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

Quantum states of the diagonal Bianchi type IX model with negative cosmological constant [Formula presented] are obtained by transforming the Chern-Simons solution in Ashtekar's variables to the metric representation. We apply our method developed earlier for [Formula presented] 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 [Formula presented] evolve into a classically interpretable universe. © 1996 The American Physical Society.