Evidence of Neutrino Enhanced Clustering in a Complete Sample of Sloan
  Survey Clusters, Implying $\sum m_{\nu}= 0.119 \pm 0.034$ eV
  The clustering amplitude of 7143 clusters from the Sloan Digital Sky Survey
(SDSS) is found to increase with cluster mass, closely agreeing with the
Gaussian random field hypothesis for structure formation. The amplitude of the
observed cluster correlation exceeds the predictions from pure cold dark matter
(CDM) simulation by $\simeq 6\%$ for the standard Planck-based values of the
cosmological parameters. We show that this excess can be naturally accounted
for by free streaming of light neutrinos, which opposes gravitational growth,
so clusters formed at fixed mass are fewer and hence more biased than for a
pure CDM density field. An enhancement of the cluster bias by 7\% matches the
observations, corresponding to a total neutrino mass, $m_{\nu} = 0.119 \pm
0.034$ eV at 67\% confidence level, for the standard relic neutrino density. If
ongoing laboratory experiments favor a normal neutrino mass hierarchy then we
may infer a somewhat larger total mass than the minimum oscillation based
value, $\sum m_{\nu} \simeq 0.056eV$, with 90\% confidence. Much higher
precision can be achieved by applying our method to a larger sample of more
distant clusters with weak lensing derived masses.
