Biaxial Bianchi type 9 quantum cosmology

Details Biaxial Bianchi type 9 quantum cosmology Biaxial Bianchi type 9 quantum cosmology

Apr 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990bbtq.book.....j&link_type=abstract

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Mathematics

Logic

1

Cosmology, Mathematical Models, Quantum Mechanics, Wave Functions, Integrals, Lie Groups

Scientific paper

We investigate the quantum cosmology of spatially homogeneous models with compact spatial sections admitting a u(2) isometry algebra. The metric ansatz in these models is that of Bianchi type IX with two scale factors set to be equal. We apply the Hartle-Hawking no-boundary path integral prescription and find the semi-classical contributions to the wave function. Exact formulae are obtainable for certain contributions and otherwise the limits of large and small anisotropy (for the pure vacuum case) and large spatial volume or small anisotropy (for the case with a positive cosmological constant) are considered. For the pure vacuum case we find no semiclassical components which would correspond to Lorentzian universes. For the case with a cosmological constant the Hartle-Hawking boundary conditions formally constrain one of the parameters in the Lorentzian solutions to be purely imaginary. Possible interpretations of this imaginary parameter are discussed.

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