Constraints on Omega(m), Omega(Lambda), and sigma(8) from galaxy cluster redshift distributions

We show that the number and redshift distribution of galaxy clusters in fut ure deep cluster surveys can place strong constraints on the matter density , Omega (m), the vacuum energy density, Omega (Lambda), and the normalizati on of the matter power spectrum, sigma (8). Degeneracies between these para meters are different from those in studies of either high-redshift Type Ia supernovae or cosmic microwave background anisotropies. Using a mass thresh old for cluster detection expected to be typical for upcoming Sunyaev-Zeldo vich 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 infor mation is known at least to z similar to 0.5 and in the absence of signific ant systematic errors. Without information past this redshift, Omega (Lambd a) is constrained to 25%. With complete redshift information, deep (M-lim s imilar to 10(14) h(-1) M-.), relatively small solid angle (similar to 12 de g(2)) surveys can further constrain Omega (Lambda) to an accuracy of simila r to 15%, while large solid angle surveys with ground-based, large-format b olometer arrays could measure Omega (Lambda) to a precision of similar to4% or better.