We set new constraints on a seven-dimensional space of cosmological parameters within the class of inflationary adiabatic models. We use the angular power spectrum of the cosmic microwave background measured over a wide range of ell in the first flight of the MAXIMA balloon-borne experiment (MAXIMA-1) and the low ell results from COBE/DMR. We find constraints on the total energy density of the universe, Omega=1.0^{+0.15}_{-0.30}, the physical density of baryons, Omega_{b}h^2=0.03 +/- 0.01, the physical density of cold dark matter, Omega_{cdm}h^2=0.2^{+0.2}_{-0.1}$, and the spectral index of primordial scalar fluctuations, n_s=1.08+/-0.1, all at the 95% confidence level. By combining our results with measurements of high-redshift supernovae we constrain the value of the cosmological constant and the fractional amount of pressureless matter in the universe to 0.45<Omega_Lambda<0.75 and 0.25<Omega_{m}<0.50, at the 95% confidence level. Our results are consistent with a flat universe and the shape parameter deduced from large scale structure, and in marginal agreement with the baryon density from big bang nucleosynthesis.
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