De Sitter Musings

TL;DR

The article surveys the physics of asymptotically de Sitter spacetimes across classical, quantum, and semiclassical regimes, emphasizing the two-observer perspective and the challenge of defining observables inside a cosmological horizon. It develops classical initial-value and boundary-value formulations, analyzes near-horizon fluid dynamics and quasinormal modes, and reviews semiclassical phenomena such as Nariai nucleation and Coleman–De Luccia bubbles. The work then explores nonperturbative holographic approaches, including dS/CFT and static patch holography, and discusses string-theoretic constructions, open questions about de Sitter entropy, and the possible emergence of time from holographic data. Altogether, it outlines a broad program for understanding quantum gravity in de Sitter space, highlighting key open problems and potential routes to a nonperturbative formulation.

Abstract

We discuss some of the issues that arise when considering the physics of asymptotically de Sitter spacetimes, and attempts to address them. Our development begins at the classical level, where several initial value problems are discussed, and ends with several proposals for holography in asymptotically de Sitter spacetimes. Throughout the paper we give a review of some basic notions such as the geometry of the Schwarzschild-de Sitter black hole, the Nariai limit, and quantum field theory in a fixed de Sitter background. We also briefly discuss some semiclassical aspects such as the nucleation of giant black holes and the Hartle-Hawking wavefunctional. We end by giving an overview of some open questions. An emphasis is placed on the differences between a static patch observer confined to live in a thermal cavity and the metaobserver who has access to a finite region of the future boundary.

Figures (7)

• Figure 1.1: Penrose diagram of de Sitter space. The full square is given by the global patch (\ref{['global']}), with each interior point being a two-sphere. Also indicated are the future triangles (green) and the Southern static patches (red), each covering a quarter of the global space.
• Figure 1.2: Left: Penrose diagram of de Sitter space depicting the de Sitter/de Sitter patch (\ref{['dsds']}) with a constant spacial dS$_3$ slice (central red diamond) and the hyperbolic patch (\ref{['h3ds']}) with a constant time $\mathcal{H}_3$ slice (top green corner). Right: Penrose diagram of future directed planar patch (\ref{['planar']}) containing $\mathcal{I}^+$ and a constant time $\mathbb{R}^3$ slice.
• Figure 2.1: The Cauchy (left) and Tamburino-Winicour (right) boundary vale problems. The data lives on the blue lines and specifies the solution in the shaded region which is either a Cauchy spacelike slice (left) or a worldline with a null line (right).
• Figure 2.2: The Sachs double null (left) and Bondi (right) boundary vale problems. The data lives on the blue lines and specifies the solution in the shaded (red) region. The green line indicates some localized radiating source in the Bondi problem.
• Figure 3.1: Region in the $(r_+, a)$-plane allowing for smooth black hole solutions. The static patch geometry lives at the origin.