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 present results from the JINA REACLIB project, an ongoing effort to maintain a current and accurate library of thermonuclear reaction rates for astrophysical applications. Ongoing updates are transparently documented and version tracked, and any set of rates is publicly available and can be downloaded via a web interface at http://groups.nscl.msu.edu/jina/reaclib/db/. We discuss here our library V1.0, a snapshot of recommended rates for stable and explosive hydrogen and helium burning. We show that the updated reaction rates lead to modest but significant changes in full network, full 1D X-ray burst model calculations, compared to calculations with previously used reaction rate sets. The late time behavior of X-ray burst light curves shows significant changes, suggesting that the previously found small discrepancies between model calculations and observations may be solved with a better understanding of the nuclear input. Our X-ray burst model calculations are intended to serve as a benchmark for future model comparisons and sensitivity studies, as the complete underlying nuclear physics is fully documented and publicly available.

We summarize and critically evaluate the available data on nuclear fusion cross sections important to energy generation in the Sun and other hydrogen-burning stars and to solar neutrino production. Recommended values and uncertainties are provided for key cross sections, and a recommended spectrum is given for 8 B solar neutrinos. We also discuss opportunities for further increasing the precision of key rates, including new facilities, new experimental techniques, and improvements in theory. This review, which summarizes the conclusions of a workshop held at the Institute for Nuclear Theory, Seattle, in January 2009, is intended as a 10-year update and supplement to Reviews of Modern Physics 70 (1998) 1265.

We reexamine the upper limits on the abundance of unstable massive relic particles provided by the success of big-bang nucleosynthesis calculations. We use the cosmic microwave background data to constrain the baryon-to-photon ratio, and incorporate an extensively updated compilation of cross sections into a new calculation of the network of reactions induced by electromagnetic showers that create and destroy the light elements deuterium, 3 He, 4 He, 6 Li and 7 Li. We derive analytic approximations that complement and check the full numerical calculations. Considerations of the abundances of 4 He and 6 Li exclude exceptional regions of parameter space that would otherwise have been permitted by deuterium alone. We illustrate our results by applying them to massive gravitinos. If they weigh ϳ100 GeV, their primordial abundance should have been below about 10 Ϫ13 of the total entropy. This would imply an upper limit on the reheating temperature of a few times 10 7 GeV, which could be a potential difficulty for some models of inflation. We discuss possible ways of evading this problem.

Big bang nucleosynthesis ͑BBN͒ and the cosmic microwave background ͑CMB͒ have a long history together in the standard cosmology. BBN accurately predicts the primordial light element abundances of deuterium, helium and lithium. The general concordance between the predicted and observed light element abundances provides a direct probe of the universal baryon density. Recent CMB anisotropy measurements, particularly the observations performed by the WMAP satellite, examine this concordance by independently measuring the cosmic baryon density. Key to this test of concordance is a quantitative understanding of the uncertainties in the BBN light element abundance predictions. These uncertainties are dominated by systematic errors in nuclear cross sections, however for helium-4 they are dominated by the uncertainties in the neutron lifetime and Newton's G. We critically analyze the cross section data, producing representations that describe this data and its uncertainties, taking into account the correlations among data, and explicitly treating the systematic errors between data sets. The procedure transforming these representations into thermal rates and errors is discussed. Using these updated nuclear inputs, we compute the new BBN abundance predictions, and quantitatively examine their concordance with observations. Depending on what deuterium observations are adopted, one gets the following constraints on the baryon density: ⍀ B h 2 ϭ0.0229Ϯ0.0013 or ⍀ B h 2 ϭ0.0216 Ϫ0.0021 ϩ0.0020 at 68% confidence, fixing N ,e f f ϭ3.0. If we instead adopt the WMAP baryon density, we find the following deuterium-based constraints on the effective number of neutrinos during BBN: N ,e f f ϭ2.78 Ϫ0.76 ϩ0.87 or N ,e f f ϭ3.65 Ϫ1.30 ϩ1.46 at 68% confidence. Concerns over systematics in helium and lithium observations limit the confidence constraints based on this data provide. BBN theory uncertainties are dominated by the following nuclear reactions: d(d,n) 3 He, d(d,p)t, d(p,␥) 3 He, 3 He(␣,␥) 7 Be and 3 He(d,p) 4 He. With new nuclear cross section data, light element abundance observations and the ever increasing resolution of the CMB anisotropy, tighter constraints can be placed on nuclear and particle astrophysics.

Using the recent WMAP determination of the baryon-to-photon ratio, 10 10 ϭ6.14 to within a few percent, big bang nucleosynthesis ͑BBN͒ calculations can make relatively accurate predictions of the abundances of the light element isotopes which can be tested against observational abundance determinations. At this value of , the 7 Li abundance is predicted to be significantly higher than that observed in low metallicity halo dwarf stars. Among the possible resolutions to this discrepancy are ͑1͒ 7 Li depletion in the atmosphere of stars, ͑2͒ systematic errors originating from the choice of stellar parameters-most notably the surface temperature, and ͑3͒ systematic errors in the nuclear cross sections used in the nucleosynthesis calculations. Here, we explore the last possibility, and focus on possible systematic errors in the 3 He(␣,␥) 7 Be reaction, which is the only important 7 Li production channel in BBN. The absolute value of the cross section for this key reaction is known relatively poorly both experimentally and theoretically. The agreement between the standard solar model and solar neutrino data thus provides additional constraints on variations in the cross section (S 34 ). Using the standard solar model of Bahcall, and recent solar neutrino data, we can exclude systematic S 34 variations of the magnitude needed to resolve the BBN 7 Li problem at the տ95% C.L., or more strongly, depending on the Li observations used. Additional laboratory data on 3 He(␣,␥) 7 Be will sharpen our understanding of both BBN and solar neutrinos, particularly if care is taken in determining the absolute cross section and its uncertainties. Nevertheless, it is already clear that this ''nuclear fix'' to the 7 Li BBN problem is unlikely; other possible solutions are briefly discussed.

A recent analysis of the 4 He abundance determined from observations of extragalactic HII regions indicates a significantly greater uncertainty for the 4 He mass fraction. The derived value is now in line with predictions from big bang nucleosynthesis when the baryon density determined by WMAP is assumed. Based on this new analysis of 4 He, we derive constraints on a host of particle properties which include: limits on the number of relativistic species at the time of BBN (commonly taken to be the limit on neutrino flavors), limits on the variations of fundamental couplings such as α em and G N , and limits on decaying particles. Standard BBNKey to BBN analysis is an accurate determination of BBN theory uncertainties, which are dominated by the errors in nuclear cross section data. To this end, several groups have

The lithium problem arises from the significant discrepancy between the primordial 7Li abundance as predicted by big bang nucleosynthesis (BBN) theory and the Wilkinson Microwave Anisotropy Probe (WMAP) baryon density, and the pre-Galactic lithium abundance inferred from observations of metal-poor (Population II) stars. This problem has loomed for the past decade, with a persistent discrepancy of a factor of 2–3 in 7Li/H. Recent developments have sharpened all aspects of the Li problem. Namely: (1) BBN theory predictions have sharpened due to new nuclear data; in particular, the uncertainty on the reaction rate for3He(α,γ)7Be has reduced to 7.4%, nearly a factor of 2 tighter than previous determinations. (2) The WMAP five-year data set now yields a cosmic baryon density with an uncertainty reduced to 2.7%. (3) Observations of metal-poor stars have tested for systematic effects. With these, we now find that the BBN+WMAP predicts7Li/H = (5.24−0.67 +0.71) × 10−10. The central value represents an increase by 23%, most of which is due to the upward shift in the3He(α,γ)7Be rate. More significant is the reduction in the7Li/H uncertainty by almost a factor of 2, tracking the reduction in the3He(α,γ)7Be error bar. These changes exacerbate the Li problem; the discrepancy is now a factor 2.4 or 4.2σ (from globular cluster stars) to 4.3 or 5.3σ (from halo field stars). Possible resolutions to the lithium problem are briefly reviewed, and key experimental and astronomical measurements highlighted.