Measurements of Omega and Lambda from 42 high-redshift supernovae

We report measurements of the mass density, Omega(M), and cosmological-cons tant energy density, Omega(Lambda), of the universe based on the analysis o f 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 Su pernova Survey, at redshifts below 0.1, to yield values for the cosmologica l parameters. All supernova peak magnitudes are standardized using a SN Ia light-curve width-luminosity relation. The measurement yields a joint proba bility 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 fla t (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). T he data are strongly inconsistent with a Lambda = 0 flat cosmology, the sim plest 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 th e identified systematic uncertainties. The best-fit age of the universe rel ative 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 s tatistical tests to check for possible systematic errors and biases. We fin d no significant differences in either the host reddening distribution or M almquist bias between the low-redshift Calan/Tololo sample and our high-red shift sample. Excluding those few supernovae that are outliers in color exc ess or fit residual does not significantly change the results. The conclusi ons are also robust whether or not a width-luminosity relation is used to s tandardize the supernova peak magnitudes. We discuss and constrain, where p ossible, hypothetical alternatives to a cosmological constant.