Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1995-04-25
Class.Quant.Grav. 13 (1996) 921-942
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
34 pages, LaTeX, no figures
Scientific paper
10.1088/0264-9381/13/5/012
Using the concept of real tunneling configurations (classical signature change) and nucleation energy, we explore the consequences of an alternative minimization procedure for the Euclidean action in multiple-dimensional quantum cosmology. In both standard Hartle-Hawking type as well as Coleman type wormhole-based approaches, it is suggested that the action should be minimized among configurations of equal energy. In a simplified model, allowing for arbitrary products of spheres as Euclidean solutions, the favoured space-time dimension is 4, the global topology of spacelike slices being ${\bf S}^1 \times {\bf S}^2$ (hence predicting a universe of Kantowski-Sachs type). There is, however, some freedom for a Kaluza-Klein scenario, in which case the observed spacelike slices are ${\bf S}^3$. In this case, the internal space is a product of two-spheres, and the total space-time dimension is 6, 8, 10 or 12.
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