Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1996-05-17
Phys.Rev. D54 (1996) 4805-4812
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
10 pages, Revtex, 8 figures included, submitted to Phys. Rev. D
Scientific paper
10.1103/PhysRevD.54.4805
Quantum states of the diagonal Bianchi type IX model with negative cosmological constant $\Lambda$ are obtained by transforming the Chern-Simons solution in Ashtekar's variables to the metric representation. We apply our method developed earlier for $\Lambda>0$ and obtain five linearly independent solutions by using the complete set of topologically inequivalent integration contours in the required generalized Fourier-transformation. A caustic in minisuperspace separates two Euclidean regimes at small and large values of the scale parameter from a single classically interpretable Lorentzian regime in between, corresponding to the fact that classically these model-Universes recollapse. Just one particular solution out of the five we find gives a normalizable probability distribution on both branches of the caustic. However, in contrast to the case of positive cosmological constant, this particular solution neither satisfies the semi-classical no-boundary condition, nor does the special initial condition it picks out for $\hbar \to 0$ evolve into a classically interpretable Universe.
Graham Robert
Paternoga Robert
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