Clusters of galaxies are important probes for the large-scale structure that allow us to test cosmological models .
With the REFLEX II galaxy cluster survey we previously derived tight constraints on the cosmological parameters for the matter density , \Omega _ { m } , and the amplitude parameter of the matter density fluctuations , \sigma _ { 8 } .
Whereas in these previous studies no effect of massive neutrinos was taken into account , we explore these effects in the present publication .
We derive cosmological constraints for the sum of the neutrino masses of the conventional three neutrino families in the range M _ { \nu } = \sum _ { i } m _ { \nu~ { } i } = 0 to 0.6 eV .
The influence on the constraints of \Omega _ { m } and \sigma _ { 8 } for the expected mass range is weak .
Interesting constraints on the neutrino properties can be derived by comparing the cluster data with those from the Planck cosmic microwave background ( CMB ) observations .
The current tension between the Planck results and clusters can formally be resolved with neutrino masses of about M _ { \nu } = 0.45 ( \pm 0.28 , 1 \sigma ) eV .
While we caution not to consider this a firm measurement because it might also be the result of unresolved systematics , it is interesting that other measurements of the local large-scale structure fluctuation amplitude , like that of cosmic lensing shear , yield similar results and additionally confirm the effect of massive neutrinos .
Among the indicators for massive neutrinos , galaxy clusters and in particular our large and well-controlled cluster survey currently provide the best potential for constraints of the total neutrino mass .