Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-12-16
Phys.Rev. D62 (2000) 043515
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Latest update of the paper at http://www.physik.fu-berlin.de/~mbach/publics.html#6
Scientific paper
10.1103/PhysRevD.62.043515
We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological model of Bianchi type I with a minimally coupled massive scalar field $\phi$ as source by generalizing the calculation of Lukash and Schmidt [1]. Contrarily to other approaches we allow strong anisotropy. Combining analytical and numerical methods, we apply an adiabatic approximation for $\phi$, and as 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 oscillating $\psi$-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 more applicable at all. This result confirms the adequateness of the introduction of a cosmological quantum boundary in quantum cosmology.
Bachmann Michael
Schmidt Hans-Jürgen
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