JT Gravity in de Sitter Space and the Problem of Time

TL;DR

This paper explores the canonical quantisation of Jackiw-Teitelboim (JT) gravity in de Sitter space, addressing the problem of time by using the dilaton as a physical clock, and finds many states satisfying physical and classical conditions.

Contribution

It demonstrates that the dilaton can serve as a satisfactory physical clock in de Sitter JT gravity and constructs numerous states meeting key physical and classical criteria.

Findings

Existence of infinitely many states with finite norm and well-defined expectation values

The dilaton effectively functions as a physical clock in this setting

Classical limit can be achieved with appropriate state restrictions

Abstract

We discuss the canonical quantisation of JT gravity in de Sitter space, following earlier work by Henneaux, with particular attention to the problem of time. Choosing the dilaton as the physical clock, we define a norm and operator expectation values for states and explore the classical limit. We find that requiring a conserved and finite norm and well-defined expectation values for operators imposes significant restrictions on states, as does the requirement of a classical limit. However, these requirements can all be met, with the dilaton providing a satisfactory physical clock. We construct several examples and analyse them in detail. We find that in fact an infinite number of states exist which meet the various conditions mentioned above.