Big bang nucleosynthesis: Present status

Big bang nucleosynthesis (BBN) describes the production of the lightest nuclides via a dynamic interplay among the four fundamental forces during the first seconds of cosmic time. A brief overview of the essentials of this physics is given, and new calculations presented of light-element abundances through ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$, with updated nuclear reactions and uncertainties including those in the neutron lifetime. Fits are provided for these results as a function of baryon density and of the number of neutrino flavors $N_{\nu }$. Recent developments are reviewed in BBN, particularly new, precision Planck cosmic microwave background (CMB) measurements that now probe the baryon density, helium content, and the effective number of degrees of freedom $N_{\text{eff}}$. These measurements allow for a tight test of BBN and cosmology using CMB data alone. Our likelihood analysis convolves the 2015 Planck data chains with our BBN output and observational data. Adding astronomical measurements of light elements strengthens the power of BBN. A new determination of the primordial helium abundance is included in our likelihood analysis. New D/H observations are now more precise than the corresponding theoretical predictions and are consistent with the standard model and the Planck baryon density. Moreover, D/H now provides a tight measurement of $N_{\nu }$ when combined with the CMB baryon density and provides a $2\sigma$ upper limit $N_{\nu }<3.2$. The new precision of the CMB and D/H observations together leaves D/H predictions as the largest source of uncertainties. Future improvement in BBN calculations will therefore rely on improved nuclear cross-section data. In contrast with D/H and ${}^4\mathrm{He}$, ${}^7\mathrm{Li}$ predictions continue to disagree with observations, perhaps pointing to new physics. This paper concludes with a look at future directions including key nuclear reactions, astronomical observations, and theoretical issues.

Figure 1

Primordial abundances of the light nuclides as a function of cosmic baryon content as predicted by SBBN (the “Schramm plot”). These results assume $N_{\nu }=3$ and the current measurement of the neutron lifetime ${\tau }_n=880.3\pm 1.1\mathrm{s}$. Curve widths show $1-\sigma$ errors.

Figure 2

The sensitivity of the ${}^4\mathrm{He}$ abundance to the neutron mean lifetime, as shown through a scatter plot of our Monte Carlo error propagation.

Figure 3

Light-element predictions using the CMB determination of the cosmic baryon density. Shown are likelihoods for each of the light nuclides, normalized to show a maximum value of 1. The solid-lined, dark-shaded (purple) curves are the $\mathrm{BBN}+\mathrm{CMB}$ predictions, based on Planck inputs as discussed in the text. The dashed-lined, light-shaded (yellow) curves show astronomical measurements of the primordial abundances, for all but ${}^3\mathrm{He}$ where reliable primordial abundance measures do not exist. For ${}^4\mathrm{He}$, the dotted-lined, medium-shaded (cyan) curve shows the CMB determination of ${}^4\mathrm{He}$.

Figure 4

The 2D likelihood function contours derived from the Planck Markov chain Monte Carlo base_yhe with fixed $N_{\nu }=3$ (points). The correlation between $Y_p$ and $\eta$ is evident. The $3\sigma$ BBN prediction for the helium mass fraction is shown with the colored band. We see that including the BBN $Y_p(\eta )$ relation significantly reduces the uncertainty in $\eta$ due to the CMB $Y_p-\eta$ correlation.

Figure 5

The likelihood distributions of the baryon-to-photon ratio parameter $\eta$ given various CMB and light-element abundance constraints.

Figure 6

The 2D likelihood function contours derived from the Planck Markov chain Monte Carlo base_nnu_yhe, marginalized over the CMB $Y_p$ (points). Thin contours are for CMB data only, while thick contours use the BBN $Y_p(\eta )$ relation, assuming no observational constraints on the light elements. We see that whereas in the CMB-only case $N_{\nu }$ and $\eta$ are almost uncorrelated, in the $\mathrm{CMB}+\mathrm{BBN}$ case a stronger correlation emerges.

Figure 7

The sensitivity of the light-element predictions to the number of neutrino species, similar to Fig. 1. Here abundances shown by different colored bands correspond to calculated abundances assuming $N_{\nu }=2$, 3, and 4.

Figure 8

The marginalized distributions for the number of neutrinos, given different combinations of observational constraints. The left panel shows the likelihood function in the case where only CMB data are used (dashed blue curve), only BBN and abundance data are used (dot-dashed red curve), and when a combination of BBN and CMB data is used (solid green curve). The four solid green curves are shown again in the right panel for better clarity.

Figure 9

The marginalized distributions for the baryon-to-photon ratio ($\eta$), given different combinations of observational constraints.

Figure 10

The resulting two-dimensional likelihood functions for the baryon-to-photon ratio ($\eta$) and the number of neutrinos ($N_{\nu }$), marginalized over the helium mass fraction $Y_p$, assuming different combinations of observational constraints on the light elements.