  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.
