Seunghwan Lim, Jounghun Lee
The mass function of superclusters is derived fully analytically with the
help of the extended excursion set theory and shown to be in excellent
agreement with the numerical results from various publicly available N-body
simulation database. We introduce a new multi-dimensional barrier model in
which the formation of superclusters occurs when the initial shear eigenvalues
that perform non-Markovian random walks enter a clustering zone surrounded by
one re ecting and two absorbing barriers. The multi-dimensional barrier heights
are determined from the first order Lagrangian perturbation theory and found to
be independent of redshift and background cosmology. With the help of our
analytic model for the supercluster mass function, the relative abundance of
the rich superclusters is analytically evaluated at a given epoch and found to
be sensitive to the growth rate of the cosmic web. Our result implies that the
relative abundance of the rich superclusters at a given epoch may be useful as
a cosmological test of gravity.
View original:
http://arxiv.org/abs/1201.1382
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