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, Omega (m), the vacuum energy density, Omega (Lambda), 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 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 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 similar to 0.5 and in the absence of significant systematic errors. Without information past this redshift, Omega (Lambda) is constrained to 25%. With complete redshift information, deep (M-lim similar to 10(14) h(-1) M-.), relatively small solid angle (similar to 12 deg(2)) surveys can further constrain Omega (Lambda) to an accuracy of similar to 15%, while large solid angle surveys with ground-based, large-format bolometer arrays could measure Omega (Lambda) to a precision of similar to4% or better.