Constraints on Omega_m, Omega_L, and Sigma_8, from Counts of Galaxy Clusters

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Abstract
We show that the counts of galaxy clusters in future deep cluster surveys can place strong constraints on the matter density, Omega_m, the vacuum energy density, Omega_L, and the normalization of the matter power spectrum, sigma_8. Degeneracies between these parameters are different from those in studies of either high--redshift type Ia Supernovae (SNe), or cosmic microwave background (CMB) anisotropies. This complementarity will allow joint constraints on parameters with improved accuracy. Using a mass threshold for cluster detection expected to be typical for upcoming SZE surveys, we find that constraints on Omega_m and sigma_8 at the level of roughly 5% or better can be expected, assuming redshift information is known at least to z=0.5. Without information past this redshift, Omega_L is constrained to 25%. With complete redshift information, deep (M_{lim}= 10^{14}h^{-1}{M_\odot}), relatively narrow ($\sim 12 {\rm deg}^2$) surveys, can further constrain Omega_L to an accuracy of 15%, while large-area surveys such as PLANCK or large ground-based bolometer arrays could measure Omega_L to a precision of 4% or better.

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