Future Island Universes in a Background Universe Accelerated by Cosmological Constant and by Quintessence

We study bound object formation in a background universe accelerated by cosmological constant and by quintessence. If the acceleration lasts forever, due to the existence of event horizon, one would have naively expected the universe to approach a state of cold death. 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. In the case with cosmological constant ($\Lambda$CDM cosmology) the condition of forming mini-universe is that the ratio of present density parameters $\Omega_{i}^0/\Omega_\Lambda$ ought to be larger than a critical value 3.63. Such mini-universes typically weigh less than $2\times 10^{14}$ solar masses, with the lighter ones having tight and compact configurations. In the case with quintessence, the final ratio $\Omega_i/\Omega_q$ of a mini-universe is found to be always larger than $w_q^2-w_q$, where $w_q$ is the equation of state parameter.