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

TL;DR

This paper explores how exotic smoothness structures on 4-manifolds can induce topology changes in 3-manifolds, offering a novel interpretation of dark energy within cosmology.

Contribution

It demonstrates that smoothness structures can influence topology and causality independently, providing a new perspective on dark energy through topology change in cosmological models.

Findings

Exotic smooth structures can cause topology change without violating causality.

Topology change in 3-manifolds can be interpreted as dark energy.

Implications for cosmology and the understanding of dark energy.

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.