Measurements^* of the Cosmological Parameters Ω and Λ from the First Seven Supernovae at z ≥ 0.35

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 find an observational dispersion in peak magnitudes of σ_MB=0.27; this dispersion narrows to σ_{MB, corr}=0.19 after "correcting" the magnitudes using the light-curve "width-luminosity" relation found for nearby (z ≤ 0.1) Type Ia supernovae from the Calán/Tololo survey (Hamuy et al.). Comparing light-curve width-corrected magnitudes as a function of redshift of our distant (z = 0.35-0.46) supernovae to those of nearby Type Ia supernovae yields a global measurement of the mass density, Ω_M=0.88^{+ 0.69}_−0.60 for a Λ = 0 cosmology. For a spatially flat universe (i.e., Ω_M + Ω_Λ = 1), we find Ω_M=0.94^{+ 0.34}_−0.28 or, equivalently, a measurement of the cosmological constant, Ω_Λ=0.06^{+ 0.28}_−0.34 ( < 0.51 at the 95% confidence level). For the more general Friedmann-Lemaître cosmologies with independent Ω_M and Ω_Λ, the results are presented as a confidence region on the Ω_M-Ω_Λ plane. This region does not correspond to a unique value of the deceleration parameter q₀. We present analyses and checks for statistical and systematic errors and also show that our results do not depend on the specifics of the width-luminosity correction. The results for Ω_Λ-versus-Ω_M are inconsistent with Λ-dominated, low-density, flat cosmologies that have been proposed to reconcile the ages of globular cluster stars with higher Hubble constant values.