We report measurements of the mass density, Ω M , and cosmological-constant energy density, Ω Λ , 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 fit 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 lightcurve width-luminosity relation. The measurement yields a joint probability distribution of the cosmological parameters that is approximated by the relation 0.8 Ω M − 0.6 Ω Λ ≈ −0.2 ± 0.1 in the region of interest (Ω M ∼ < 1.5). For a flat (Ω M + Ω Λ = 1) cosmology we find Ω flat M = 0.28 +0.09 −0.08 (1σ 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 non-zero 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 flat 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 Calán/Tololo sample and our high-redshift sample. Excluding those few supernovae which 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.

We have developed a technique to systematically discover and study high-redshift supernovae that can be used to measure the cosmological parameters. We report here results based on the initial seven of more than 28 supernovae discovered to date in the high-redshift supernova search of the Supernova Cosmology Project. We Ðnd an observational dispersion in peak magnitudes of this disperp MB \ 0.27 ; sion narrows to after "" correcting ÏÏ the magnitudes using the light-curve "" widthp MB,corr \ 0.19 luminosity ÏÏ relation found for nearby (z ¹ 0.1) Type Ia supernovae from the Cala n/Tololo survey (Hamuy et al.). Comparing light-curve widthÈcorrected magnitudes as a function of redshift of our distant (z \ 0.35È0.46) supernovae to those of nearby Type Ia supernovae yields a global measurement of the mass density, for a " \ 0 cosmology. For a spatially Ñat universe (i.e., not correspond to a unique value of the deceleration parameterWe present analyses and checks q 0 . for statistical and systematic errors and also show that our results do not depend on the speciÐcs of the width-luminosity correction. The results for are inconsistent with "-dominated, low-) " -versus-) M density, Ñat cosmologies that have been proposed to reconcile the ages of globular cluster stars with higher Hubble constant values.

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-We present a measurement of the rate of distant Type Ia supernovae derived using 4 large subsets of data from the Supernova Cosmology Project. Within this fiducial sample, which surveyed about 12 square degrees, thirty-eight supernovae were detected at redshifts 0.25-0.85. In a spatially-flat cosmological model consistent with the results obtained by the Supernova Cosmology Project, we derive a rest-frame Type Ia supernova rate at a mean redshift z ≃ 0.55 of 1.53 +0.28 −0.25 +0.32 −0.31 10 −4 h 3 Mpc −3 yr −1 or 0.58 +0.10 −0.09 +0.10−0.09 h 2 SNu (1 SNu = 1 supernova per century per 10 10 L B⊙ ), where the first uncertainty is statistical and the second includes systematic effects. The dependence of the rate on the assumed cosmological parameters is studied and the redshift dependence of the rate per unit comoving volume is contrasted with local estimates in the context of possible cosmic star formation histories and progenitor models.