On the tension between Large Scale Structures and Cosmic Microwave
  Background
  Recent years have brought strong observational evidences for the standard
LCDM cosmological model. Cosmic microwave background (CMB) anisotropy and large
scale structure (LSS) probes do not favour any extensions of the standard
model. Nevertheless, in this framework, the preferred cosmological parameters
may differ from probe to probe, from experiment to experiment. This is the well
known case of the tension between CMB and Sunyaev Zel'dovich (SZ) galaxy
clusters (GC) from Planck. In 2013, the Planck team has shown that the
preferred matter content ({\Omega}M) and density fluctuation power spectrum
amplitude ({\sigma}8), the two main cosmological parameters probed by the
galaxy cluster number count, are different in the CMB analyses and in the SZ
cluster analyses at more than 2 sigmas (a result confirmed in subsequent
analyses). We present the results of our new analysis using more recent
measurements of the CMB, SZ clusters and SZ power spectrum of 2016 and show
that the tension on ({\Omega}M,{\sigma}8) is mostly releaved. The lower value
of the reionisation optical depth and thus of {\sigma}8 in the recent Planck
studies is the main reason. We also show that basic extensions of the standard
model (massive neutrinos or non-lambda dark energy) do not help improving the
agreement between the probes. In order to fully reconcile SZ clusters with CMB
best model, the mass of the galaxy clusters derived from hydrostatic
equilibrium should be 40% lower than the true mass. While current numerical
simulations and weak lensing measurements agree for a mass bias of 20%,
investigations are still going on to explain such disagreement on the mass
bias. We show that considering a mass bias evolving with redshift or mass does
not help in eliminating the discrepancy.
