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2.1. Nucleosynthetic yields

What are the relative abundances of the nuclides generated during this period of cosmic nuclear activity? How do they compare with observations?

The abundances are related to two key-parameters of the physical conditions during the expansion: a) the neutron to proton ratio and b) the nucleon to photon ratio during the active nuclear phase (T between 1 and 0.01 MeV).

The n/p ratio is related to the decoupling Td and hence to the value of g* defined in eq. (7). In the standard model, the value of g* is fixed by the assumed demography of the universe. We shall discuss later the implications of models with different values of g*.

Let us focus our attention on the fate of the neutrons after decoupling. They may either beta-decay (with a lifetime of approximately one thousand seconds) or interact with a proton to form D. The probability of this last issue is proportional to the density of nucleons (baryons) rhob. At low rhob the neutrons beta-decay as illustrated in fig. 3; at higher rhob they undergo nuclear reactions and are essentially all processed to 4He, (with very minor formation of the other light nuclides of mass-2 mass-3 and mass-7). For baryonic densities smaller than the critical density, the yields of other nuclides is negligible as shown in fig 3.

Figure 3a
Figure 3b

Figure 3. Element production in the early universe, neglecting the possible effects of the quark-hadron phase transition, as a function of the present baryonic density. This early calculation by Wagoner (a) is now superseded by the results presented in (b) where the abcissa is logeta = n(nucleons) / n(photons). These figures illustrate the fact that for densities less than the critical density (10-29 g/cm3) only the nuclides with mass 2, 3, 4, and 7 are produced in interesting quantities. This feature appear to remain valid when the Q-H phase transition is taken into account.

In order to identify the density-temperature profile of cosmic matter during primordial nucleosynthesis we use the fact that no important entropy generating processes are believed to have taken place from T = 0.1 MeV till now. Thus the nucleon to photon ratio should have remained constant. This number is usually characterized by the baryonic number: eta = n(baryon) - n(antibaryon) / n(photons). The strategy would be to find the value of eta today and to use it to fix the nucleonic density-temperature profile in the past.

We shall discuss later the important possible effects of the quark-hadron phase transition on the state of the universe at BBN. We may expect to have an inhomogeneous baryonic density universe and an inhomogeneous proton to neutron ratio. In the present chapter, however, we shall the situation in terms of the mean baryonic density of the universe in BBN.

As discussed before if the number of photons is well known (400 per cm3) the number of baryons is very poorly known from astronomical observations. A lower limit is given by the density of luminous matter (Omega(luminous) = 0.003) corresponds (for H = 75) to rhob = 3 × 10-32 g/cm3 or eta > 5 × 10-11. The best choice of Omega = 0.1 from large scale studies gives (assuming pure baryonic component) rhob = 10-30 g/cm3 or eta = 1.5 × 10-9, while the upper limit Omega = 3 yields eta < 4.5 × 10-8. Because of the various uncertainties these values are uncertain by a factor of three each way. The present number of antibaryons is negligible. This will be the range of our investigation.

For eta > 5 × 10-11 (our lower limit) the fractional amount of beta-decaying neutrons is very small and essentially all the neutrons present at decoupling find their way into a 4He nucleus (fig. 3). Thus the abundance of this isotope is strongly related to the n/p ratio. It is a good monitor of value of the weak decoupling Td and hence of the value of g*, G, and GF (through eq. (10)) for cosmological models in which those parameters would be assumed to take different values. On the other hand it is only weakly dependent on the baryonic number eta as shown in fig. 3.

The abundance of D the other hand depends strongly upon the baryonic number (figs. 3a and 3b). At higher rhob the fractional abundance of D surviving the destruction by p or n capture to produce mass-3 nuclides becomes very small. For instance, if the baryons had the critical density the D/H ratio would be 10-12, seven order of magnitude above the observed values. The mass-3 nucleides have a similar behaviour but somewhat less pronounced. The mass-7 show a more complex behaviour with a bump (from 7Li formation), a hole and a rising slope (from 7Be) at higher eta.

There are four nuclides which are candidates for primordial nucleosynthesis: D,3He,4He,7Li. In the so-called standard BBN (which assumes an homogeneous baryonic density) there are only two parameters: the n/p ratio and the mean baryonic number. (Actually as we shall see later the n/p ratio is essentially fixed by the latest LEP results.) The relevant abundances obtained from astronomical observations and extrapolated to the early universe will be discussed shortly. It turns out that all four abundances can be accounted for by an appropriate choice of these two parameters. If the n/p ratio is fixed by the standard model particle physics and taking into account the uncertainties on the Q-H phase transition, the value of eta lies between 3 and 15 × 10-10 corresponding to 2 and 10 × 10-31 g/cm3. This agreement gives us acceptable reasons to believe that our universe was once at temperatures larger than one MeV.

We shall later return to this point in order to discuss the problems brought by the quark-hadron phase transition. New parameters have to be introduced which complicate to some extent the whole picture of BBN.

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