A quantum cosmological approach to Kaluza-Klein theory and the boundary condition of 'no boundary'

Details A quantum cosmological approach to Kaluza-Klein theory and the boundary condition of 'no boundary' A quantum cosmological approach to Kaluza-Klein theory and the boundary condition of 'no boundary'

Jan 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cqgra...4...23c&link_type=abstract

Classical and Quantum Gravity (ISSN 0264-9381), vol. 4, Jan. 1, 1987, p. 23-35. Research supported by the Yukawa Foundation.

Mathematics

Logic

9

Boundary Conditions, Boundary Value Problems, Cosmology, Quantum Theory, Astronomical Models, Einstein Equations, Scalars, Wave Functions

Scientific paper

A quantum cosmological model of the Kaluza-Klein theory is investigated. The Wheeler-De Witt equation of (D + 1) dimensional gravity with a (D-4)th rank antisymmetric sensor field (ATF) is analyzed, restricting the investigation to a minisuperspace of topology R x S3 x Sn. The initial condition problem is discussed, and the boundary condition of 'no boundary' for a universe corresponding to a manifold with topology of Kaluza-Klein type is formulated. However, in the minisuperspace approximation of Kaluza-Klein theory, the definition of the boundary condition of 'no boundary' becomes obscure, and the problem is discussed. The analysis, using the WKB approximation, shows that a subclass of classical paths which contribute to the wavefunction consists of bounce solutions. Furthermore, it is found that initial values of the classical paths, leading to universes of large scale and a compactified internal space of Planck size, can be localized in a very restricted region.

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