Abstract
Clusters of galaxies and large structures provide tests and diagnostics to help solve the big questions in cosmology. First , what is the nature of dark matter, what is its distribution relative to visible mass, and in particular what is the bias as a function of redshift (bias = 1if baryons and dark matter have the same distribution, the same contrast). The nature of dark energy could be clarified by knowing the law of the expansion of the Universe as a function of time. This requires standard rules, such as BAO (Baryonic Acoustic Oscillations), the measurement of cosmic shear (weak gravitational lensing), and the determination of redshift-space distortions . Cluster growth as a function of time will provide constraints on modified gravity. By making all these observations, we will also learn how baryons assemble in structures, and what role the environment, groups and clusters play in galaxy formation and evolution. Current observations, which combine all these diagnostics with those provided by the cosmological fund (Planck satellite), show good agreement with the LCDM standard model, but with some tensions : in particular, the value of the Hubble constant, i.e. 67 km/s/Mpc is favoured by Planck, whereas direct measurement gives rather 74 km/s/Mpc, and the amplitude of σ8 density fluctuations, which is predicted to be too large by the CMB (Planck). The tension on the Hubble constant could be resolved by varying another parameter, such as neutrino mass. In any case, this tension is interesting, as it points the way to modifying the Standard Model. Measuring gravitationalredshift would be an independent test of cosmology.
