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 SNe, at redshifts between 0.18 and 0.83, are fit jointly with a set of SNe from the Calan/Tololo Supernova Survey, at redshifts below 0.1, to yield values for the cosmological parameters. All SN peak magnitudes are standardized using a SN Ia lightcurve 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 ~= -0.2 +/- 0.1 in the region of interest (Omega_M <~ 1.5). For a flat (Omega_M + Omega_Lambda = 1) cosmology we find Omega_M = 0.28{+0.09,-0.08} (1 sigma statistical) {+0.05,-0.04} (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 non-zero 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 = 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 Calan/Tololo sample and our high-redshift sample. The conclusions are robust whether or not a width-luminosity relation is used to standardize the SN peak magnitudes.

The Supernova Cosmology Project has discovered over 28 supernovae (SNs) at 0.35 < z < 0.65 in an ongoing program that uses Type Ia SNs (SN Ia’s) as high-redshift distance indicators. Here we present measurements of the ratio between the locally observed and global Hubble constants, HL0/HG0, based on the first seven SNs of this high-redshift data set compared with 18 SNs at z ≤ 0.1 from the Calán/Tololo survey. If ΩM ≤ 1, then light-curve width corrected SN magnitudes yield HL0/HG0 < 1.10 (95% confidence level) in both a Λ = 0 and a flat universe. The analysis using the SN Ia’s as standard candles without a light-curve width correction yields similar results. These results rule out the hypothesis that the discrepant ages of the Universe derived from globular clusters and recent measurements of the Hubble constant are attributable to a locally underdense bubble. Using the Cepheid-distance-calibrated absolute magnitudes for SN Ia’s of Sandage et al., we can also measure the global Hubble constant, HG0. If ΩM ≥ 0.2, we find that HG0 < 70 km s-1 Mpc-1 in a Λ = 0 universe and HG0 < 78 km s-1 Mpc-1 in a flat universe, correcting the distant and local SN apparent magnitudes for light-curve width. Lower results for HG0 are obtained if the magnitudes are not width-corrected.

Photometric measurements show that, as a group, nearby Type Ia supernovae follow similar light curves and reach similar peak magnitudes (Branch & Tammann 1992). Thus, these supernovae may serve as standard candles or calibrated candles at cosmological distances. Magnitudes of local and distant supernovae, both in the same filter band, are compared using a K correction to account for the different spectral regions incident on that filter. A generalized approach compares magnitudes in different bands for the nearby and distant supernovae, bands that are selected to give sensitivity in corresponding regions of the unredshifted and redshifted spectra. Thus, R magnitudes for supernovae at z ~ 0.5 are compared with $B$ magnitudes of local supernovae. We compute these generalized K corrections over a range of redshifts and bandpass pairs and discuss their advantages over the traditional single-band K correction. In particular, errors near maximum light can be kept below 0.05 mag out to at least z = 0.6, whereas the traditional K correction is less accurate and can be difficult to determine beyond z > 0.2.