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Published online by Cambridge University Press: 25 May 2016
We derive the gas mass function of clusters of galaxies to measure the density fluctuation spectrum on cluster scales. The baryon abundance confined in rich clusters is computed from the gas mass function and compared with the mean baryon density in the universe which is predicted by the BBN. This baryon fraction and the slope of the gas mass function put constraints on σ8 and the slope of the fluctuation spectrum. Adopting the density parameter of baryons Ωbh2 = 0.0175 ± 0.0075 and assuming that , we find for h = 0.7 ± 0.1. Our value of σ8 is independent of Ω0 and thus we can estimate Ω0 by combining σ8 as obtained in this study with those from Ω0-dependent analyses to date. Constraints are also derived for CDM and CHDM models.