Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-04-04
Phys.Rev. D52 (1995) 5760-5772
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
25 pages, latex, five figures (appended as uuencoded postscript file)
Scientific paper
10.1103/PhysRevD.52.5760
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.
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