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 by a cosmological constant and by quintessence. If the acceleration lasts forever, due to the existence of an 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 miniuniverses, provided that their present matter densities exceed some critical value. In the case with a cosmological constant $(\Lambda$ cold dark matter cosmology), the condition for forming a miniuniverse is that the ratio of the present density parameters ${\Omega }_i^0/{\Omega }_{\Lambda }$ should be larger than a critical value $\mathrm{3.63.}$ Such miniuniverses 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 miniuniverse is found to be always larger than $w_q^2-w_q,$ where $w_q$ is the equation-of-state parameter.