Big Bang nucleosynthesis

In physical cosmology, Big Bang nucleosynthesis is a model for the production of light nuclei during the first ~20 minutes of the evolution of the universe. The predictions of BBN rely on a combination of thermodynamic arguments and measurements of rates of nuclear reactions that are expected to be active in the early universe. Refined models tend to agree well with observations of these light element abundances. The model is one of the key concepts in standard cosmology.
Elements heavier than lithium are instead created in appreciable amounts at later times via stellar nucleosynthesis, through the formation, evolution and death of stars.

History

The history of Big Bang nucleosynthesis research began with George Gamow, a nuclear physicist who thought that Victor Goldschmidt's data on the abundance of elements in the universe might be predicted by nuclear reactions. Early in the 1940s Gamow realized that very high temperatures and pressures needed for nuclear reactions implied an explosion followed by expansion. Calculations by his student Ralph Alpher, published in the famous Alpher–Bethe–Gamow paper, outlined an early theory of light-element production in the early universe. These early efforts did not involve specific nuclear reactions. When Enrico Fermi and Anthony L. Turkevich tried, they found they would predict hydrogen and helium, but no higher elements. The key problem was a "mass gap": there no nuclei with masses of 5 and 8 atomic mass units needed for the reactions to reach higher masses. In 1953 this problem seemed insurmountable and cast doubt on the entire concept.
The competing cosmological model, the steady state model, appearing in two 1948 publications by Fred Hoyle and by Herman Bondi and Thomas Gold, had no mass-gap issue because it ignored nuclear processes initially. In 1957, Hoyle teamed up with Margaret Burbidge, Geoffrey Burbidge, William A. Fowler to develop a
detailed model of nucleosynthesis in stars. This theory matched the abundance of the almost all of the elements except for the hydrogen and helium, the elements correctly predicted by the Big Bang theory.
The discovery of the cosmic microwave background radiation in 1965 strongly supported the Big Bang theory and it also allowed Jim Peebles to use the estimated background temperature, 3K, in the first detailed calculations of the primordial isotopic abundances, showing a He abundance between 26 and 28%. The following year Hoyle, Fowler, and Robert Wagoner showed that the very light elements like He require higher temperatures than stars provide, evidence that most scientists took as support for the Big Bang model.
In 1972 the Copernicus satellite began to provide accurate measurements of deuterium abundance. Since primordial synthesis of deuterium depends more strongly on baryon density than does synthesis of ³He, the deuterium abundance could be used to infer primordial density. By the 1990s additional measurements concluded that this density implied there must be mass other than baryons in the universe, an idea that came to be called dark matter.
These nucleosynthesis methods have been refined over the years using updated estimates of the input nuclear reaction rates. The first systematic Monte Carlo study of how nuclear reaction rate uncertainties impact isotope predictions, over the relevant temperature range, was carried out in 1993.

Physical Description

Big Bang nucleosynthesis describes the production of atomic nuclei from protons and neutrons in the expanding and cooling early universe. The process occurs at equilibrium with protons and neutrons combining to create nuclei and the nuclei disintegrating. As the temperature and pressure drops, equilibrium shifts to favor a few light element nuclei. Further expansion stops the BBN processes, setting the initial cosmic abundance of these elements.
The cosmic expansion process during BBN is described by the Friedmann-Robertson-Walker model. These equations completely determine the rate of expansion of the universe, as well as the evolution of the energy densities of different particle species. In particular, these equations indicate that the universe becomes less dense and the temperature of particles in the Standard Model falls as BBN proceeds.
At temperatures above 1-2 MeV, protons and neutrons interconverted via the weak interaction. As the temperature dropped, these reactions fell out of equilibrium, neutrons primarily decayed to protons, and the neutron-to-proton ratio fell to around 1/7. This sets the initial conditions for the onset of the formation of light nuclei.
BBN began in earnest when the temperature of Standard Model particles dropped below roughly 1 MeV. At this temperature, the average energy of photons in the early universe was too low to break apart deuterium as it formed, but the universe remained hot and dense enough for fusion reactions to occur at a significant rate. This meant a substantial population of deuterium formed.
This deuterium then fused to heavier nuclei, including tritium, helium-3, helium-4, and lithium-7. Helium-4 has a large binding energy, which means that once a helium-4 nucleus is formed, it is difficult to break apart and incorporate its constituents into heavier nuclei. Therefore matter in the universe is primarily hydrogen and helium-4 after BBN. Standard BBN predicts, by the time BBN ends, the universe is composed of about 75% of hydrogen and 25% helium-4 by mass. Roughly 1 nucleus in 100,000 is deuterium or helium-3, and 1 nucleus in 1,000,000,000 is lithium-7. Even smaller amounts of heavier elements, as heavy as oxygen-20, have been predicted to form.
BBN coincides or nearly coincides with two other important events in cosmology. Neutrino decoupling occurred when the weak interaction fell out of equilibrium, just before BBN began. Electron–positron annihilation occurred during BBN, at around 0.5 MeV, when photons no longer had enough energy to convert back to electrons and positrons to maintain equilibrium. This resulted in the depletion of the abundance of positrons in the universe, and heated photons. Since electron-positron annihilation occurred after neutrino decoupling, neutrinos did not heat alongside photons when electrons and positrons annihilated, and photons developed a separate temperature from neutrinos. This has important consequences for the rates of proton-neutron interconversion and the prediction of light element abundances.

Light Element Nucleosynthesis

Important Parameters

The creation of light elements during BBN was dependent on nuclear reaction rate parameters and two cosmological input parameters neutron–proton ratio and the baryon-photon ratio. The nuclear reaction rates are well-known from detailed laboratory studies at similar temperatures to those that appear in BBN.

Baryon-to-photon ratio

Light element abundances, and in particular deuterium, are sensitive to the value of the baryon-to-photon number ratio, η, which is the ratio of the number density of baryons to the number density of photons. Its value is small, at roughly 6 × 10⁻¹⁰. This parameter is proportional to the baryon density and controls the entropy of the universe, which in turn determines the temperature at which nuclear fusion can begin. High entropy prevents light element nuclei from forming, which delays the onset of BBN; low entropy conversely lets BBN last longer, and therefore depletes the abundances of light elements that can fuse into helium-4.
Deuterium in particular is extremely sensitive to the value of the baryon-to-photon ratio; decreasing η by a factor of 10 leads to a corresponding increase in the abundance of primordial deuterium by a factor of roughly 50.

Expansion rate

Particles and nuclei fall out of equilibrium when their rates of interaction become slower than the rate of the expansion of the universe. If the rate keeping a nuclear species in equilibrium drops below the expansion rate, the relative abundance of that species stops evolving.
During BBN, the universe is radiation dominated, and so the expansion of the universe is primarily determined by the energy density in radiative species like photons and neutrinos. Light element abundances are therefore sensitive to the energy densities of these species.

Sequence

BBN begins shortly after neutrinos decouple from the Standard Model and processes interconverting protons and neutrons fall out of equilibrium. By roughly 20 seconds after the big bang, the universe had cooled sufficiently to allow deuterium nuclei to survive disruption by high-energy photons. At this time there were about six protons for every neutron.
As the universe expanded and cooled, other light elements began to form, becoming heavier through nuclear fusion. At temperatures below 0.3 MeV, conditions were right for helium-4 to form, and below 0.1 MeV the abundance of deuterium climbed high enough for a burst of element formation. However, very shortly thereafter, around twenty minutes after the Big Bang, the temperature and density became too low for any significant fusion to occur. At this point, the elemental abundances were nearly fixed. Further changes were the result of the radioactive decay of the two major unstable products of BBN, tritium and beryllium-7, as well as continued decay of neutrons that did not fuse into any nuclei. At the end of nucleosynthesis there were about seven protons to every neutron, and almost all the neutrons were in Helium-4 nuclei.

Neutron–proton interconversion

At temperatures above roughly 2 MeV, protons and neutrons interconverted via reactions involving electrons, positrons, neutrinos, and antineutrinos:
At times much earlier than 1 second, these reactions were fast and maintained a neutron/proton ratio close to 1. Neutrons are slightly heavier than protons, so even though these rates remained in equilibrium as the temperature began to drop, equilibrium shifted in favor of protons and the neutron/proton ratio smoothly decreased. Around a temperature of 2 MeV, these reactions fell out of equilibrium as neutrinos decoupled from the rest of the Standard Model. After this time, interconversion between protons and neutrons became inefficient, and the neutron-proton ratio was fixed to about 1/6.
However, this fraction continued to evolve during BBN, since free neutrons are unstable with a lifetime of about 15 minutes. Had nucleosynthesis not occurred, this ratio would have fallen to 0, but since neutrons are usually stable when bound in nuclei the neutron/proton ratio settles to about 1/7 by the end of BBN. Virtually all of these remaining neutrons are therefore incorporated into nuclei at the end of BBN.