Running gravitational coupling

This post is a bit late. Mohamed Anber and I have written a paper that provides counter-examples to the idea that there is a running gravitational coupling. Here is the link. We feel that this is a crucial rebuttal to the idea of a running gravitational coupling in the perturbative region. If this problem extends past the Planck scale, then it would seem that there would be problems for the idea of Asymptotic Safety.