Quantum topologically massive gravity in de Sitter space

We consider three dimensional gravity with a positive cosmological constant and non-zero gravitational Chern-Simons term. This theory has inflating de Sitter solutions and local metric degrees of freedom. The Euclidean signature partition function of the theory is evaluated including both perturbative and non-perturbative corrections. The perturbative one-loop correction is computed using heat kernel techniques. The non-perturbative corrections come from gravitational instantons with non-trivial topology which can be enumerated explicitly. We compute the sum over an infinite class of geometries and show that, unlike the case of pure Einstein gravity, the partition function is finite. This demonstrates that the inclusion of non-trivial local degrees of freedom can render the sum over geometries convergent.