We explore the cosmological implications of seven deep survey fields observed at the Berkeley-Illinois-Maryland 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 via the Sunyaev-Zeldovich effect (SZE). 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 parameters ΩM and σ8, ruling out those models that overproduce galaxy clusters. Using only these seven BIMA fields, we calculate a 2 σ upper limit of σ8 1.00Ω 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, given the sensitivity and solid angle of the deepest SZE survey to date, we conclude that no cluster detections were to be expected in a low-ΩM universe. Because of the redshift-independent nature of the SZE, our constraint is driven by the absence of sufficiently massive clusters in the redshift range 0.5 ≤ z ≤ 1, making this analysis quite different and complementary to the deepest existing X-ray cluster survey analyses.
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