Cosmological Implications of the Bima 30 Ghz Sunyaev-zel’dovich Effect Galaxy Cluster Survey

We explore the cosmological implications of 7 deep survey fields observed at the Berkeley-IllinoisMaryland Association (BIMA) Array with 30 GHz receivers. These observations probe the Cosmic Microwave Background anisotropy on scales corresponding to l ∼ 5500, and an earlier analysis of these data detected no galaxy clusters. We use numerical cluster simulations and mock observations to characterize the cluster detection efficiency for each of the BIMA fields. With these detection efficiencies we derive constraints on the cosmological parmaters ΩM and σ8, ruling out those models which overproduce galaxy clusters. Using only these seven BIMA fields, we calculate a 2σ upper limit of σ8 < 1.00Ω −0.43ΩM−0.22 M for flat models with 0.1 ≤ ΩM ≤ 1. When the power spectrum of density fluctuations is COBE normalized, we find ΩM < 0.63 at 95% confidence level for flat models. This constraint includes our estimate of the large uncertainties in the SZE flux–virial mass relationship as well as published uncertainties in the Hubble parameter, the COBE power spectrum normalization and the primordial power spectrum index. In addition, we account for the effects of sample variance. Thus, we conclude that the non–detections are to be expected in a low ΩM universe, given the sensitivity and solid angle of the deepest SZE survey to date. Subject headings: cosmology: observation – galaxies: clusters – cosmic microwave background