Is The Universe Infinite Or Is It Just Really Big?
  The global geometry of the universe is in principle as observable an attribute as local curvature. Previous studies have established that if the universe is wrapped into a flat hypertorus, the simplest compact space, then the fundamental domain must be at least 0.4 times the diameter of the observable universe. Despite a standard lore that the other five compact, orientable flat spaces are more weakly constrained, we find the same bound holds for all. Our analysis provides the first limits on compact cosmologies built from the identifications of hexagonal prisms. 
Janna Levin, Evan Scannapieco and Joseph Silk