Cosmological Parameters: Fashion and Facts

We are at a specific period of modern cosmology, during which the large increase of the amount of data relevant to cosmology, as well as their increasing accuracy, leads to the idea that the determination of cosmological parameters has been achieved with a rather good precision, may be of the order of 10%. There is a large consensus around the so-called concordance model. Indeed this model does fit an impressive set of independent data, the most impressive been: CMB Cl curve, most current matter density estimations, Hubble constant estimation from HST, apparent acceleration of the Universe, good matching of the power spectrum of matter fluctuations. However, the necessary introduction of a non zero cosmological constant is an extraordinary new mystery for physics, or more exactly the come back of one of the ghost of modern physics since its introduction by Einstein. Here, I would like to emphasize that some results are established beyond reasonable doubt, like the (nearly) flatness of the universe and the existence of a dark non-baryonic component of the Universe. But also that the evidence for a cosmological constant may not be as strong as needed to be considered as established beyond doubt. In this respect, I will argue that an Einstein-De Sitter universe might still be a viable option. Some observations do not fit the concordance picture, but they are generally considered as not to be taken into account. I discuss several of the claimed observational evidences supporting the concordance model, and will focus more specifically on the observational properties of clusters which offer powerful constraints on various quantities of cosmological interest. They are particularly interesting in constraining the cosmological density parameter, nicely complementing the CMB result and the supernova probe. While early estimations were based on the of the M/L ratio, i.e. a local indirect measure of the mean density which needs an extrapolation over several orders of magnitude, new tests have been proposed during the last ten years which are global in nature. Here, I will briefly discuss three of them: 1) the evolution of the abundance of clusters with redshift 2) the baryon fraction measured in local clusters 3) apparent evolution of the baryon fraction with redshift. I will show that these three independent tests lead to high matter density for the Universe in the range 0.6− 1.. I therefore conclude that the dominance of vacuum to the various density contributions to the Universe is presently an interesting and fascinating possibility, but it is still premature to consider it as an established scientific fact.