Constraints on the Density of Baryons in the Universe [and Discussion]

It is shown that not only does Big Bang nucleosynthesis provide an upper limit on the baryon density of the Universe, but if one takes into account arguments concerning the production of $^{3}$He in stars, one can show that the $^{3}$He plus deuterium abundance can also provide a lower limit on the baryon density of the Universe. The derived constraints are that the baryon:photon ratio, $\eta $, must be between 1.5 $\times $ 10$^{-10}$ and 7 $\times $ 10$^{-9}$ with a best fit between 3 and 6 $\times $ 10$^{-10}$. This small range for $\eta $ has implications for our limits on numbers of neutrino types, for Big Bang baryosynthesis, and for arguments about the nature of the dark matter in clusters of galaxies. With reference to the dark matter, the derived baryon density for Big Bang nucleosynthesis corresponds very closely with the implied density of matter in binaries and small groups of galaxies. This implies that non-baryonic matter is not dominant by a large factor on scales as large as binaries and small groups of galaxies. It is also shown that the constraints on the lower limit on the baryon density constrain the lower limit on the primordial $^{4}$He abundance. Consistency seems to be possible only if the primordial $^{4}$He is between 23 and 25% by mass if there are three or four species of neutrinos.