Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology

We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological Bianchi type-I model with a minimally coupled massive scalar field φ 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 φ, 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 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of a “cosmological quantum boundary” is well defined, because, sharply beyond that boundary, the WKB approximation is no longer applicable at all. This result confirms the adequateness of the introduction of a cosmological quantum boundary in quantum cosmology.