### Abstract

We study the evolution of the cluster correlation function and its richness dependence from z = 0 to z = 3 using large-scale cosmological simulations. A standard flat LCDM model with Ω_{m} = 0.3 and, for comparison, a tilted Ω_{m} = 1 model (TSCDM) are used. The evolutionary predictions are presented in a format suitable for direct comparisons with observations. We find that the cluster correlation strength increases with redshift: high-redshift clusters are clustered more strongly (on a comoving scale) than low-redshift clusters of the same mass. The increased correlation with redshift, in spite of the decreasing mass correlation strength, is caused by the strong increase in cluster bias with redshift: clusters represent higher density peaks of the mass distribution as the redshift increases. The richness-dependent cluster correlation function, presented as the correlation scale versus cluster mean separation relation, R_{0}-d, is found to be, remarkably, independent of redshift to z ≲ 2 for LCDM and z ≲ 1 for TSCDM for a fixed correlation function slope and a cluster mass within a fixed comoving radius. The nonevolving R_{0}-d relation implies that both the comoving clustering scale and the cluster mean separation increase with redshift for the same mass clusters, so that the R_{0}-d relation remains essentially unchanged. For LCDM, this relation is R_{0}(Z) ≃ 2.6[d(z}]^{1/2} for z ≲ 2 in comoving h^{-1} Mpc scales. The TSCDM model has smaller correlation scales, as expected. Evolution in the relation is seen at z ≳ 2 for LCDM and z ≳ 1 for TSCDM, where the amplitude of the relations declines. The evolution of the R_{0}-d relation from z ∼ 0 to z ∼ 3 provides an important new tool in cosmology; it can be used to break degeneracies that exist at z ∼ 0 and provide precise determination of cosmological parameters.

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

Number of pages | 6 |

Journal | Astrophysical Journal |

Volume | 603 |

Issue number | 1 I |

DOIs | |

State | Published - Mar 1 2004 |

### 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*,

*603*(1 I), 1-6. https://doi.org/10.1086/381386