Factorization of topology changing amplitudes in the Regge calculus approach to quantum cosmology
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We study the form of topology changing amplitudes within the Regge calculus approach to four-dimensional gravity. The four-dimensional simplicial complex is chosen to be a cone over the disjoint union of a number of topologically distinct lens spaces. By restricting attention to a simplicial minisuperspace, the analytic properties of the Regge action can be identified explicitly. The classical extrema and convergent steepest descent contours defining these amplitudes are determined, and a factorization property is established. In the cases studied, we find ground state wave functions which predict Lorentzian oscillatory behaviour in the late universe.
KeywordsWave Function Regge Action Differential Geometry Disjoint Union Simplicial Complex
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