Born-Infeld gravity with a unique vacuum and a massless graviton

We construct an n-dimensional Born-Infeld-type gravity theory that has the same properties as Einstein's gravity in terms of the vacuum and particle content: Namely, the theory has a unique viable vacuum (maximally symmetric solution) and a single massless unitary spin-2 graviton about this vacuum. The Born-Infeld gravity, in some sense, is the most natural, minimal generalization of Einstein's gravity with a better UV behavior and hence is a potentially less singular theory at small distances. The Gauss-Bonnet combination plays a nontrivial role in the construction of the theory. As an extreme example, we consider the infinite-dimensional limit where an interesting exponential gravity arises.