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

TL;DR

This paper investigates quantum cosmology models using an alternative Euclidean action minimization, predicting a preferred 4D universe with specific topologies and exploring higher-dimensional scenarios with different topologies.

Contribution

It introduces a new minimization approach for Euclidean action in quantum cosmology, leading to specific predictions about the universe's dimension and topology.

Findings

Favored 4D universe with ${\bf S}^1 \times {\bf S}^2$ topology

Higher-dimensional scenarios with ${\bf S}^3$ slices and product of two-spheres

Predictions include universe dimensions 4, 6, 8, 10, or 12

Abstract

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.