Locating Bound Structure in an Accelerating Universe
  Given the overwhelming evidence that the universe is currently undergoing an
accelerated expansion, the question of what are the largest gravitationally
bound structures remains. A couple of groups, Busha et al. 2003 (B03) and
Dunner et al. 2006 (D06), have attempted to analytically define these limits,
arriving at substantially different estimates due to differences in their
assumptions about the velocities at the present epoch. In an effort to locate
the largest bound structures in the universe, we selected the Aquarius (ASC),
Microscopium (MSC), Corona Borealis (CBSC), and Shapley (SSC) superclusters for
study, due to their high number density of rich Abell clusters. Simple N-body
simulations, which assumed negligible intercluster mass, were used to assess
the likelihood of these structures being gravitationally bound, and the
predictions of the models of B03 and D06 were compared with those results. We
find that ASC, and MSC contain pairs of clusters which are gravitationally
bound, A2541/A2546 and A3695/A3696 respectively, with no other structures
having a significant chance of being bound. For SSC, we find a group of five
clusters, A3554, A3556, A3558, A3560, and A3562 that are bound, with an
additional pair, A1736/A3559, having a slight chance of being bound. We find
that CBSC has no extended bound structure, contrary to the findings of Small et
al. 1998, who claim that the entire supercluster is bound. In regards to the
analytical models, we find that B03 will identify structure that is definitely
bound, but tends to underestimate the true extent of the structure, while D06
will identify all structure that is bound while overestimating its extent.
Combined, the two models can provide lower and upper limits to the extent of
bound structures so long as there are no other significant structures nearby or
no significant dark matter exterior to the clusters.
