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

Jorma Louko
Phys. Rev. D 51, 586 – Published 15 January 1995
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Abstract

The Chern-Simons functional SCS is an exact solution to the Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero cosmological constant. In this paper we consider SCS in Bianchi type IX cosmology with S3 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–NUT–de Sitter metrics. For a nonzero cosmological constant, exp(iSCS) 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

Authors & Affiliations

Jorma Louko

  • Department of Physics, University of Wisconsin(enMilwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201

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Vol. 51, Iss. 2 — 15 January 1995

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