Constraints on the Energy Content of the Universe from a Combination of Galaxy Cluster Observables

We demonstrate that constraints on cosmological parameters from the distribution of clusters as a function of redshift (dN/dz) are complementary to accurate angular diameter distance (DA) measurements to clusters, and their combination significantly tightens constraints on the energy density content of the Universe. The number counts can be obtained from X–ray and/or SZ (Sunyaev-Zel’dovich effect) surveys, and the angular diameter distances can be determined from deep observations of the intra-cluster gas using their thermal bremsstrahlung X–ray emission and the SZ effect. We combine constraints from simulated cluster number counts expected from a 12 deg2 SZ cluster survey and constraints from simulated angular diameter distance measurements based on the X-ray/SZ method assuming a statistical accuracy of 10% in the angular diameter distance determination of 100 clusters with redshifts less than 1.5. We find that Ωm can be determined within about 25%, ΩΛ within 20%, and w within 16%. We show that combined dN/dz + DA constraints can be used to constrain the different energy densities in the Universe even in the presence of a few percent redshift dependent systematic error in DA. We also address the question of how best to select clusters of galaxies for accurate diameter distance determinations. We show that the joint dN/dz + DA constraints on cosmological parameters for a fixed target accuracy in the energy density parameters are optimized by selecting clusters with redshift upper cut–offs in the range 0.5<∼ z <∼1. Subject headings: cosmological parameters – cosmology: theory – galaxies:clusters: general