarized by the requirement that scrambling and complexity growth must be "hyperfast." In the later part of the paper I show that a certain limit of SYK is a concrete, computable, holographic model of de Sitter space. Calculations are described which support the conjecture.

Figures (12)

• Figure 1: The near horizon region of de Sitter space is approximately Rindler space. The Rindler time $\omega$ is a hyperbolic angle. The stretched horizon is the hyperbola at a distance $\rho$ from the bifurcate horizon.
• Figure 2: Penrose diagram for dS and stretched horizon
• Figure 3: A $t=0$ slice of dS and the stretched horizons shown as purple great circles. The red surface is homologous to the light blue horizon. It can be shrunk to a point.
• Figure 4: A spatial slice through dS. In the right panel the geometry of the slice is shown.
• Figure 5: The red curve represents the minimal surface lying between the two stretched horizons shown in purple. There are two such surfaces, only one of which is shown, lying right on top of the horizons.