**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
*T*_{d} 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) _{b}. At low
_{b}
the neutrons beta-decay as illustrated in fig. 3;
at higher
_{b}
they undergo nuclear reactions and
are essentially all processed to ^{4}*He*, (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.

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:
=
*n*(baryon) - *n*(antibaryon) / *n*(photons). The
strategy would be to find the value of
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
cm^{3}) the number of baryons is very poorly known from astronomical
observations. A lower limit is given by the density of luminous matter
((luminous) = 0.003)
corresponds (for *H* = 75) to
_{b} =
3 × 10^{-32} g/cm^{3}
or > 5
× 10^{-11}. The best choice of
= 0.1 from
large scale studies gives (assuming pure baryonic component)
_{b} =
10^{-30} g/cm^{3} or
= 1.5 ×
10^{-9}, while the upper limit
= 3 yields
< 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 > 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 ^{4}*He*
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 *T*_{d}
and hence of the value of *g*^{*}, *G*, and
*G*_{F} (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
as
shown in fig. 3.

The abundance of *D* the other hand depends strongly upon the baryonic
number (figs. 3a and 3b).
At higher
_{b}
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 ^{7}*Li* formation), a hole and a rising
slope (from ^{7}*Be*)
at higher .

There are four nuclides which are candidates for primordial
nucleosynthesis:
*D*,^{3}*He*,^{4}*He*,^{7}*Li*.
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
lies
between 3 and 15 × 10^{-10} corresponding to 2 and
10 × 10^{-31} g/cm^{3}. 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.