  In this paper, we construct and study solutions of Einstein's equations in
vacuum with a positive cosmological constant which can be considered as
inhomogeneous generalizations of the Nariai cosmological model. Similar to this
Nariai spacetime, our solutions are at the borderline between gravitational
collapse and de-Sitter-like exponential expansion. Our studies focus in
particular on the intriguing oscillatory dynamics which we discover. Our
investigations are carried out both analytically (using heuristic mode analysis
arguments) and numerically (using the numerical infrastructure recently
introduced by us).
