The Excursion Set Mass Function of Superclusters

Details The Excursion Set Mass Function of Superclusters The Excursion Set Mass Function of Superclusters

2012-01-06

arxiv.org/abs/1201.1382v1

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

32 pages, 9 figures

Scientific paper

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.

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