BIG BANG NUCLEOSYNTHESIS

The search for the origin of our universe and its contents, including the Earth and its living organisms, is a fundamental object of human curiosity. Following the discovery by Hubble that the galaxies of the universe all recede from each other, a simple projection back in time allowed Gamow to estimate that the universe must have originated from a very dense and hot condition that allowed the formation of the chemical elements out of more elementary constituents. By turning the problem around to deduce conditions in the early universe, the investigation of Big Bang nucleosynthesis provides one of the most powerful probes of the origin of the universe.

In Big Bang models there is a time of precisely zero when the scale of the universe becomes zero. Although this zero point itself is outside the domain of the physical model, arbitrarily small times near but not equal to zero are within the scope of the model. For these earliest times the density of matter and energy as well as the temperature become arbitrarily high. The words "arbitrarily near zero" mean that there can be as many zeros between the decimal point and the first nonzero number as one may sensibly describe. With time measured in seconds, the limit of physical theories is now at what is called Planck time, with forty-two zeros preceding the first digit. Quantifying the evolution of the universe from this early time until the present is a central goal of modern cosmology.

The fundamental forces of nature in the present universe include gravity, which binds matter into planets; the weak interaction, which allows the creation of electrons and neutrinos when a neutron decays into a proton; the electromagnetic force, which binds electrons and atomic nuclei into atoms and molecules as well as the creation of photons from moving electrons; and the strong force, which holds together nuclei. Associated with these forces are different classes of particles. The strongly interacting particles are composed of two or three quarks and are known as hadrons. The weakly interacting particles are known as leptons and include the electrons, muons, tau particles, and their associated neutrinos. The hadrons include the baryon subgroup that includes protons and neutrons.

At high density and temperature, the universe is filled with particles of many unfamiliar types. With the extreme temperature and energy, the forces of nature lose some of their distinct properties and combine into a more unified form called a Grand Unified Theory (GUT) or still further a theory of everything (TOE) if gravity is included. So far combinations beyond weak forces and electromagnetic fields are only a goal of particle physics and cosmology. As the expansion continues, more familiar particles like protons, neutrons, electrons, and photons begin to appear. Initially, there are both matter and antimatter particles. The matter particles are found today, whereas the antiparticles were annihilated by matter prior to the time of nucleosynthesis. At present just the excess of matter particles over antimatter particles remains in existence. One of the first questions that must be confronted in understanding the formation of the elements is as follows: "Why is there an excess of matter over antimatter?" There is no evidence that any regions of the universe contain pockets of anti-matter, so some asymmetry in the conservation laws governing the early universe must favor that form of matter that prevails today. Either form of matter could have been favored by this asymmetry, and naturally one refers to the form one is not made of "antimatter." The study of this question is called barygenesis.

A successful barygenesis model must include forces that favor particles instead of antiparticles. This, however, is not enough and the forces must include other nonsymmetric aspects. All particles are described by sets of numbers that specify their properties. An example of such a property is the charge. Another property is called the parity, and it depends on the handedness of a particle. A normal corkscrew goes down into the cork when it is turned clockwise as viewed from above. An anticorkscrew would have to be turned counterclockwise to penetrate the cork. The forces between particles depend on their parities and charges. If the force depends on these properties in a nonsymmetric manner, the force is said to violate CP symmetry. Andrei Sakharov pointed out in 1967 that in order for a process favoring matter over anti-matter to succeed in leaving our present universe with the observed matter excess, there must be an asymmetry between the forces on the particles and anti-particles and there must be a force that violates CP symmetry. Models that have both these features are not developed to the level where they can reproduce the observed baryon density in the universe, and Big Bang nucleosynthesis beyond barygenesis treats the baryon density as a free parameter from which the relative abundances of the light elements are deduced.

FIGURE 1

As one follows the expansion of the universe past the time when the baryon density is established, there are two general principles that govern the unfolding of the universe's content: (1) The more matter and energy the universe contains per volume at a given time, the more rapidly it expands, and (2) many constituents of the universe are not in balance with other constituents. The first point is true because the universe is in the reverse of a free-fall collapse—a free expansion. Neither free fall nor free expansion involve frictional processes, and so these two processes are time-reversed versions of each other. It is easy to see that the more mass attracting an object in free fall, the more rapidly the object will accelerate. Because of this effect, if the energy content in one model of the universe is larger than that of a second model of the universe at a moment of time, its rate of expansion will also be larger. The second point says that the relative abundances of the elements need not be in thermodynamic equilibrium with each other. During the key period of the universe expansion, various isotopic species have abundances that differ from those characteristic of a steady thermo-dynamic equilibrium. When the temperature changes more rapidly than the forward and backward reaction rates can follow, the abundances become fixed near values appropriate to this last equilibrium temperature. Different isotopes are characterized by different last equilibrium temperatures. This process is described as the freeze-out of particle species.

In the time prior to element building, neutrinos are formed in equilibrium with their associated electrons, muons, and tau particles. The number of distinct leptons governs the number of neutrino families that can be created during the lepton era. This, in turn, governs the energy density of the universe since a larger number of distinct neutrino types increases the energy in the form of neutrinos. Because of the free expansion character of the early evolution of the universe, a larger number of neutrino types increases the rate at which the universe expands and reduces the time available for element building. Consequently, the abundances predicted by the Big Bang nucleosynthesis models constrain the number of independent neutrino families.

The temperature drops during the universe expansion until the neutrons and protons have frozen out. The era of element building is somewhat later than the neutron/proton freeze-out, but the time interval is short enough that the decay of the free neutrons has no major impact on nucleosynthesis. Although reactions involving leptons and the neutron-proton conversions are generally slow, their reaction rates are very temperature-dependent and initially the neutron/proton ratio is the thermodynamic equilibrium value. This ratio depends on temperature since the mass energy of the neutron at rest is larger that of the proton—a higher temperature gives a higher neutron/proton ratio. For a more rapid expansion the freeze-out temperature is higher so that a more rapidly expanding universe has a greater neutron abundance and ultimately a greater ⁴He abundance.

After the neutron/proton ratio has become frozen, the building of the light isotopic species ²D, ³He, ⁴He, and ⁷Li can take place. If one is able to determine the present abundances of these species and be sure that no other process has contributed to their production, these abundances may be used to learn about conditions during the early universe. As a complication, nucleosynthesis also occurs in stellar cores, and the production or destruction of species can alter their present abundance.

To distinguish between stellar and Big Bang nucleosynthesis one can use the fact that the early universe differs from stellar cores in two important respects: (1) The product of matter density and the time available for nucleosynthesis is very small compared to conditions in stellar cores, and (2) with few exceptions there are no free neutrons in stellar cores. These two differences have consequences that permit the identification of nuclei that have been produced exclusively by Big Bang nucleosynthesis and those that have been altered by star-based nucleosynthesis. In particular, ¹²C, ¹³C, ¹⁴N, and ¹⁶O as well as most other heavy isotopes require longer times and higher densities than are available during the Big Bang; they are considered to be the products of nucleosynthesis in star cores or supernovae. In contrast, the light isotopes except for ⁴He are destroyed in stellar interiors, and ⁴He is generally not ejected back into space from stars with a higher abundance than is found in the interstellar gas. Thus, the light isotope abundances are the best evidence about conditions during Big Bang nucleosynthesis.

Big Bang nucleosynthesis begins with the individual baryons—the protons and neutrons. The neutrons are unstable as free particles, but due to the shortness of time during the nucleosynthesis era of the Big Bang, their abundance is only slightly reduced by this decay. In order to build up multiple baryon isotopes, pairs of the individual baryons must combine. In the absence of the neutrons, the first step would have to combine two protons to form a product described as ²He. This combination cannot exist even briefly unless one of the protons is converted into a neutron to produce deuterium. However, this conversion involves a weak interaction and is too slow to occur during the Big Bang. Consequently, the presence of the neutrons at the beginning of Big Bang nucleosynthesis is a critical requirement for the formation of the light isotopes. With neutrons starting the sequence, the nuclei with more than two nucleons are easily created by adding either protons or neutrons until ⁴He is reached as the dominant product. Heavier nuclei are more difficult to build due to the absence of nuclei having five or eight nucleons. The combination of ⁴He with one of the lighter intermediate species permits the mass 5 gap to be bridged but at the expense of a reduced duced abundance of the product. Big Bang nucleosynthesis is effective in the production of isotopes up to ¹¹B. Of the light isotopes useful observational constraints are available for ²D, ⁴He, and ⁷Li. Observed abundances are also available for ³He, but these are not as useful because of possible alterations by stellar processing.

The comparison between models of Big Bang nucleosynthesis and observations requires both good observations and good model calculations. The input parameters to the model calculation include the density of baryons relative to the cosmic background radiation, the number of neutrino families, and a set of nuclear reaction rates derived from laboratory observations. Figure 2 shows the output abundances provided by one of these model calculations as reported

FIGURE 2

by M. S. Turner in 1999. Compared to the models and shown as the cross-hatched bands are recent estimates of the abundances and their uncertainties reported by K. A. Olive, G. Steigman, and T.P. Walker in 2000 (OSW[2000] in Figure 2) and S. Burles, K. M. Nollett, and M. S. Turner in 2001 (BNT[2001] in Figure 2). The vertical grey band indicates the density range where there is good agreement between the model and the observations of ²D. The observations of ²D in the interstellar gas along lines of sight to distant quasars provide the most precise constraint on the baryon density. The abundance of ⁴He restricts the number of independent lepton families to three or possibly four. The final species shown in Figure 2 is ⁷Li. Although there are stellar processes that form and destroy ⁷Li, there is a large set of measurements for stars believed to be members of an older population, and the distribution of the abundances shows a plateau that is interpreted as the primordial abundance. This interpretation is subject to systematic uncertainty, for which an estimate is included in the plotted abundance range.

The application of Big Bang nucleosynthesis provides three important results:

1. The widely distributed isotopic species of ²D, ⁴He, and ⁷Li can be produced from a fully self-consistent model.
2. There are no more than three or possibly four independent families of leptons and their associated neutrinos.
3. The baryons can only account for about 8 percent of the mass needed to achieve a closed universe. Other methods of determining the amount of matter in the universe show that the baryons represent only a small fraction of the mass density.

See also:Big Bang; CP Symmetry Violation; Symmetry Principles

Bibliography

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Burles, S.; Nollett, K. M.; and Turner, M. S. "What Is the Big-Bang Nucleosynthesis Prediction for ht Baryon Density and How Reliable Is It?" Physical Review D63 , 063512-1– 063512-5 (2001).

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Roger K. Ulrich