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In this article, we extend a construction of 6 to obtain a large class of vacuum cosmological spacetimes that do not contain any CMC Cauchy surfaces. The allowed spatial topologies for these examples are of the form M \# M, where M is any closed, oriented, irreducible 3-manifold which is not spherical. This complements the recent results of 19, where, instead of initial data methods, global spacetime gluing arguments were used. The study of such examples is sure to yield insight into Bartnik's cosmological splitting conjecture 1.
Ling et al. (Wed,) studied this question.