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.