Abstract
We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological Bianchi type-I model with a minimally coupled massive scalar field $\ensuremath{\varphi}$ as the source by generalizing the calculation of Lukash and Schmidt [Astron. Nachr. 309, 25 (1988)]. Contrary to other approaches we allow strong anisotropy. Combining analytical and numerical methods, we apply an adiabatic approximation for $\ensuremath{\varphi},$ and as a new feature we find a period-doubling bifurcation. This bifurcation takes place near the cosmological quantum boundary, i.e., the boundary of the quasiclassical region with an oscillating $\ensuremath{\psi}$ function where the WKB approximation is good. The numerical calculations suggest that such a notion of a ``cosmological quantum boundary'' is well defined, because, sharply beyond that boundary, the WKB approximation is no longer applicable at all. This result confirms the adequateness of the introduction of a cosmological quantum boundary in quantum cosmology.
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