Origin of the Light Elements

Weak interaction freeze-out

At high temperature, the matter in the Big Bang consisted only of its most elementary constituents. When the temperature dropped below a few hundred MeV, ordinary nucleons (or baryons) could form: these are protons and neutrons since no heavier nuclei would have survived the high temperatures. In addition there are the light particles (leptons), such as electrons, neutrinos and photons. Neutrons and neutrinos interact with electrons and protons by means of the weak nuclear interaction. This is the interaction that is responsible for radioactive decays of unstable isotopes. When the temperature of the universe drops below about 1 MeV (or 10^{10}K), the weak interaction rate becomes slower than the rate of expansion of the universe. At this stage, about 1 second has elapsed of cosmic time since the Big Bang. Once the weak interaction have effectively halted, the residual number of neutrons (and neutrinos) is fixed. There is approximately one neutron remaining for every ten protons.

Primordial nucleosynthesis

The lifetime of a free neutron to decay is about ten minutes. However most neutrons do not have time to decay. After only about three minutes have elapsed, something else occurs. Neutrons interact with protons to form nuclei of deuterium, or heavy hydrogen. The deuterium soon gains another neutron to form tritium, which in turn rapidly absorbs a proton to form a helium nucleus of mass 4, consisting of two protons and two neutrons. There is no stable element of mass 5, nor of mass 8, so additional nucleosynthesis via He + p or He + He is generally not possible although trace amounts of one or two heavier elements, most notably lithium (of mass 7) do form. One finds that practically every neutron ends up in a helium nucleus. The Big Bang therefore predicts that there should be one helium nucleus for every ten protons, created in the first three minutes of the expansion. Approximately 25 percent by mass of the matter in the universe is now in the form of helium nuclei: the rest consists of protons. For the Sun helium is about 30%, since some of the hydrogen has already been processed through stars (including the Sun itself!), ie the solar material is not "primordial".

A Helium abundance of about 1/4 by mass turns out to be a robust prediction of the Big Bang theory, and depends only on the fact that the very early universe passed through a high temperature, high density phase, much like the center of a star. This abundance is in fact just what we observe when we look at material which we believe to be close to primordial. Other important predictions include small amounts of deuterium and lithium, although the final abundances of these elements, deuterium especially, depend on the precise value of Omega_b. If the density of ordinary matter (baryons) is high, the early nucleosynthesis is efficient, and one makes essentially no deuterium. If the baryon density is low, however, one makes an amount of deuterium that is comparable to what is observed by astronomers in the absorption spectra of distant quasars.


Helium is synthesized inside stars by thermonuclear fusion. However, most stars, like the sun, are still burning hydrogen and so have made little helium, and certainly dispersed none of it. The synthesized helium is deep inside the stellar interior. Yet the universe indeed is observed to contain one helium atom for every ten atoms of hydrogen: by mass, it is about 25 percent helium. This is close to the case for the sun, it is as observed in solar cosmic rays, for interstellar gas in HII regions, and for hot stars, where the helium emission lines are excited. Moreover, when we compare stars which are metal-rich with metal-poor stars, one finds essentially the same helium abundance. There are metal-deficient galaxies which contain almost the same helium abundance. This confirms that helium has mostly not been synthesized along with the heavier elements, such as the metals, but was made prior to the formation of the first stars. The coincidence between observation and prediction of the helium abundance in the universe provides one of the major pieces of evidence for the Big Bang theory.

Deuterium and the baryon density

Unlike helium, deuterium is a very fragile element. It burns at a temperature of only 10^6 K, well below the temperature in the solar core. A considerable fraction of any primordial deuterium at the beginning of the galaxy would have been destroyed by the present time. This is confirmed by observation: interstellar clouds contain deuterium, as do protostars, stars which have not yet developed nuclear burning cores, whereas evolved stars have essentially no deuterium. By studying clouds of gas at very high redshift in the medium between galaxies one can infer the amount of deuterium relative to that of hydrogen. Comparison with the Big Bang prediction requires one to choose a density that cannot exceed about a tenth of the critical density for closure of the universe, otherwise too little primordial deuterium would have been synthesized. There is no alternative to the Big Bang for synthesizing deuterium: stars destroy it rather than produce it. The significance of this result is that most of the matter in the universe must be non baryons, for example it could consist of weakly interacting neutral particles that did not participate in the nuclear reactions that led to deuterium production.

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