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We investigate the gas mass function of clusters of galaxies to measure thedensity fluctuation spectrum on cluster scales. The baryon abundance confinedin rich clusters is computed from the gas mass function and compared with themean baryon density in the universe which is predicted by the Big BangNucleosynthesis. This baryon fraction and the slope of the gas mass functionput constraints on $\sigma_8$, the rms linear fluctuation on scales of$8h^{-1}\Mpc$, and the slope of the fluctuation spectrum, where $h$ is theHubble constant in units of 100 $\kms \oMpc$. We find $\sigma_8 = 0.80 \pm0.15$ and $n \sim -1.5$ for $0.5 \le h \le 0.8$, where we assume that thedensity spectrum is approximated by a power law on cluster scales: $\sigma(r)\propto r^{-{3+n\over{2}}}$. Our value of $\sigma_8$ is independent of thedensity parameter, $\Omega_0$, and thus we can estimate $\Omega_0$ by combining$\sigma_8$ obtained in this study with those from $\Omega_0$-dependent analysesto date. We find that $\sigma_8(\Omega_0)$ derived from the cluster abundancesuch as the temperature function gives $\Omega_0 \sim 0.5$ while$\sigma_8(\Omega_0)$ measured from the peculiar velocity field of galaxiesgives $\Omega_0 \sim 0.2-1$, depending on the technique used to analyzepeculiar velocity data. Constraints are also derived for open, spatially flat,and tilted Cold Dark Matter models and for Cold + Hot Dark Matter models.Comment: 9 pages, LaTeX (aaspp4), 6 PostScript figures, submitted to Ap

Measuring the Density Fluctuation from the Cluster Gas Mass Function