Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology

Abstract

We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological model of Bianchi type I with a minimally coupled massive scalar field $ϕ$ 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 $ϕ$, 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 $ψ$-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.