  We construct nonsingular cyclic cosmologies that respect the null energy
condition, have a large hierarchy between the minimum and maximum size of the
universe, and are stable under linearized fluctuations. The models are
supported by a combination of positive curvature, a negative cosmological
constant, cosmic strings and matter that at the homogeneous level behaves as a
perfect fluid with equation of state -1 < w < -1/3. We investigate analytically
the stability of the perturbation equations and discuss the role of parametric
resonances and nonlinear corrections. Finally, we argue that Casimir energy
contributions associated to the compact spatial slices can become important at
short scales and lift nonperturbative decays towards vanishing size. This class
of models (particularly in the static limit) can then provide a useful
framework for studying the question of the ultimate (meta)stability of an
eternal universe.
