According to Gibbons and Hawking the entropy of a dS universe is encoded in the Euclidean gravitational path integral over compact manifolds with dominant sphere saddle. In this talk I will report on recent work in which we explicitly calculate this gravitational path integral in two spacetime dimensions. Whereas the Euclidean two-dimensional gravitational path integral is in general highly fluctuating, it admits a semiclassical two-sphere saddle, if coupled to a matter CFT with either very large and positive or very large and negative central charge. I will discuss the two-sphere partition function for both cases. In the latter case, choosing the CFT to be the non-unitary (2,2m-1) minimal models, I will also discuss the compact higher genus expansion of the gravitational path integral and its conjectured completion in terms of a random matrix integral. This could provide hints and constraints for a possible microscopic theory of a two-dimensional de Sitter universe.

https://princeton.zoom.us/j/97195348538?pwd=bEhjczRmbnNIZjNydFpYQXN0bXZWQT09