Dimensionality, topology, energy, the cosmological constant and signature change

Abstract

Using the concept of real tunnelling 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 spacetime dimension is 4, the global topology of spacelike slices being (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 . In this case, the internal space is a product of 2-spheres, and the total spacetime dimension is 6, 8, 10 or 12.