Abstract
The Chern-Simons functional is an exact solution to the Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero cosmological constant. In this paper we consider in Bianchi type IX cosmology with spatial surfaces. We show that among the classical solutions generated by 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() therefore provides a semiclassical estimate to the Bianchi type IX no-boundary wave function in Ashtekar’s variables.
- Received 26 August 1994
DOI:https://doi.org/10.1103/PhysRevD.51.586
©1995 American Physical Society