### Abstract

We use the halo model formalism to provide expressions for cluster abundances and bias, as well as estimates for the correlation matrix between these observables. Off-diagonal elements due to scatter in the mass-tracer scaling with mass are included, as are observational effects such as biases/scatter in the data, detection rates (completeness), and false detections (purity). We apply the formalism to a hypothetical volume limited optical survey where the cluster mass-tracer is chosen to be the number of satellite galaxies assigned to a cluster. Such a survey can strongly constrain σ<inf>8</inf> (Δσ<inf>8</inf> ≈ 0.05), the power law index α where 〈N<inf>gal</inf>|m〉 = (m/M<inf>1</inf>) <sup>α</sup> (Δα ≈ 0.03), and perhaps even the Hubble parameter (Δh ≈ 0.07). We find cluster abundances and bias are not well suited for constraining Ω<inf>m</inf> or the amplitude M<inf>1</inf>. We also find that without bias information σ<inf>8</inf> and α are degenerate, implying constraints on the former are strongly dependent on priors used for the latter and vice-versa. The degeneracy stems from an intrinsic scaling relation of the halo mass function, and hence it should be present regardless of the mass-tracer used in the survey.

Original language | English (US) |
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Article number | 083008 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 70 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2004 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematical Physics

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*70*(8), [083008]. https://doi.org/10.1103/PhysRevD.70.083008