Biaxial Bianchi Type IX Quantum Cosmology

Technical Report · Sun Apr 01 04:00:00 EDT 1990

DOI:https://doi.org/10.2172/6099351· OSTI ID:6099351

Jensen, Lars Gerhard ^[1]; Louko, Jorma ^[2]; Ruback, Peter J. ^[3]

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1. Univ. of Washington, Seattle, WA (United States)
2. Univ. of Alberta, Edmonton, AB (Canada)
3. European Organization for Nuclear Research (CERN), Geneva (Switzerland)

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.

• Research Organization: Univ. of Washington, Seattle, WA (United States)
• Sponsoring Organization: USDOE; Natural Sciences and Engineering Research Council of Canada (NSERC)
• DOE Contract Number: AS06-88ER40423
• OSTI ID: 6099351
• Report Number(s): DOE/ER/40423--06-P90; CERN-TH--5618/90; ON: DE91009610
• Country of Publication: United States
• Language: English

Related Subjects

640106* -- Astrophysics & Cosmology-- Cosmology
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
COSMOLOGICAL CONSTANT
COSMOLOGICAL MODELS
COSMOLOGY
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
HAMILTON-JACOBI EQUATIONS
INTEGRALS
LIE GROUPS
MATHEMATICAL MODELS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM MECHANICS
SYMMETRY GROUPS
U GROUPS
U-2 GROUPS
WAVE FUNCTIONS