Chern-Simons functional and the no-boundary proposal in Bianchi type IX quantum cosmology

The Chern-Simons functional S_CS is an exact solution to the Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero cosmological constant. In this paper we consider S_CS in Bianchi type IX cosmology with S³ spatial surfaces. We show that among the classical solutions generated by S_CS there is a two-parameter family of Euclidean spacetimes that have a regular NUT-type closing. When two of the three scale factors are equal, these spacetimes reduce to a one-parameter family within the Euclidean Taub-NUT-de Sitter metrics. For a nonzero cosmological constant, exp(iS_CS) therefore provides a semiclassical estimate to the Bianchi type IX no-boundary wave function in Ashtekar's variables.