Enhanced instability of de Sitter space in Einstein-Gauss-Bonnet gravity

We show that the addition of a topological Gauss-Bonnet term to the gravitational action can greatly increase the instability of four-dimensional de Sitter space by favoring the nucleation of black holes. The pair-production rate given by the Euclidean action for the instanton takes the form $\exp (\Delta S)$ where $S$ is the entropy in Einstein-Gauss-Bonnet theory. The coefficient of the Gauss-Bonnet term in the action sets a stability bound on the curvature of empty de Sitter space. For that coefficient in the low-energy effective action of heterotic string theory, the maximal curvature of de Sitter space is, in general, much lower than the Planck scale.