Almost-standard big-bang nucleosynthesis withΩBh20>>0.015: A reexamination of neutrino chemical potentials andΔG

The homogeneous standard big-bang nucleosynthesis (SBBN) yields of D, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ are computed allowing independent variations of ${\mu }_1$, the chemical potential for electron neutrinos, and ${\mu }_2$, the chemical potential of $\mu$ neutrinos (or equivalently of ${\mathrm{Gg}}_R$, the product of Newton's constant and the number of effective relativistic degrees of freedom at the epoch of nucleosynthesis). This follows up previous investigations of chemical-potential variations, which however considered only [${}_{}{}^7{}_{}{}^{}\mathrm{Li}$]/[H]≃${10}^{-9\mathrm{}}$. It is found that even with a primordial ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$ abundance of ${10}^{-10\mathrm{}}$ the hydrogen abundance ${\Omega }_B{h}_0^2\sim 0.1$ is permitted as is ${\Omega }_B{h}_0^2\sim 1$; however, the required chemical potential for the ${\nu }_e$ is ${\mu }_1\approx T$. The required chemical potential for ${\nu }_{\mu }$ and/or ${\nu }_{\tau }$ is ${\mu }_2\approx \mathrm{}(5-25)T$ (for ${\Omega }_B{h}_0^2\simeq 0.1 \mathrm{and} 1$, respectively), or equivalently $\left({\mathrm{Gg}}_R\right)\approx (\mathrm{few}-{10}^3){\left({\mathrm{Gg}}_R\right)}_{\mathrm{SBBN}}$. Thus baryonic dark matter may be incorporated into the standard bigbang nucleosynthesis model albeit with dramatic requirements for lepto-genesis and/or the constancy of the gravitational coupling. It is also found that the "lithium dip" tracks the primordial deuterium abundance and thus may not be an independent measure of the parameters of the SBBN model.