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

Abstract

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

9 pages, REVTeX v3.0. (One reference added.)

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Cited by in corpus (4)

• Physical states of Bianchi type IX quantum cosmologies described by the Chern-Simons functional
• The exact cosmological solution to the dynamical equations for the Bianchi IX model
• Bibliography of publications related to Classical and Quantum Gravity in terms of Connection and Loop Variables
• Particles, Forces and the Early Universe