Some Thoughts on the Quantum Theory of de Sitter Space

TL;DR

This paper discusses the quantum theory of de Sitter space, emphasizing its finite state nature, the implications for measurement and ambiguity, and presents a toy model illustrating these concepts.

Contribution

It introduces the idea that the quantum theory of de Sitter space has a finite number of states and explores the resulting measurement limitations and mathematical ambiguities.

Findings

Finite states in de Sitter quantum theory imply measurement constraints.

Universal class of theories yield same local measurement results.

Different theories predict varied behaviors on Poincare recurrence time.

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.