The proposal of Vilenkin in the Bianchi-III minisuperspace model.

Details The proposal of Vilenkin in the Bianchi-III minisuperspace model. The proposal of Vilenkin in the Bianchi-III minisuperspace model.

Nov 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997jzheu..31..723c&link_type=abstract

J. Zhejiang Univ., Vol. 31, No. 6, p. 723 - 730

Mathematics

Logic

Cosmology: Bianchi Models

Scientific paper

The boundary condition of the initial universe proposed by Vilenkin (1988) was studied for Einstein gravitation with a positive cosmological constant in the minisuperspace model based on the Bianchi-III manifold. The classical equations of motion can be reduced to the motion equations of free particle in Minkowski spacetime by the special choice of local coordinate and lapse function. The Wheeler-DeWitt equation was obtained in terms of the canonical quantization approach, which is equivalent to that in the homogeneous and isotropic model of the universe. The Wheeler-DeWitt equation is also similar to the Klein-Gordon equation with a negative massive term by using the same local coordinate. We derived the single parameter and double parameter wave function by means of Vilenkin's proposal. We also found that this proposal just confined the set of solutions but could not determine solely the wave function of the universe.

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