### Abstract

The evolution of the cluster mass function and the cluster correlation function from z = 0 to 3 is determined using ∼106 clusters obtained from high-resolution simulations of the current best-fit ACDM cosmology (Ω_{m} = 0.27, σ_{8} = 0.84, h = 0.7). The results provide predictions for comparisons with future observations of high-redshift clusters. A comparison of the predicted mass function of low-redshift clusters with observations from early Sloan Digital Sky Survey data and the predicted abundance of massive distant clusters with observational results favor a slightly larger amplitude of mass fluctuations (σ_{8} ∼ 0.9) and lower density parameter (Ω_{m} ∼ 0.2); these values are consistent within 1 σ with the current observational and model uncertainties. The cluster correlation function strength increases with redshift for a given mass limit; the clusters were more strongly correlated in the past because of their increasing bias with redshift - the bias reaches b ∼ 100 at z = 2 for M > 5 × 10^{13} h^{-1} M_{⊙} clusters. The richness-dependent cluster correlation function, represented by the correlation scale versus cluster mean separation relation, R_{0}-d, is generally consistent with observations. This relation can be approximated as R_{0} = 1.7d^{0.6} h^{-1} Mpc for d ∼ 20-60 h ^{-1} Mpc. The R_{0}-d relation exhibits surprisingly little evolution with redshift for z < 2; this finding can provide a new test of the current ACDM model when compared with future observations of high-redshift clusters.

Original language | English (US) |
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Pages (from-to) | 1-6 |

Number of pages | 6 |

Journal | Astrophysical Journal |

Volume | 622 |

Issue number | 1 I |

DOIs | |

State | Published - Mar 20 2005 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

- Cosmological parameters
- Cosmology: observations
- Cosmology: theory
- Dark matter galaxies: clusters: general
- Large-scale structure of universe

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## Cite this

*Astrophysical Journal*,

*622*(1 I), 1-6. https://doi.org/10.1086/428114