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We present spectral and photometric observations of 10 Type Ia
supernovae (SNe Ia) in the redshift range 0.16 ≤
z ≤ 0.62. The luminosity distances of these objects are
determined by methods that employ relations between SN Ia
luminosity and light curve shape. Combined with previous data from
our High-
z Supernova Search Team and recent results by Riess et al.,
this expanded set of 16 high-redshift supernovae and a set of 34
nearby supernovae are used to place constraints on the following
cosmological parameters: the Hubble constant (
H
0), the mass density (Ω
M
), the cosmological constant (i.e., the vacuum energy
density, Ω
Λ), the deceleration parameter (
q
0), and the dynamical age of the universe (
t
0). The distances of the high-redshift SNe Ia are, on
average, 10%–15% farther than expected in a low mass density
(Ω
M
= 0.2) universe without a cosmological constant. Different
light curve fitting methods, SN Ia subsamples, and prior
constraints unanimously favor eternally expanding models with
positive cosmological constant (i.e., Ω
Λ > 0) and a current acceleration of the
expansion (i.e.,
q
0 < 0). With no prior constraint on mass density
other than Ω
M
≥ 0, the spectroscopically confirmed SNe Ia are
statistically consistent with
q
0 < 0 at the 2.8 σ and 3.9 σ confidence
levels, and with Ω
Λ > 0 at the 3.0 σ and 4.0 σ
confidence levels, for two different fitting methods, respectively.
Fixing a "minimal" mass density, Ω
M
= 0.2, results in the weakest detection, Ω
Λ > 0 at the 3.0 σ confidence level from
one of the two methods. For a flat universe prior (Ω
M
+ Ω
Λ = 1), the spectroscopically confirmed SNe Ia
require Ω
Λ > 0 at 7 σ and 9 σ formal
statistical significance for the two different fitting methods. A
universe closed by ordinary matter (i.e., Ω
M
= 1) is formally ruled out at the 7 σ to 8 σ
confidence level for the two different fitting methods. We estimate
the dynamical age of the universe to be 14.2 ± 1.7 Gyr
including systematic uncertainties in the current Cepheid distance
scale. We estimate the likely effect of several sources of
systematic error, including progenitor and metallicity evolution,
extinction, sample selection bias, local perturbations in the
expansion rate, gravitational lensing, and sample contamination.
Presently, none of these effects appear to reconcile the data with
Ω
Λ = 0 and
q
0 ≥ 0.