During the last ten years astrophysical cosmology has brou- ght a remarkable result of deep impact for fundamental physics: the domination of the density of the acceleration of the expansion of universe univers. This last is probably the most revolutionizing one in modern physics: the scientific review Sciences has considered twice results on this question as Breakthrough of the Year (for 1998 and 2003). However, direct evidence of acceleration are still rather weak, and the strength of the standard scenario relies more on the “concordance” argument rather than on the robustness of direct evidences. Supernovae evolution could mimic an accelerating expansion. Furthermore, recent data on distant x-ray clusters obtained from XMM and Chandra indicate that the observed abundances of clusters at high redshift taken at face value favors an Einstein de Sitter model and are hard to reconcile with the concordance model. However, recent results on large scale structure has brought decisive pieces of information on this question: galaxy distribution on large scales cannot be reproduced by matter power in Einstein de Sitter model.