On 4-dimensional Lorentz-structures, Dark energy and Exotic smoothness

Abstract

Usually, the topology of a 4-manifolds $M$ is restricted to admit a global hyperbolic structure $\Sigma \times \mathbb{R}$. The result was obtained by using two conditions: existence of a Lorentz structure and causality (no time-like closed curves). In this paper we study the influence of the smoothness structure to show its independence of the two conditions. Then we obtain the possibility for a topology-change of the 3-manifold $\Sigma$ keeping fix its homology. We will study the example $S^3\times \mathbb{R}$ with an exotic differential structure more carefully to show some implications for cosmology. Especially we obtain an interpretation of the transition in topology as dark energy.

7 pages, no figures, PACS 04.20.Gz, 98.80.Jk, 95.36.+x an obvious error in the notation of the hyperbolic 3-manifold was fixed

References in corpus (1)

• The optimal phase of the generalised Poincare dodecahedral space hypothesis implied by the spatial cross-correlation function of the WMAP sky maps