Semiclassical expanding discrete space-times

Given the close ties between general relativity and geometry one might reasonably expect that quantum effects associated with gravitation might also be tied to the geometry of space-time, namely, to some sort of discreteness in space-time itself. In particular we suppose space-time to consist of a discrete lattice of points rather than the usual continuum. Since astronomical evidence seems to suggest that the universe is expanding, we also demand that the lattice is expanding. Some of the implications of such a model are that the proton should presently be stable, and the universe should be closed although the mechanism for closure is quantum mechanical.