  The high precision measurements of the cosmic microwave background by the
Planck survey yielded tight constraints on cosmological parameters and the
statistics of the density fluctuations at the time of recombination. This
provides the means for a critical study of structure formation in the Universe
by comparing the microwave background results with present epoch measurements
of the cosmic large-scale structure. It can reveal subtle effects such as how
different forms of Dark Matter may modify structure growth. Currently most
interesting is the damping effect of structure growth by massive neutrinos.
Different observations of low redshift matter density fluctuations provided
evidence for a signature of massive neutrinos. Here we discuss the study of the
cosmic large-scale structure with a complete sample of nearby, X-ray luminous
clusters from our REFLEX cluster survey. From the observed X-ray luminosity
function and its reproduction for different cosmological models, we obtain
tight constraints on the cosmological parameters describing the matter density,
Omega_m, and the density fluctuation amplitude, sigma_8. A comparison of these
constraints with the Planck results shows a discrepancy in the framework of a
pure LambdaCDM model, but the results can be reconciled, if we allow for a
neutrino mass in the range of 0.17 to 0.7 eV. Also some others, but not all of
the observations of the nearby large-scale structure provide evidence or trends
for signatures of massive neutrinos. With further improvement in the
systematics and future survey projects, these indications will develop into a
definitive measurement of neutrino masses.
