Dark-energy wormholes in generalized Kaluza–Klein gravity

This paper discusses traversable wormholes in a dark-energy setting by starting with a model due to Sung-Won Kim. This model, based on the Friedmann–Lemaître–Robertson–Walker model, is combined with a generalized Kaluza–Klein model. It is well known that phantom dark energy can in principle support traversable wormholes due to the violation of the null energy condition (NEC), a necessary condition for holding a wormhole open. Since the phantom divide constitutes a serious barrier, we retain the dark-energy assumption \(a''(t)>0\) $a^{\prime \prime }(t)>0$ but stay below the phantom divide. To show that the violation of the NEC can only come from the fifth dimension requires a careful analysis of the scale factor a(t). While needed in the overall model, certain 1-forms lack this scale factor since the extra dimension, often assumed to be compactified, would not be affected by the cosmological expansion. The result is a viable wormhole model of the Sung-Won-Kim type. Our main conclusion involves Morris–Thorne wormholes: due to the Kaluza–Klein gravity, we obtain a valid wormhole solution without crossing the phantom divide.