Measurements of Ω and Λ from 42 high-redshift supernovae

We report measurements of the mass density, Omega(M), and cosmological-constant energy density, Omega(Lambda), of the universe based on the analysis of 42 type Ia supernovae discovered by the Supernova Cosmology Project. The magnitude-redshift data for these supernovae, at redshifts between 0.18 and 0.83, are fitted jointly with a set of supernovae from the Calan/Tololo Supernova Survey, at redshifts below 0.1, to yield values for the cosmological parameters. All supernova peak magnitudes are standardized using a SN Ia light-curve width-luminosity relation. The measurement yields a joint probability distribution of the cosmological parameters that is approximated by the relation 0.8 Omega(M) - 0.6 Omega(Lambda), approximate to -0.2 +/- 0.1 in the region of interest (Omega(M) less than or similar to 1.5). For a flat (Omega(M) + Omega(Lambda) = 1) cosmology we find Omega(M)(flat) = 0.28(-0.08)(+0.09) (1 sigma statistical)(-0.04)(+0.05) (identified systematics). The data are strongly inconsistent with a Lambda = 0 flat cosmology, the simplest inflationary universe model. An open, Lambda = 0 cosmology also does not fit the data well: the data indicate that the cosmological constant is nonzero and positive, with a confidence of P(Lambda > 0)= 99%, including the identified systematic uncertainties. The best-fit age of the universe relative to the Hubble time is t(0)(flat) = 14.9(-1.1)(+1.4)(0.63/h) Gyr for a flat cosmology. The size of our sample allows us to perform a variety of statistical tests to check for possible systematic errors and biases. We find no significant differences in either the host reddening distribution or Malmquist bias between the low-redshift Calan/Tololo sample and our high-redshift sample. Excluding those few supernovae that are outliers in color excess or fit residual does not significantly change the results. The conclusions are also robust whether or not a width-luminosity relation is used to standardize the supernova peak magnitudes. We discuss and constrain, where possible, hypothetical alternatives to a cosmological constant.