Some Thoughts on the Quantum Theory of de Sitter Space

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.