Some Thoughts on the Quantum Theory of de Sitter Space

TL;DR

The paper argues that quantum gravity with a positive cosmological constant $\Lambda>0$ has a compact phase space and a finite number of states, with most entropy carried by horizon degrees of freedom and only a subleading portion describable by local field theory. It introduces observer complementarity and a finite-state toy model on a fuzzy sphere to realize horizon–vacuum decomposition and a dense low-energy horizon spectrum that gives rise to the de Sitter temperature $T_{dS}$. It emphasizes measurement limits in de Sitter space, predicting a universality class of Hamiltonians that agree on all observable physics within these limits, while predicting ambiguity for Poincaré-recurrence-scale dynamics. In the $\Lambda\to 0$ limit, a Poincaré-invariant sector emerges, decoupled from the horizon dynamics and consistent with asymptotically flat scattering. These ideas aim to reconcile finite-d-state de Sitter quantum gravity with semiclassical thermodynamics and provide a framework for further modeling of horizon states.

Abstract

This is a summary of two lectures I gave at the Davis Conference on Cosmic Inflation. I explain why the quantum theory of de Sitter (dS) space should have a finite number of states and explore gross aspects of the hypothetical quantum theory, which can be gleaned from semiclassical considerations. The constraints of a self-consistent measurement theory in such a finite system imply that certain mathematical features of the theory are unmeasurable, and that the theory is consequently mathematically ambiguous. There will be a universality class of mathematical theories all of whose members give the same results for local measurements, within the {\it a priori} constraints on the precision of those measurements, but make different predictions for unmeasurable quantities, such as the behavior of the system on its Poincare recurrence time scale. A toy model of dS quantum mechanics is presented.