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

The Chern-Simons functional SCS is an exact solution to the AshtekarHamilton-Jacobi equation of general relativity with a nonzero cosmological constant. In this paper we consider SCS in Bianchi type IX cosmology with S spatial surfaces. We show that among the classical solutions generated by SCS, 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-NUTde Sitter metrics. For a nonzero cosmological constant, exp(iSCS) therefore provides a semiclassical estimate to the Bianchi IX no-boundary wave function in Ashtekar’s variables. Pacs: 04.60.Kz, 04.60.Ds, 04.60.Gw Typeset using REVTEX