Quantum gravity on dS₃

We study quantum gravity on dS₃ using the Chern–Simons formulation of three-dimensional gravity. We derive an exact expression for the partition function for quantum gravity on dS₃ in a Euclidean path integral approach. We show that the topology of the space relevant for studying de Sitter entropy is a solid torus. The quantum fluctuations of de Sitter space are sectors of configurations of point masses taking a discrete set of values. The partition function gives the correct semiclassical entropy. The sub-leading correction to the entropy is logarithmic in horizon area, with a coefficient −1. We discuss this correction in detail, and show that the sub-leading correction to the entropy from the dS/CFT correspondence agrees with our result. A comparison with the corresponding results for the AdS₃ BTZ black hole is also presented.