Cobordism Effects in the Regge Calculus Approach to Quantum Cosmology

Abstract

We study the ground state wave function for a universe which is topologically a lens space within the Regge calculus approach. By restricting the four dimensional simplicial complex to be a cone over the boundary lens space, described by a single internal edge length, and a single boundary edge length, one can analyze in detail the analytic properties of the action in the space of complex edge lengths. The classical extrema and convergent steepest descent contours of integration yielding the wave function are found. Both the Hartle-Hawking and Linde-Vilenkin type proposals are examined and, in all cases, we find wave functions which predict Lorentzian oscillatory behaviour in the late universe. A factorization property of topology changing amplitudes within a restricted edge length class of cone type complexes is established. The behaviour of the results under subdivision of the boundary universe is also presented.

25 pages, latex, five figures (appended as uuencoded postscript file)

References in corpus (4)

• Simplicial Quantum Gravity
• Generalized Sums over Histories for Quantum Gravity I. Smooth Conifolds
• Generalized Sums over Histories for Quantum Gravity II. Simplicial Conifolds
• Simplicial Quantum Gravity

Cited by in corpus (6)

• Complex, Lorentzian, and Euclidean simplicial quantum gravity: numerical methods and physical prospects
• Simplicial minisuperspace models in the presence of a scalar field
• Truly Lorentzian quantum cosmology
• Anisotropic simplicial minisuperspace model
• Simplicial minisuperspace models in the presence of a massive scalar field with arbitrary scalar coupling
• A Closed Contour of Integration in Regge Calculus