The extended ROSAT-ESO Flux-Limited X-ray Galaxy Cluster Survey (REFLEX
  II) VI. Effect of massive neutrinos on the cosmological constraints from
  clusters
  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 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 observations. The current tension between the Planck
results and clusters can formally be resolved with neutrino masses of about
M_nu = 0.45 (+- 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.
