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 [Formula Presented] ([Formula Presented]), the power law index [Formula Presented] where [Formula Presented] ([Formula Presented]), and perhaps even the Hubble parameter ([Formula Presented]). We find cluster abundances and bias are not well suited for constraining [Formula Presented] or the amplitude [Formula Presented]. We also find that without bias information [Formula Presented] and [Formula Presented] 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)|
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|State||Published - 2004|
ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)