In this paper I have presented a personal point of view on the observational determination of cosmological parameters and especially on question of the possible non-zero value of the cosmological constant. Although, the concordance model provides a nice agreement with several observational data sets, I have argued that i) the only direct case foran accelerating universe, implying the domination of the vacuum density over the other type of dark matter already assumed to be present in the Universe (baryonic dark matter, non-baryonic dark matter), is coming from the distant SNIa and is not sufficient to be considered as robustly established. ii) some evidences against the concordance model are systematically rejected, because they are judged as insufficiently robust. The global picture drawn by the concordance model might be right after all! But I still consider that the case for a cosmological constant is oversold. It would be crucial in order to strength the case to have independent evidence either direct or indirect. A possible way for this would be to achieve a reliable measurement of the matter density of the Universe, which in conjunction with the CMB evidence for flatness, would allow an estimate of the cosmological constant. I have argued that clusters are in several ways the best tool to achieve such a measurement. Again contrary to a common prejudice I have illustrated that there are different values obtained by such methods, some corresponding to high matter density consistent with an Einstein-de Sitter model.
Summarizing results on clusters, I have shown an up-to-date local temperature distribution function obtained from a flux limited ROSAT sample comprising fifty clusters. When compared to Henry's sample at z = 0.33, obtained from the EMSS, this sample clearly indicates that the TDF is evolving. This evolution is consistent with the evolution detected up to redshift z = 0.55 by Donahue et al. (2000). This indicates converging evidences for a high density universe, with a value of m consistent with what Sadat et al. (1998) inferred previously from the full EMSS sample taking into account the observed evolution in the Lx - Tx relation (which was found moderately positive and consistent with no evolution). From such analyses, low density universes with m 0.35 are excluded at the two-sigma level. This conflicts with some of the previous analyses on the same high redshift sample. Actually, lower values obtained from statistical analysis of X-ray samples were primarily affected by the biases introduced by the local reference sample, which lead to a lower local abundance and a flatter spectrum for primordial fluctuations (Henry, 1997, 2000; Eke et al., 1998; Donahue and Voit, 2000). Our result is consistent with the conclusion of Viana and Liddle (1999), Reichert et al. (1999) and Sadat et al (1988). The possible existence of high temperature clusters at high redshift, MS0451 (10 keV) and MS1054 (12 keV), cannot however be made consistent with this picture of a high density universe, unless their temperatures are overestimated by a large factor or the primordial fluctuations are not gaussian. The baryon fraction in clusters is another global test of m, provided that a reliable value for b is obtained. However, it seems that the mean baryon fraction could have been overestimated in previous analysis, possibly being closer to 10% rather than to 15%-25%. This is again consistent with a high density universe. Finally, we have seen in one case that the apparent evolution of the baryon fraction in clusters could also be consistent with a high density universe.
In conclusion, I pretend that the determination of cosmological parameters and especially the evidence for a non-zero cosmological constant is still an open question which needs to be comforted and that the exclusion of an Einstein de Sitter model is over-emphasized.