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 0.056 eV , 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 .