Future island universes in a background universe accelerated by a cosmological constant and by quintessence

We study bound object formation in a background universe accelerated bycosmological constant and by quintessence. If the acceleration lasts forever,due to the existence of event horizon, one would have naively expected theuniverse to approach a state of cold death. However, we find that many localregions in the universe can in fact be protected by their own gravity to formmini-universes, provided that their present matter densities exceed somecritical value. In the case with cosmological constant ($\Lambda$CDM cosmology)the condition of forming mini-universe is that the ratio of present densityparameters $\Omega_{i}^0/\Omega_\Lambda$ ought to be larger than a criticalvalue 3.63. Such mini-universes typically weigh less than $2\times 10^{14}$solar masses, with the lighter ones having tight and compact configurations. Inthe case with quintessence, the final ratio $\Omega_i/\Omega_q$ of amini-universe is found to be always larger than $w_q^2-w_q$, where $w_q$ is theequation of state parameter.Comment: RevTex 21 pages including 3 figures. Title modified and major changes in the text by extending the discussions to include bound object formation in quintessence models. Version to appear in PR