Measurements of Ω and Λ from 42 High-Redshift Supernovae

We report measurements of the mass density, Ω<SUB>M</SUB>, and cosmological-constant energy density, Ω<SUB>Λ</SUB>, 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 Calán/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 0.8Ω<SUB>M</SUB>-0.6Ω<SUB>Λ</SUB>~-0.2+/-0.1 in the region of interest (Ω<SUB>M</SUB><~1.5). For a flat (Ω<SUB>M</SUB>+Ω<SUB>Λ</SUB>=1) cosmology we find Ω<SUP>flat</SUP><SUB>M</SUB>=0.28<SUP>+0.09</SUP><SUB>-0.08</SUB> (1 σ statistical) <SUP>+0.05</SUP><SUB>-0.04</SUB> (identified systematics). The data are strongly inconsistent with a Λ=0 flat cosmology, the simplest inflationary universe model. An open, Λ=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(Λ>0)=99%, including the identified systematic uncertainties. The best-fit age of the universe relative to the Hubble time is t<SUP>flat</SUP><SUB>0</SUB>=14.9<SUP>+1.4</SUP><SUB>-1.1</SUB>(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 Calán/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.