Cosmological Constraints from a 31 GHz Sky Survey with the Sunyaev-Zel'dovich Array

We present the results of an analysis of 4.4 deg(2) selected from a 6.1 deg(2) survey for clusters of galaxies via their Sunyaev-Zel'dovich effect at 31 GHz. From late 2005 to mid 2007, the Sunyaev-Zel'dovich Array observed four fields of roughly 1.5 deg(2) each. One of the fields shows evidence for significant diffuse Galactic emission, and is therefore excised from this analysis. We estimate the cluster detectability for the survey using mock observations of simulations of clusters of galaxies and determine that, at intermediate redshifts (z similar to 0.8), the survey is 50% complete to a limiting mass (M-200 (rho) over bar) of similar to 6.0 x 10(14) M-circle dot, with the mass limit decreasing at higher redshifts. We detect no clusters at a significance greater than five times the rms noise level in the maps, and place an upper limit on sigma(8), the amplitude of mass density fluctuations on a scale of 8 h(-1) Mpc, of 0.84 + 0.04 + 0.04 at 95% confidence, where the first uncertainty reflects an estimate of additional sample variance due to non-Gaussianity in the distribution of clusters and the second reflects calibration and systematic effects. This result is consistent with estimates from other cluster surveys and cosmic microwave background anisotropy experiments.