Exact quantum states for the diagonal Bianchi type IX model with negative cosmological constant

Robert Paternoga and Robert Graham
Phys. Rev. D 54, 4805 – Published 15 October 1996
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Abstract

Quantum states of the diagonal Bianchi type IX model with negative cosmological constant Λ are obtained by transforming the Chern-Simons solution in Ashtekar's variables to the metric representation. We apply our method developed earlier for Λ>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 with the case of positive cosmological constant, this particular solution neither satisfies the semiclassical no-boundary condition, nor does the special initial condition it picks out for 0 evolve into a classically interpretable universe.

  • Received 20 May 1996

DOI:https://doi.org/10.1103/PhysRevD.54.4805

©1996 American Physical Society

Authors & Affiliations

Robert Paternoga and Robert Graham

  • Fachbereich Physik, Universität-Gesamthochschule Essen, 45117 Essen, Germany

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Issue

Vol. 54, Iss. 8 — 15 October 1996

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