3.2. The main physical processes in BBN
At early times, weak reactions keep the n/p ratio close to the equilibrium Boltzmann ratio. As the temperature, T, drops, n/p decreases. The n/p ratio is fixed (``frozen in'') at a value of about 1/6 after the weak reaction rate is slower than the expansion rate. This is at about 1 second, when T 1MeV. The starting reaction n+p D + makes D. At that time photodissociation of D is rapid because of the high entropy (low ) and this prevents significant abundances of nuclei until, at 100 sec., the temperature has dropped to 0.1 MeV, well below the binding energies of the light nuclei. About 20% of free neutrons decay prior to being incorporated into nuclei. The 4He abundance is then given approximately by assuming that all remaining neutrons are incorporated into 4He.
The change in the abundances over time for one value is shown in Figure 1, while the dependence of the final abundances on is shown in Figure 2, together with some recent measurements.
Figure 1. Mass fraction of nuclei as a function of temperature for = 5.1 x 10-10, from Nollet & Burles (1999) and Burles et al. (1999).
In general, abundances are given by two cosmological parameters, the expansion rate and . Comparison with the strength of the weak reactions gives the n/p ratio, which determines Yp . Yp is relatively independent of because n/p depends on weak reactions between nucleons and leptons (not pairs of nucleons), and temperature. If is larger, nucleosynthesis starts earlier, more nucleons end up in 4He , and Yp increases slightly. D and 3He decrease simultaneously in compensation. Two channels contribute to the abundance of 7Li in the range of interest, giving the same 7Li for two values of .
Figure 2. Abundances expected for the light nuclei 4He, D, 3He and 7Li (top to bottom) calculated in standard BBN. New estimates of the nuclear cross-section errors from Burles et al. (1999a) and Nollet & Burles (1999) were used to estimate the 95% confidence intervals which are shown by the vertical widths of the abundance predictions. The horizontal scale, , is the one free parameter in the calculations. It is expressed in units of the baryon density or critical density for a Hubble constant of 65 kms-1 Mpc-1. The 95% confidence intervals for data, shown by the rectangles, are from Izotov and Thuan 1998a (4He); Burles & Tytler 1998a (D); Gloeckler & Geiss 1996 (3He); Bonifacio and Molaro 1997 (7Li extended upwards by a factor of two to allow for possible depletion).