Constraints on Ωm, ΩΛ, and σ8 from galaxy cluster redshift distributions

We show that the number and redshift distribution of galaxy clusters in future deep cluster surveys can place strong constraints on the matter density, Ωm, the vacuum energy density, ΩΛ, and the normalization of the matter power spectrum, σ8. Degeneracies between these parameters are different from those in studies of either high-redshift Type Ia supernovae or cosmic microwave background anisotropies. Using a mass threshold for cluster detection expected to be typical for upcoming Sunyaev-Zeldovich effect surveys, we find that constraints on Ωm and σ8 at the level of roughly 5% or better can be expected, assuming redshift information is known at least to z ~ 0.5 and in the absence of significant systematic errors. Without information past this redshift, ΩΛ is constrained to 25%. With complete redshift information, deep (Mlim ~ 1014 h-1 M☉), relatively small solid angle (~12 deg 2) surveys can further constrain ΩΛ to an accuracy of ~15%, while large solid angle surveys with ground-based, large-format bolometer arrays could measure ΩΛ to a precision of ~4% or better.