Relation between the Chern-Simons functional and the no-boundary proposal

We study classical solutions generated by the Chern-Simons functional in general relativity with a cosmological constant. We assume the background geometry to be a Friedmann-Robertson-Walker universe. We show that the Chern-Simons functional does not give regular solutions for generic small perturbations of the geometry. Hence the Chern-Simons wave function is not related to the Hartle-Hawking state as suggested by Louko.