  We present new determinations of the cosmic expansion history from
red-envelope galaxies. We have obtained for this purpose high-quality spectra
with the Keck-LRIS spectrograph of red-envelope galaxies in 24 galaxy clusters
in the redshift range 0.2 < z < 1.0. We complement these Keck spectra with
high-quality, publicly available archival spectra from the SPICES and VVDS
surveys. We improve over our previous expansion history measurements in Simon
et al. (2005) by providing two new determinations of the expansion history:
H(z) = 97 +- 62 km/sec/Mpc at z = 0.5 and H(z) = 90 +- 40 km/sec/Mpc at z =
0.8. We discuss the uncertainty in the expansion history determination that
arises from uncertainties in the synthetic stellar-population models. We then
use these new measurements in concert with cosmic-microwave-background (CMB)
measurements to constrain cosmological parameters, with a special emphasis on
dark-energy parameters and constraints to the curvature. In particular, we
demonstrate the usefulness of direct H(z) measurements by constraining the
dark- energy equation of state parameterized by w0 and wa and allowing for
arbitrary curvature. Further, we also constrain, using only CMB and H(z) data,
the number of relativistic degrees of freedom to be 4 +- 0.5 and their total
mass to be < 0.2 eV, both at 1-sigma.
