The LBT $Y_{\rm p}$ Project V: Cosmological Implications of a New Determination of Primordial $^4$He

Abstract: The primordial abundance of $^4$He plays a central role in big-bang nucleosynthesis (BBN) and in the cosmic microwave background (CMB). The LBT $Y_{\rm p}$ Project's new measurement of the primordial $^4$He mass fraction $Y_{\rm p} =0.2458 \pm 0.0013$ is the most precise determination to date. In this paper, we combine our new $Y_{\rm p}$ value with the latest primordial deuterium measurement, and assess the consequences for cosmology. For Standard BBN, where the number of light neutrino species is fixed at $N_ν=3$, the single free parameter is the cosmic baryon density; the CMB measures this independently, with results consistent with each other. Combining $Y_{\rm p}$ , D/H, BBN, and the CMB, gives the cosmic baryon-to-photon ratio $η= (6.120 \pm 0.038) \times 10^{-10}$, corresponding to a baryon density parameter $Ω{\rm B} h^2 = 0.02236 \pm 0.00014$. We then allow $Nν$ to vary and thus measure relativistic species present during nucleosynthesis. We find $η= (6.101 \pm 0.044) \times 10^{-10}$ or $Ω{\rm B} h^2= 0.02229 \pm 0. 00016$, and $Nν= 2.925 \pm 0.082$, and for $N_ν\ge 3$, $ΔN_ν= N_ν-3 \le 0.125$ (95\% CL) during BBN and the CMB. Our results demonstrate consistency with the Standard Model of particle physics, and with the standard cosmology that links BBN at $\sim 1 \ \rm sec$ and the CMB at $\sim 400,000$ yr.