The measurements of matter density perturbations amplitude from
  cosmological data
  We compare various physically different measurements of linear matter density
perturbation amplitude, $sigma_8$, which are obtained from the observations of
CMB anisotropy, galaxy cluster mass function, weak gravitation lensing, matter
power spectrum and redshift space distortions. We show that $\sigma_8$
measurement from CMB gravitational lensing signal based on Planck CMB
temperature anisotropy data at high multipoles, $\ell>1000$, contradict to all
other measurements obtained both from remaining Planck CMB anisotropy data and
from other cosmological data, at about $3.7\sigma$ significance level.
Therefore, these data currently should not be combined with other data to
constrain cosmological parameters.
  With the exception of Planck CMB temperature anisotropy data at high
multipoles, all other measurements are in good agreement between each other and
give the following measurements of linear density perturbation amplitude:
$\sigma_8=0.792\pm0.006$, mean density of the Universe:
$\Omega_m=0.287\pm0.007$, and Hubble constant: $H_0 = 69.4\pm
0.6$~km~s$^{-1}$~Mpc$^{-1}$. Taking in account the data on baryon acoustic
oscillations and (or) direct measurements of the Hubble constant, one can
obtain different constraints on sum of neutrino mass and number of relativistic
species.
