Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology

Michael Bachmann and Hans-Jürgen Schmidt
Phys. Rev. D 62, 043515 – Published 25 July 2000
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Abstract

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of a “cosmological quantum boundary” is well defined, because, sharply beyond that boundary, the WKB approximation is no longer applicable at all.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.

  • Received 15 December 1999

DOI:https://doi.org/10.1103/PhysRevD.62.043515

©2000 American Physical Society

Authors & Affiliations

Michael Bachmann* and Hans-Jürgen Schmidt

  • Institut für Mathematik, Universität Potsdam, PF 601553, D-14415 Potsdam, Germany
  • Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany

  • *Email address: mbach@physik.fu-berlin.de
  • Email address: hjschmi@rz.uni-potsdam.de

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Vol. 62, Iss. 4 — 15 August 2000

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