Baryonic Mass Fraction in Rich Clusters and the Total Mass Density in the Cosmos

Direct observations of the supposedly universal primordial deuterium abundance imply a relatively large baryon density $\Omega_B= (0.019-0.030)h^{-2}$ (95% C.L.). On the other hand, concordance between the previously accepted ${}^{4}He$ and ${}^{7}Li$ abundances and standard Big Bang Nucleosynthesis requires the thrice smaller value ${\mathrm{\Omega }}_B=(0.005-0.010)h^{-2}$ (95% C.L.). For each ${\mathrm{\Omega }}_B$, we use X-ray and Sunyaev-Zeldovich observations of the baryon fraction $f_B$ in rich clusters of galaxies, in order to obtain limits on the total mass density ${\mathrm{\Omega }}_{cl}$ in clusters of galaxies. The higher-${\mathrm{\Omega }}_B$ values are consistent with clusters being a fair sample of the Universe, and then imply ${\mathrm{\Omega }}_m=(0.3-0.9)$, a medium or critical density Universe. Said otherwise, the observed limits $f_B>0.1,{\mathrm{\Omega }}_m>0.3$ imply ${\mathrm{\Omega }}_B>0.03$. If the newer${}^{4}He$ abundance observations are accepted, this is consistent with standard BBN.