  While 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 large and positive central charge. In Weyl gauge this gravity
theory is known as timelike Liouville theory, and is conjectured to be a
non-unitary two-dimensional CFT. We explore the semiclassical limit of timelike
Liouville theory by calculating the two-sphere partition function from the
perspective of the path integral to three-loop order, extending the work in
2106.01665. We also compare our result to the conjectured all-loop sphere
partition function obtained from the DOZZ formula. Since the two-sphere is the
geometry of Euclidean two-dimensional de Sitter space our discussion is tied to
the conjecture of Gibbons-Hawking, according to which the dS entropy is encoded
in the Euclidean gravitational path integral over compact manifolds.
