Measurements of the Cosmological Parameters $Ω$ and $Λ$ from the First 7 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 $>$28 supernovae discovered to date in the high-redshift supernova search of the Supernova Cosmology Project. We find a dispersion in peak magnitudes of $\sigma_{M_B} = 0.27$ this dispersion narrows to $\sigma_{M_B,{\rm corr}} = 0.19$ after ``correcting'' the magnitudes using the light-curve ``width-luminosity'' relation found for nearby ($z \le 0.1$) type Ia supernovae from the Cal\'{a}n/Tololo survey (Hamuy {\em et~al.} 1996). Comparing lightcurve-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, $\Omega_{\rm M} = 0.88 \;^{+0.69}_{-0.60}$ for a $\Lambda = 0$ cosmology. For a spatially flat universe (i.e., $\Omega_{\rm M} +\Omega_\Lambda = 1$), w e find $\Omega_{\rm M} = 0.94 \;^{+0.34}_{-0.28}$ or, equivalently, a measurement of the cosmological constant, $\Omega_\Lambda = 0.06 \;^{+0.28}_{-0.34}$ ($<$0.51 at the 95\% confidence level). For the more general Friedmann-Lema\^{\i}tre cosmologies with independent $\Omega_{\rm M}$ and $\Omega_\Lambda$, the results are presented as a confidence region on the $\Omega_{\rm M}$--$\Omega_\Lambda$ plane. This region does not correspond to a unique value of the deceleration parameter $q_0$. 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 $\Omega_\Lambda$-versus-$\Omega_{\rm M}$ are inconsistent with $\Lambda$-dominated, low density, flat cosmologies that have been proposed to reconcile the ages of globular cluster stars with higher Hubble constant values.