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We explore the cosmological implications of 7 deep survey fields observed atthe Berkeley-Illinois-Maryland Association (BIMA) Array with 30 GHz receivers.These observations probe the Cosmic Microwave Background anisotropy on scalescorresponding to l=5500, and an earlier analysis of these data detected nogalaxy clusters. We use numerical cluster simulations and mock observations tocharacterize the cluster detection efficiency for each of the BIMA fields. Withthese detection efficiencies we derive constraints on the cosmologicalparmaters OmegaM and sigma8, ruling out those models which overproduce galaxyclusters. Using only these seven BIMA fields, we calculate a 2sigma upper limitof sigma8 < 1.00OmegaM**(-0.43OmegaM-0.22) for flat models with 0.1<OmegaM<1.When the power spectrum of density fluctuations is COBE normalized, we findOmegaM < 0.63 at 95% confidence level for flat models. This constraint includesour estimate of the large uncertainties in the SZE flux-virial massrelationship as well as published uncertainties in the Hubble parameter, theCOBE power spectrum normalization and the primordial power spectrum index. Inaddition, we account for the effects of sample variance. Thus, we conclude thatthe non-detections are to be expected in a low OmegaM universe, given thesensitivity and solid angle of the deepest SZE survey to date.Comment: Latex 11 pages and 6 figures, submitted to ApJ June 28, 200

Cosmological Implications of the BIMA 30 GHz Sunyaev‐Zeldovich Effect Galaxy Cluster Survey