  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-Lemaitre-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
$a''(t)>0$ 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 complete
wormhole solution without crossing the phantom divide.
