  We present updated cosmological constraints from measurements of the gas mass
fractions ($f_{gas}$) of massive, dynamically relaxed galaxy clusters. Our new
data set has greater leverage on models of dark energy, thanks to the addition
of the Perseus Cluster at low redshifts, two new clusters at redshifts
$z>0.97$, and significantly longer observations of four clusters at
$0.6<z<0.9$. Our low-redshift ($z<0.16$) $f_{gas}$ data, combined with the
cosmic baryon fraction measured from the cosmic microwave background (CMB),
imply a Hubble constant of $h = 0.722 \pm 0.067$. Combining the full $f_{gas}$
data set with priors on the cosmic baryon density and the Hubble constant, we
constrain the dark energy density to be $\Omega_\Lambda = 0.865 \pm 0.119$ in
non-flat $\Lambda$CDM (cosmological constant) models, and its equation of state
to be $w = -1.13_{-0.20}^{+0.17}$ in flat, constant-w models, respectively 41
and 29 per cent tighter than our previous work, and comparable to the best
constraints available from other probes. Combining $f_{gas}$, CMB, supernova,
and baryon acoustic oscillation data, we also constrain models with global
curvature and evolving dark energy. For the massive, relaxed clusters employed
here, we find the scaling of $f_{gas}$ with mass to be consistent with a
constant, with an intrinsic scatter that corresponds to just 3 per cent in
distance.
