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We report on the cosmological parameters derived from observations with the Cosmic Background Imager (CBI), covering 40 square degrees and the multipole range 300 <~ l <~ 3500. These unique, high-resolution observations show the seeds that gave rise to clusters of galaxies and also show damping in the power spectrum to l ~ 2000. Because the observations extend to much higher l the CBI results provide information complementary to that probed by the BOOMERANG, DASI, and MAXIMA experiments. When the CBI observations are used in combination with those from COBE-DMR, we find evidence for a flat universe, Omega (tot) =0. 99 +/- 0. 12 (1-sigma), a power law index of primordial fluctuations, nₛ = 1. 05 (-0. 08, +0. 09), and densities in cold dark matter, Omega (cdm) h² = 0. 17 (-0. 06, +0. 08), and baryons, Omega (b) h² = 0. 022 (-0. 009, +0. 15). With the addition of large scale structure priors the Omega (cdm) h² value is sharpened to 0. 12 (-0. 03, +0. 03), and we find Omega (Lambda) = 0. 64 (-0. 14, +0. 11). In the l < 1000 overlap region with the BOOMERANG, DASI, and MAXIMA experiments, the agreement between these four experiments is excellent, and we construct optimal power spectra in the CBI bands which demonstrate this agreement. We derive cosmological parameters for the combined CMB experiments and show that these parameter determinations are stable as we progress from the weak priors using only CMB observations and very broad restrictions on cosmic parameters, through the addition of information from large scale structure surveys, Hubble parameter determinations and Supernova-1a results. abridged
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