Weighing the Giants IV: Cosmology and Neutrino Mass
  We employ robust weak gravitational lensing measurements to improve
cosmological constraints from measurements of the galaxy cluster mass function
and its evolution, using X-ray selected clusters detected in the ROSAT All-Sky
Survey. Our lensing analysis constrains the absolute mass scale of such
clusters at the 8 per cent level, including both statistical and systematic
uncertainties. Combining it with the survey data and X-ray follow-up
observations, we find a tight constraint on a combination of the mean matter
density and late-time normalization of the matter power spectrum,
$\sigma_8(\Omega_m/0.3)^{0.17}=0.81\pm0.03$, with marginalized, one-dimensional
constraints of $\Omega_m=0.26\pm0.03$ and $\sigma_8=0.83\pm0.04$. For these two
parameters, this represents a factor of two improvement in precision with
respect to previous work, primarily due to the reduced systematic uncertainty
in the absolute mass calibration provided by the lensing analysis. Our new
results are in good agreement with constraints from cosmic microwave background
(CMB) data, both WMAP and Planck (plus WMAP polarization), under the assumption
of a flat $\Lambda$CDM cosmology with minimal neutrino mass. Consequently, we
find no evidence for non-minimal neutrino mass from the combination of cluster
data with CMB, supernova and baryon acoustic oscillation measurements,
regardless of which all-sky CMB data set is used (and independent of the recent
claimed detection of B-modes on degree scales). We also present improved
constraints on models of dark energy (both constant and evolving),
modifications of gravity, and primordial non-Gaussianity. Assuming flatness,
the constraints for a constant dark energy equation of state from the cluster
data alone are at the 15 per cent level, improving to $\sim 6$ per cent when
the cluster data are combined with other leading probes.
