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

TL;DR

This study delivers the most precise primordial ${}^4{\rm He}$ abundance to date, ${Y_p = 0.2458 \pm 0.0013}$, from the LBT Y_p project and combines it with the latest primordial ${\rm D/H}$ and CMB data to test Standard BBN and the number of relativistic species. The analysis shows that, with a fixed $N_\nu=3$, the baryon density yields $\eta = (6.120 \pm 0.038) \times 10^{-10}$ and $\Omega_B h^2 = 0.02236 \pm 0.00014$, while allowing $N_\nu$ to vary gives $\eta = (6.101 \pm 0.044) \times 10^{-10}$, $\Omega_B h^2 = 0.02229 \pm 0.00016$, and $N_\nu = 2.925 \pm 0.082$ with a 95% CL upper limit $\Delta N_\nu \le 0.125$ for $N_\nu \ge 3$. The results are in strong agreement with the Standard Model and standard cosmology, providing robust cross-checks between BBN and CMB epochs and reinforcing constraints on physics beyond the Standard Model.

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 $N_ν$ 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 $N_ν= 2.925 \pm 0.082$, 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.

Figures (5)

• Figure 1: The likelihood functions for $Y_{\rm p}$ (left) and D/H (right). The upper panels are taken from the analysis in Yeh:2022heq, and are compared with those derived here, shown in the lower panels. BBN+CMB predictions are shown in the dark-shaded (purple) solid curves, and use Planck inputs. Observational determinations for the $Y_{\rm p}$ and D/H primordial abundances appear as light-shaded (yellow) dashed curves. The independent CMB determination of ${}^{4}{\rm He}$ appears as the medium-shaded (cyan) dotted curve.
• Figure 2: As in Fig. \ref{['fig:2x2abs_2d']}, the light element abundance likelihood functions using the CMB determination of the cosmic baryon density when $N_\nu$ is not fixed.
• Figure 3: Likelihood distributions for $N_\nu$ using various combinations of BBN and CMB data. The initial likelihood functions have been marginalized over the baryon-to-photon ratio $\eta$. Older results based on $Y_p = 0.2448 \pm 0.0033$ from Aver:2021rwi are shown in panels (a,b) while results from this work using Eq. (\ref{['Ypnew']}) are shown in panels (c,d). We show in panels (a,c) the likelihood distributions for BBN-only, CMB-only, and combined limits. In panels (b,d) we zoom into BBN+CMB joint limits to highlight results for different combinations of light element abundances. The last three columns of Table \ref{['tab:etannu']} summarize these results.
• Figure 4: The 2D likelihood ${\cal L}(\eta,N_\nu)$. Older results based on $Y_p = 0.2448 \pm 0.0033$ from Aver:2021rwi are shown in panels (a,b) while results from this work using Eq. (\ref{['Ypnew']}) are shown in panels (c,d). In panels (a,c) the dotted contours show BBN-only results, while solid contours give combined BBN+CMB results. In panels (b,d) the dotted contours correspond to the CMB-only likelihood, with solid contours showing again the BBN+CMB combined result.
• Figure 5: Forecast of expected precision in the measurement of $N_\nu$, shown as a function of the precision of the $Y_{\rm p,obs}$ measurement. The green curve shows the precision of BBN-only measurements, which show a nearly linear scaling as in eq. (\ref{['eq:sig-scaling']}). The blue curve shows the improvement when adding Planck CMB measurements. Vertical lines are the previous (magenta) and present (red) $Y_{\rm p,obs}$ precision. We see that an additional factor $\sim 2$ improvement in $\sigma(Y_{\rm p,obs})$ promises to bring the $N_\nu$ precision around the value due to neutrino heating in the early Universe, shown in the horizontal line.