  We present a class of nonsingular, bouncing cosmologies that evade
singularity theorems through the use of vorticity in compact extra dimensions.
The vorticity combats the focusing of geodesics during the contracting phase.
The construction requires fluids that violate the null energy condition (NEC)
in the compact dimensions, where they can be provided by known stable NEC
violating sources such as Casimir energy. The four dimensional effective theory
contains an NEC violating fluid of Kaluza-Klein excitations of the higher
dimensional metric. These spacetime metrics could potentially allow dynamical
relaxation to solve the cosmological constant problem. These ideas can also be
used to support traversable Lorentzian wormholes.
