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

Jorma Louko
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Abstract

The Chern-Simons functional $S_{\rm CS}$ is an exact solution to the Ashtekar-Hamilton-Jacobi equation of general relativity with a nonzero cosmological constant. In this paper we consider $S_{\rm CS}$ in Bianchi type IX cosmology with $S^3$ spatial surfaces. We show that among the classical solutions generated by~$S_{\rm CS}$, 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, $\exp(iS_{\rm CS})$ therefore provides a semiclassical estimate to the Bianchi~IX no-boundary wave function in Ashtekar's variables.

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Jorma Louko. 1995-02-15. Chern-Simons functional and the no-boundary proposal in Bianchi IX quantum cosmology. https://doi.org/10.1103/physrevd.51.586

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