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. We briefly overview the essentials of this physics, and present new calculations of light element abundances through Li predictions continue to disagree with observations, perhaps pointing to new physics. We conclude with a look at future directions including key nuclear reactions, astronomical observations, and theoretical issues.2

We assess the status of big-bang nucleosynthesis (BBN) in light of the final Planck data release and other recent developments, and in anticipation of future measurements. Planck data from the recombination era fix the cosmic baryon density to 0.9% precision, and now damping tail measurements determine the helium abundance and effective number of neutrinos with precision approaching that of astronomical and BBN determinations respectively. All three parameters are related by BBN. In addition, new high-redshift measurements give D/H to better precision than theoretical predictions, and new Li/H data reconfirm the lithium problem. We present new 7 Be(n, p) 7 Li rates using new neutron capture measurements; we have also examined the effect of proposed changes in the d(p, γ) 3 He rates. Using these results we perform a series of likelihood analyses. We assess BBN/CMB consistency, with attention to how our results depend on the choice of Planck data, as well as how the results depend on the choice of non-BBN, non-Planck data sets. Most importantly the lithium problem remains, and indeed is more acute given the very tight D/H observational constraints; new neutron capture data reveals systematics that somewhat increases uncertainty and thus slightly reduces but does not essentially change the problem. We confirm that d(p, γ) 3 He theoretical rates brings D/H out of agreement and slightly increases 7 Li; new experimental data are needed at BBN energies. Setting the lithium problem aside, we find the effective number of neutrino species at BBN is N ν = 2.86±0.15. Future CMB Stage-4 measurements promise substantial improvements in BBN parameters: helium abundance determinations will be competitive with the best astronomical determinations, and N eff will approach sensitivities capable of detecting the effects of Standard Model neutrino heating of the primordial plasma. 7 Li(p, α) 4 He 7 Li(p, γ) 4 He 4 He Also following [29], we model the uncertainty distribution as a lognormal distribution.This is motivated physically by the idea that the experimental nuclear rates are controlled by several multiplicative factors whose uncertainties thus take this form [17]. In practice the errors are usually sufficiently small that the choice of a lognormal versus Gaussian distribution does not have a large impact on our result.

We consider the effect on Big Bang Nucleosynthesis (BBN) of new measurements of the d(p,γ)3 cross section by the LUNA Collaboration. These have an important effect on the primordial abundance of D/H which is also sensitive to the baryon density at the time of BBN. We have re-evaluated the thermal rate for this reaction, using a world average of cross section data, which we describe with model-independent polynomials; our results are in good agreement with a similar analysis by LUNA. We then perform a full likelihood analysis combining BBN and Planck cosmic microwave background (CMB) likelihood chains using the new rate combined with previous measurements and compare with the results using previous rates. Concordance between BBN and CMB measurements of the anisotropy spectrum using the old rates was excellent. The predicted deuterium abundance at the Planck value of the baryon density was (D/H)BBN+CMB old = (2.57 ± 0.13) × 10−5 which can be compared with the value determined from quasar absorption systems (D/H)obs = (2.55 ± 0.03) × 10−5. Using the new rates we find (D/H)BBN+CMB = (2.51 ± 0.11) × 10−5. We thus find consistency among BBN theory, deuterium and 4 observations, and the CMB, when using reaction rates fit in our data-driven approach. We also find that the new reaction data tightens the constraints on the number of relativistic degrees of freedom during BBN, giving the effective number of light neutrino species Nν = 2.880 ± 0.144 in good agreement with the Standard Model of particle physics. Finally, we note that the observed deuterium abundance continues to be more precise than the BBN+CMB prediction, whose error budget is now dominated by d(d,n)3 and d(d,p)3 H. More broadly, it is clear that the details of the treatment of nuclear reactions and their uncertainty have become critical for BBN.

We present new Big Bang Nucleosynthesis (BBN) limits on the cosmic expansion rate or relativistic energy density, quantified via the number Nν of equivalent neutrino species. We use the latest light element observations, neutron mean lifetime, and update our evaluation for the nuclear rates d + d ⟶ 3He + n and d + d ⟶ 3H+ p. Combining this result with the independent constraints from the cosmic microwave background (CMB) yields tight limits on new physics that perturbs Nν and η prior to cosmic nucleosynthesis: a joint BBN+CMB analysis gives Nν = 2.898 ± 0.141, resulting in Nν < 3.180 at 2σ. We apply these limits to a wide variety of new physics scenarios including right-handed neutrinos, dark radiation, and a stochastic gravitational wave background. The strength of the independent BBN and CMB constraints now opens a new window: we can search for limits on potential changes in Nν and/or the baryon-to-photon ratio η between the two epochs. The present data place strong constraints on the allowed changes in Nν between BBN and CMB decoupling; for example, we find -0.708 < Nν CMB - Nν BBN < 0.328 in the case where η and the primordial helium mass fraction Yp are unchanged between the two epochs; we also give limits on the allowed variations in η or in (η, Nν ) jointly. We discuss scenarios in which such changes could occur, and show that BBN+CMB results combine to place important constraints on some early dark energy models to explain the H0 tension. Looking to the future, we forecast the tightened precision for Nν arising from both CMB Stage 4 measurements as well as improvements in astronomical 4He measurements. We find that CMB-S4 combined with present BBN and light element observation precision can give σ(Nν ) ≃ 0.03. Such future precision would reveal the expected effect of neutrino heating (Neff -3 = 0.044) of the CMB during BBN, and would be near the level to reveal any particle species ever in thermal equilibrium with the standard model. Improved Yp measurements can push this precision even further.

We have identified and corrected two errors in our code that in a few cases made small effects on our results. These slightly shift our constraints on the number N ν of neutrino species, giving N ν = 2.843 ± 0.154. In all cases the changes are small compared to the uncertainties. None of our conclusions are changed.