A de Sitter Farey Tail

Understand

We consider quantum Einstein gravity in three dimensional de Sitter space.

• The Euclidean path integral is formulated as a sum over geometries, including both perturbative loop corrections and non-perturbative instanton corrections coming from geometries with non-trivial topology.
• These non-trivial geometries have a natural physical interpretation.
• Conventional wisdom states that the sphere is the unique Euclidean continuation of de Sitter space.