Effects of sterile neutrino and extra-dimension on big bang nucleosynthesis

By assuming the existence of extra-dimensional sterile neutrinos in big bang nucleosynthesis (BBN) epoch, we investigate the sterile neutrino ($\nu_{\rm s}$)effectsontheBBNandconstrainsomeparametersassociatedwiththe$\nu_{\rm s}$ properties. First, for cosmic expansion rate, we take into account effects of a five-dimensional bulk and intrinsic tension of the brane embedded in the bulk, and constrain a key parameter of the extra dimension by using the observational element abundances. Second, effects of the $\nu_{\rm s}$ traveling on or off the brane are considered. In this model, the effective mixing angle between a ${\nu }_{\mathrm{s}}$ and an active neutrino depends on energy, which may give rise to a resonance effect on the mixing angle. Consequently, reaction rate of the ${\nu }_{\mathrm{s}}$ can be drastically changed during the cosmic evolution. We estimated abundances and temperature of the ${\nu }_{\mathrm{s}}$ by solving the rate equation as a function of temperature until the sterile neutrino decoupling. We then find that the relic abundance of the ${\nu }_{\mathrm{s}}$ is drastically enhanced by the extra-dimension and maximized for a characteristic resonance energy $E_{\mathrm{r}\mathrm{e}\mathrm{s}}\gtrsim 0.01$ GeV. Finally, some constraints related to the ${\nu }_{\mathrm{s}}$, mixing angle and mass difference, are discussed in detail with the comparison of our BBN calculations corrected by the extra-dimensional ${\nu }_{\mathrm{s}}$ to observational data on light element abundances.