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 (D-A) 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 Sunyaev-Zel'dovich (SZ) effect surveys, and the angular diameter distances can be determined from deep observations of the intracluster gas using its thermal bremsstrahlung X-ray emission and the SZ effect. We combine constraints from simulated cluster number counts expected from a 12 deg(2) 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 Omega(m) can be determined within about 25%, Omega(Lambda) within 20%, and w within 16%. We show that combined dN/dz + D-A 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 D-A. 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 + D-A constraints on cosmological parameters for a fixed target accuracy in the energy density parameters are optimized by selecting clusters with redshift upper cutoffs in the range 0.5 less than or similar to z less than or similar to 1.