COSMOLOGY, NUCLEOGENESIS ROBERT V. WAGONER The matter that fills the universe today retains a significant imprint of its history: the relative abundances of the wide variety of atomic nuclei. These abundances have been determined in many different sites; either directly (by analyzing meteorites, cosmic rays, etc.) or, most commonly, indirectly (via spectra of stars, interstellar gas, other galaxies, quasars, etc.). Using these data, astrophysicists can become "cosmic archaeologists," sifting through these ashes for clues to the nature of the universe's past. It is now clear that most of the heavier elements were produced by nuclear reactions within stars and in other locations during the recent history of the universe. However, it is also clear that the bulk of the lightest elements (hydrogen, helium, and lithium, with the exception of the isotope ***) were probably formed throughout the universe, during an epoch in the remote past. The consequences of this process of nucleosynthesis, which produces our deepest direct probe of the early universe, are the subject of this entry. As we shall see, the agreement between the observed and calculated abundances of these lightest nuclei provides strong evidence for the validity of the standard Hot Big Bang model of the universe, which leads to an estimate of the amount of ordinary matter in the present universe as well as constraints on new types of elementary particles. Although the concept that our universe may have expanded from a state of much higher density was developed in the period around 1930 (mostly via Lemaitre's "primeval atom"), the knowledge of nuclear reactions necessary to calculate the abundances produced during such an era was not yet available. The first such calculations were carried out in the late 1940s by Ralph Alpher, George Gamow, and Robert Herman, who argued that the temperature was also very high at that time. Although the correct physical description of this era was developed by 1953, the nuclear abundances were not recalculated until the 1960s (apparently because of the great success of stellar nucleosynthesis and the realization that only the lightest nuclei could be produced in the expanding and cooling "primeval fireball"). The discovery of the cosmic microwave radiation in 1965 reinvigorated the Hot Big Bang model, and soon thereafter nuclear-reaction network calculations had produced unambiguous predictions. In the simplest ("standard") model, the resulting abundances [***** (protons), ** (deuterium), ***, ***, and ***] depended only on the total density of baryons (i.e., nuclei) at a given temperature. Various developments during the subsequent two decades strengthened the argument that these nuclei were indeed relics of such a remote epoch. Around 1970, calculations began to show that those light nuclei whose observed abundances were too high to fit a fireball-production model (***, ***, ***, and ***) were precisely those produced by collisions of cosmic ray nuclei with the interstellar gas. Meanwhile, the belief that stellar interiors or other galactic sites could produce all the heavier nuclei continued to grow. In 1973, the Copernicus satellite detected deuterium in the nearby interstellar gas. The resulting abundance determination was the first not subject to the large uncertainties of chemical fractionation, and was of critical importance. Deuterium is difficult to produce after the Big Bang era is over, and stars easily consume it. Therefore, it was argued, the Big Bang deuterium abundance must have been at least as great as the abundance presently observed. The predicted Big Bang abundance is a decreasing function of the assumed density of baryons. The deuterium measurement therefore implied an upper limit on the amount of "ordinary" (baryonic) matter in the universe today. A third important discovery was that there are galaxies with a significant deficiency of heavy elements but an almost normal abundance of helium. It was natural to assume that these were systems in which stellar processing had not yet occurred to a great extent, so that the addition to the primordial helium (mostly ***) was small. Thus a more relevant value was also obtained for this abundance. The next major advance began with the discovery (in 1982) of old stars which appeared to have formed from gas containing about 10 times less lithium than the previous "cosmic" abundance. It could be argued that this new determination was more likely to represent the primordial abundance. At about the same time, improved nuclear-reaction rate data led to an increase in the predicted abundance of ***. It was remarkable that the observed and predicted primordial abundances then came into agreement for that value of the cosmic density which also produced agreement for the other nuclear abundances. PRODUCTION OF NUCLEI IN THE EARLY UNIVERSE The framework within which one calculates the primordial synthesis of nuclei is provided by a model of the structure and dynamics of the universe as a whole. We shall first discuss the results obtained within the standard Big Bang model, which represents the simplest extrapolation of our present knowledge into the past. This model is essentially constructed from the assumptions that (a) general relativity governs the expansion of the universe, (b) the properties of the universe were independent of position (homogeneity) and direction (isotropy) at any particular time in the deep past (before structures like galaxies formed), and (c) only the known particles were present. A key property of the early universe which emerges from this model is its expansion rate, ************************** (1) Where V is any small volume containing a fixed number of nucleons (neutrons plus protons), and p is the total density of matter (including radiation). A more familiar property is the cooling of the gas due to this expansion, with the cube of its temperature ** proportional to ***, in turn proportional to the density of these nucleons (which provide most of the mass of ordinary matter). But because the density of relativistic particles (photons, neutrinos, and electron-positron pairs) was proportional to **, they dominated during the epoch of interest, which began when the temperature was about **** K. (The present temperature of the relic photons is 3K.) It is extremely fortunate that the rates of the reactions among these particles were faster than the expansion rate (1) at this time (****** after the Big Bang). This meant that they were in equilibrium with each other, so that their properties (such as density) were fixed, independent of the previous history of the universe! The sole exceptions were the conserved quantities: the number of baryons (nucleons), electron-leptons (electrons plus electron neutrinos minus their antiparticles), plus other flavors of leptons (muon and tau neutrinos); they must be specified. In the standard model all three lepton numbers are taken to be so small that the corresponding neutrinos are nondegenerate, with roughly equal numbers of leptons and antileptons. The first event of importance during this era occurred when the temperature had dropped almost to **** K, at which time the reactions ********* and *********, which had kept the neutrons and protons at a relative abundance ***********************, (2) dropped out of equlibrium. equilibrium. Subsequently this ratio remained almost fixed, until the next major event-the emergence of other nuclei. This is shown in Fig.1, which depicts the evolution of the nuclear abundances during the expansion of a particular model. It should be noted that then (and now) there were ********* photons per nucleon. Since the average energy of the photons was decreasing as the universe cooled, eventually their ability to dissociate deuterium into nucleons decreased to the point (near ********) where a sufficient abundance of ** existed to allow further nuclear reactions to proceed quickly. Roughly 30 such reactions among the nuclei shown played a role in determining the final abundances. Thanks to the heroic efforts of many nuclear physicists, essentially all of the relevant nuclear cross sections have been measured, so that we can have confidence in these predicted abundances. This cannot yet be said about any process occurring earlier in the history of the universe. COMPARISON WITH OBSERVED ABUNDANCES The abundances which emerge from this process are compared with the range of observed abundances which might represent their primordial values in Fig.2. Agreement can be achieved for those standard models in the range indicated. Let us first explore the consequences of the abundance of ***, which has the most precisely determined mass fraction: ***********. If the expansion rate had differed from Eq.(1), the neutrons and protons would have ceased to be in equilibrium at a different temperature, producing a different "frozen-out" relative abundance [from Eq.(2)]. Because almost all neutrons are eventually incorporated into ***, its abundance is directly affected. Thus powerful constraints can be put upon other theories of gravitation, the amount of anisotropy, the degree of neutrino degeneracy [which can also change Eq.(2)], and any other factor which affects the expansion rate. In particular, if more types of neutrino [or any other particle which contributed to the density in Eq.(1)] existed, more helium would have been produced. This constraint has very recently been spectacularly confirmed at the Stanford Linear Collider and at CERN, where the decay rate of the Z* particle produced by electron-positron collisions has shown that there are only three types of light neutrinos, consistent with the limit obtained from the helium abundance. Another major consequence, which follows mainly from the other abundances, is the pair of upper and lower limits on the present density of ordinary (baryonic) matter. The range shown in Fig. 2 corresponds to at most about 20% of that required to produce a universe with no spatial curvature (favored by many on aesthetic grounds). But more importantly, this upper limit may turn out to be less than the measured total density of matter, which can be determined by its gravitational influences on observed matter (galaxies, etc.). If so, it would indicate that a new form of matter pervades the universe. The desire to avoid this conclusion has recently motivated two other modifications of the standard model, which attempt to produce an agreement with observed abundances for larger values of the baryon density. The first invokes a first-order phase separation during the quark-hadron transition that formed the protons and neutrons, which could have produced large inhomogeneities in their abundances. However, this model has great difficulty avoiding overproduction of ***. The second involves late-decaying massive particles, whose electromagnetic and hadronic showers strongly affect most products of the previous standard nucleosynthesis. The resulting abundances can be made consistent with those observed, but the predicted excess of *** relative to *** may prove to be a fatal problem. FUTURE The quest for truly primordial abundances is the key challenge for the future. Mapping the space and time (redshift) dependence of the amounts of these light nuclei with the largest ground-based telescopes as well as from space (with the Hubble Space Telescope, initially) will be required. On the theoretical side, we must be wary of being channeled into a parochial view of the scope of possible universes. (Could a very early generation of the stars ("Population III") have produced the helium and lithium, as well as the cosmic microwave radiation?) But the standard model has thus far withstood the powerful test provided by these nuclear relics. Additional Reading Boesgaard, A.M. and Steigman, G.(1985). Big Bang nucleosynthesis: Theories and observations. Ann. Rev. Astron. Ap. 23 319. Schramm, D.N. and Steigman, G.(1988). Particle accelerators test cosmological theory. Scientific American 258 (No. 6)66. Schramm, D.N. and Wagoner, R.V.(1977). Element production in the early universe. Ann. Rev. Nucl. Sci. 27 37. Silk, J.(1989). The Big Bang. W.H. Freeman and Co., New York. Wagoner, R.V. and Goldsmith, D.W.(1983). Cosmic Horizons. W.H. Freeman and Co., San Francisco. See also Cosmology, Big Bang Theory; Cosmology, Population III; Dark Matter, Cosmological; Stars, Chemical Composition; Supernova Remnants, Evidence for Nucleosynthesis.