| Abstract
| - The abundance of local clusters is a traditional way to derive the amplitude of matter fluctuations, commonly specified by $\sigma_8$, but which suffers from a systematic uncertainty arising from the lack of accurate knowledge of the mass temperature relation. In the present work, by assuming that the observed baryon content of clusters is representative of the universe, we show that the mass temperature relation ( $M-T$) can be specified for any cosmological model. WMAP constraints on the baryonic content of the Universe and the $\Omega_{\rm M}-H_0$ relation allows one further improvement in tightening this $M-T$ relation. This approach allows one to remove most of the above uncertainty, and to provide an estimation of $\sigma_8$ whose uncertainty is essentially statistical. The values we obtain are fortuitously almost independent of the matter density of the Universe ( $\sigma_8\sim 0.6{-}0.63$) with an accuracy better than 5%. Quite remarkably, the amplitude of matter fluctuations can be also tightly constrained to similar accuracy from existing CMB measurements alone, once the dark matter content is specified. However, the amplitude inferred in this way in a concordance model ( $\Lambda\rm CDM$) is significantly larger than the value derived from the above method based on X-ray clusters. Such a discrepancy would almost disappear if the actual optical thickness of the Universe was 0 but could also be alleviated from more exotic solutions: for instance the existence of a new non-baryonic light dark component in the Universe as massive neutrinos, with $\Omega_{\rm d} \sim 0.01{-}0.03$. However, recent other indications of $\sigma_8$ favor a high normalization. In this case, the assumption that the baryonic content observed in clusters actually reflects the primordial value has to be relaxed: either there exists a large baryonic dark component in the Universe with $\Omega_{\rm d} \sim 0.01{-}0.03 \sim 0.5 \Omega_{\rm b}$ or baryons in clusters have undergone a large depletion during the formation of these structures. We concluded that the baryon fraction in clusters is not representative and therefore that an essential piece of the physics of baryons in clusters is missing in standard structure formation scenario.
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