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 cos mological constant ii are obtained by transforming the Chem Simons sol ution in Ashtekar's variables to the metric representation. We apply o ur method developed earlier for Lambda>0 and obtain five linearly inde pendent solutions by using the complete set of topologically inequival ent integration contours in the required generalized Fourier transform ation. A caustic in minisuperspace separates two Euclidean regimes at small and large values of the scale parameter from a single classicall y interpretable Lorentzian regime in between, corresponding to the fac t that classically these model universes recollapse. Just one particul ar solution out of the five we find gives a normalizable probability d istribution 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 th e special initial condition it picks out for h-->0 evolve into a class ically interpretable universe.