Aspects of black hole and cosmological horizons

We discuss the need for calculable observables in de Sitter and suggest using known results in Chern-Simons theory to relate the Euclidean physics of the gravitational path integral to the Lorentzian physics of a single static patch. We examine Chern-Simons theory on the manifold DR, which we argue is related to the static patch of de Sitter. We then compute the entropy of its edge mode theory, and compare the result to the entropy found from the partition function on S3, which is related to Euclidean de Sitter. Using this method, we make progress in understanding the entanglement entropy between distantly separated regions of de Sitter. The benefit of using Chern-Simons theory is its semiclassical equivalence to 3D gravity. The examples we study include an abelian complexified Chern-Simons theory toy model of problem, and we find that by complexifying the contour of integration in the edge mode theory, we arrive at the result that comes from the three-sphere partition function. We extend this discussion to three-dimensional gravity with a positive cosmological constant and also comment on the relation to the AdS_4/CFT_3 correspondence.