Abstract
We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological Bianchi type-I model with a minimally coupled massive scalar field 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 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 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of a “cosmological quantum boundary” is well defined, because, sharply beyond that boundary, the WKB approximation is no longer applicable at all.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.
- Received 15 December 1999
DOI:https://doi.org/10.1103/PhysRevD.62.043515
©2000 American Physical Society