It's not an assumption, it's a derived result. Aside from the papers suggested by Spiff, see Future Island Universes in a Background Universe Accelerated by Cosmological Constant and by Quintessence, Tzihong Chiueh & Xiao-Gang He, Physical Review D, 65, paper no. 123518. The authors conclude, as stated in the abstract, ..."However, we find that many local regions in the universe can in fact be protected by their own gravity to form mini-universes, provided that their present matter densities exceed some critical value. Furthermore, they conclude in the paper that our own Local Group of galaxies will be one of their "absolutely stable" mini-universes.

This is a result derived from the physics of cosmology, and is not an assumption. If general relativity, and our understanding of the physics of an accelerated universe, are correct, then it will be so.