The light elements are essential, because their primordial abundances are linked to the general parameters of the universe (at least in the Big Bang theory). Some of the light elements are fragile, and the interpretation of their abundances in stars requires a good knowledge of the stellar structure. The stellar abundances have to be known with a considerable accuracy, challenging the current level of representation of the stellar atmospheres. It is also difficult to reach accurate abundances in the gas : interstellar, H II regions, PN, intergalactic¨.

On the other hand, the fragile light elements are important probes of the stellar interiors, and their observation helps to the determination of reliable models, which in turn will improve the accuracy of stellar abundances. A part of this symposium is devoted to this probing aspect.

The talks (and many high quality posters) which build this symposium, cover all these aspects. I will try here to point out the controversial points and the reasonably well known facts. We expect from discussions, both formal and informal, a number of (eagerly awaited for) clarifications.

The physics of the standard hot big bang cosmology ensures that the early Universe was a primordial nuclear reactor, synthesizing the light nuclides (D, 3He, 4He, and 7Li) in the first 20 minutes of its evolution. After an overview of nucleosynthesis in the standard model (SBBN), the primordial abundance yields will be presented, followed by a status report (intended to stimulate further discussion during this symposium) on the progress along the road from observational data to inferred primordial abundances. Theory will be confronted with observations to assess the consistency of SBBN and to constrain cosmology and particle physics. Some of the issues/problems key to SBBN in the new millenium will be highlighted, along with a wish list to challenge theorists and observers alike.

Standard big bang nucleosynthesis (SBBN) has been remarkably successful, and it may well be the correct and sufficient account of what happened. However, interest in variations from the standard picture come from two sources: First, big bang nucleosynthesis can be used to constrain physics of the early universe. Second, there may be some discrepancy between predictions of SBBN and observations of abundances. Various alternatives to SBBN include inhomogeneous nucleosynthesis, nucleosynthesis with antimatter, and nonstandard neutrino physics.

We show that the available constraints relating to 6LiBeB Galactic evolution can be accounted for by the so-called superbubble model, according to which particles are efficiently accelerated inside superbubbles out of a mixture of supernova ejecta and ambient interstellar medium. The corresponding energy spectrum is required to be flat at low energy (in E−1 below 500 MeV/n, say), as expected from Bykov's acceleration mechanism. The only free parameter is also found to have the value expected from standard SB dynamical evolution models. Our model predicts a slope 1 (primary) and a slope 2 (secondary) behaviour at respectively low and high metallicity, with all intermediate slopes achieved in the transition region, between 10−2 and 10−1Z⊙.

The various modes of spallative LiBeB production are summarized, and classified according to their dependence or independence on the abundance of medium heavy elements (CNO) illustrated by that of oxygen in the interstellar medium. The predictions of the models are confronted to the available observational correlations (Be, B vs O). Clearly, a primary mechanism should lead to a slope one in the lg(Be/H) vs [O/H] plot and a secondary mechanism to a slope two. Due to the ambiguity of the O data, another criterion, based on energetics, can help us to select an adequate model. A purely secondary origin in the very early Galaxy is much more energy demanding than a primary one. Indeed, magnesium seems to be a possible surrogate of oxygen and iron since i) it is spectroscopically more easy to cope with and ii) its nucleosynthetic yield is independent of the mass cut and does not depend on metallicity.

We consider the three principal LiBeB evolutionary models, CRI in which the cosmic-ray source at all epochs of Galactic evolution is the average ISM, CRI+LECR in which metal enriched low energy cosmic rays (LECRs) are superimposed onto the CRI cosmic rays, and CRS in which the cosmic-ray source, accelerated in superbubbles, is constant, independent of the ISM metallicity. By considering the evolutionary trend of log(Be/H) vs. both [Fe/H] and [O/H], we demonstrate that the CRI model is energetically untenable. We present evolutionary trends for 11B/10B and B/Be which, combined with future precision measurements, could distinguish between the CRS and CRI+LECR models. We show that delayed LiBeB synthesis in the CRS model, due to the transport of the cosmic rays, could explain why log(Be/H) is steeper vs. [O/H] than vs. [Fe/H]. We also show that delayed deposition of Fe into star forming regions, due to its incorporation into high velocity dust, could provide an explanation for the possible rise of [O/Fe] with decreasing [Fe/H]. Observations of refractory and volatile α-elements could test this scenario. There seems to be a need for pregalactic or extragalactic 6Li sources.

The fragile light elements lithium, beryllium, and boron (Li, Be, B) are easily destroyed in stellar interiors, and are thus superb probes of physical processes occuring in the outer stellar layers. The light elements are also excellent tracers of the chemical evolution of the Galaxy, and can test big bang nucleosynthesis (BBN). These inter-related topics are reviewed with an emphasis on stellar physics.

In Part I (presented by CPD), an overview is given of the physical processes which can modify the surface abundances of the light elements, with emphasis on Population I dwarfs - convection; gravitational settling, thermal diffusion, and radiative levitation; slow mixing induced by gravity waves or rotation. We will discuss the increasingly large body of data which begin to enable us to discern the relative importance of these mechanisms in Population I main sequence stars. In Part II (presented by MHP), discussion is extended to the issue of whether or not the halo Li plateau is depleted, and includes the following topics: Li dispersion in field and globular cluster stars, Li production vs. destruction in Li-rich halo stars, and constraints from 6Li. Also discussed are trends with metal abundance and Teff and implications for chemical evolution and BBN. In Part III (presented by CC), evidence is reviewed that suggests that in situ mixing occurs in evolved low mass Population I and Population II stars. Theoretical mechanisms that can create such mixing are discussed, as well as their implications in stellar yields.

See the abstract given in Part I (Deliyannis, Pinsonneault, Charbonnel, hereafter DPC, in these proceedings). In Part II we discuss the lithium data for metal-poor stars and the constraints it places on stellar depletion. There are a variety of indicators that place interesting bounds on the degree of stellar depletion, and in contrast to the other two sections the data for Population II stars provides weaker evidence for stellar lithium depletion. We review both the theoretical studies and the observational data, and critically evaluate the degree of stellar depletion consistent with the data.

See the abstract given in Part I (Deliyannis, Pinsonneault, Charbonnel, hereafter DPC, this volume). In Part III, we first discuss the LiBeB observations in subgiant stars and the constraints they bring on the transport processes occuring on the main sequence. Evidence is then reviewed that suggests that in situ mixing occurs in evolved low mass Population I and Population II stars. Theoretical mechanisms that can create such mixing are discussed, as well as their implications for the evolution of the LiBeB and 3He.

Early in this decade our theoretical work demonstrated that all AGB stars in the mass range ˜ 4 to ˜ 7 M⊙ pass through a stage when a tremendous amount of lithium [up to log ε(7Li) ˜ 4.5] is created and transported to the surface. These lithium-rich AGB stars are predicted to occupy a narrow luminosity range between Mbol = −6 and −7, in excellent agreement with the observations of Smith & Lambert (1989), and might be useful as approximate standard candles. Recently, we found that even low mass stars (˜ 1 to ˜ 2 M⊙) on the RGB could create a tremendous amount of surface lithium. In both the AGB and RGB cases, it is the Cameron-Fowler mechanism that is responsible for the lithium creation.

In the AGB stars, it is hot bottom burning (nuclear burning at the base of the convective envelope) that produces the lithium. In the RGB stars, it is “cool bottom processing” that can lead to either lithium production or destruction. Cool bottom processing results when extra mixing (presumably rotation-induced) transfers material from the cool convective envelope down to the outer wing of the hydrogen-burning shell (where nuclear reactions can take place) and back out to the envelope. If the extra mixing is slow, 7Li is destroyed; if it is fast enough, then 7Li is created - for sufficiently fast and deep extra mixing, log ε(7Li) ˜ 4 is possible.

Unlike 7Li, the 3He abundance is almost independent of the mixing speed, and is constrained by observations of 12C/13C or [C/Fe] on the RGB. Cool bottom processing causes low mass stars of sub-solar metallicity to be net destroyers of 3He, rather than net producers. This is in contrast to previous theoretical predictions, and has a far-reaching effect on our understanding of galactic chemical evolution of 3He.

The back reaction of effective gravitons created during noninflationary epochs due to the inequivalence of vacuum states at different eras is examined in the context of primordial nucleosynthesis. Our final purpose is to obtain limits on the model employed to study such a process.

The limits from big bang nucleosynthesis on a class of models with time-varying A-term are reexamined. In particular, it is discussed how the stringent bounds previously derived may be relaxed.

In hot big bang cosmologies, the irreversible process of continous photon creation may phenomenologically be described through a thermodynamic approach. In these models, the radiation temperature law depends on a phenomenological parameter β which is closely related to the photon creation rate. It is shown that a stringent constraint on the value of this parameter is imposed from primordial nucleosynthesis.

We recently showed that the energy density of a plasma is appreciably different than previously thought when high frequency plasma fluctuations, ω ≥ kB/ħ, are taken into account (M. Opher &R. Opher, 1999). A change in the primordial plasma energy density changes the primordial expansion rate of the universe, the neutron temperature freeze-out, and the primordial nucleosythesis abundances. The change in the primordial abundances due to the change in the primordial plasma energy density is evaluated, taking into account the high frequency, as well as the low frequency fluctuations of the plasma.

The effects of a time-dependent A term in the recombination epoch are analysed taking into account the main physical processes occurring in the primordial plasma. For a vacuum decaying into photons, we show that the recombination begins when the Universe was smaller and denser, leading to a greater recombination rate. These results may have several implications to the large scale structure. In particular, the earlier recombination means that more time is available to the evolution of density perturbations.

We present a new method to incorporate laboratory nuclear data directly into the standard big-bang nucleosynthesis calculation. Using the quoted uncertainties on the data in a Monte Carlo procedure, we estimate likelihood distributions of the predicted abundances. Our results indicate significantly narrower confidence limits for the predictions than those presently in use. This technique provides error estimates that become smaller as more input data are added, and it allows new nuclear data to be incorporated easily as they become available.

Big Bang Nucleosynthesis (BBN) is the synthesis of the light nuclei, Deuterium (D or 2H), 3He, 4He and 7Li during the first few minutes of the universe. In this review we concentrate on recent data which give the primordial deuterium (D) abundance.

We have measured the primordial D/H in gas with very nearly primordial abundances. We use the Lyman series absorption lines seen in the spectra of quasars. We have measured D/H towards three QSOs, while a fourth gives a consistent upper limit. All QSO spectra are consistent with a single value for D/H: 3.325+0.22−0.25X10−5. From about 1994 − 1996, there was much discussion of the possibility that some QSOs show much higher D/H, but the best such example was shown to be contaminated by H, and no other no convincing examples have been found. Since high D/H should be much easier to detect, and hence it must be extremely rare or non-existent.

The new D/H measurements give the most accurate value for the baryon to photon ratio, η, and hence the cosmological baryon density: ωb = 0.0190 ± 0.0009 (1σ) A similar density is required to explain the amount of Lyα absorption from neutral Hydrogen in the intergalactic medium (IGM) at redshift z ≃ 3, and to explain the fraction of baryons in local clusters of galaxies. The D/H measurements lead to predictions for the abundances of the other light nuclei, which generally agree with measurements. The remaining differences with some measurements can be explained by a combination of measurement and analysis errors or changes in the abundances after BBN. The measurements do not require physics beyond the standard BBN model. Instead, the agreement between the abundances is used to limit the non-standard physics.