Abstract

Here 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$_{M}^{flat}$=0.28$^{+0.09}_{-0.08}$ (1 σ statistical) $^{+0.05}_{-0.04}$ (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$_{0}^{flat}$=14.9$^{+1.4}_{-1.1}$(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.