There are a few complications predicting the abundances. One of the complications is tracking the abundances of few dif ferent nuclei instead of just a single element hydrogen. Next problem is that neutrons are unstable when not in a nucleus. They have a half-life of about 11 minutes. Third, several light nuclei end products have very small binding energies, therefore delaying the freeze-out.
BBN has it's own shortcomings earlier on like not being able to produce the observed abundances of all of the element isotopes, primarily due to the unstable nuclei with atomic number A = 5 and A = 8. Therefore as Burbidge et al. (1957) correctly noted stellar nucleosynthesis caught attention of the astrophysicists. If we assumes that 4He is entirely of stellar origin, then we should be able to find places in the universe in which the 4He mass fraction 25% . The data for 4He ( The helium(Y) vs oxygen (O=H) abundances in extragalactic HII regions emphasized
the lack of low 4He regions. [ref: Olive (1999)] shows the fact that no such region with low 4He has been observed and that leads to a conclusion that BBN nucleosynthesis is responsible for 4He abundance and should be part of any cosmological model.
The element abundances depend on the number of baryons per photon, or on
or 
.Big Bang nucleosyntheis therefore makes very clear predictions for the
primordial abundances of elements created in the first half hour of the Universe's
existence. These predictions can be tested, and the overall level of agreement with
observations is one of the many successes of the Big Bang model. However, the
tricky part of the experiment is to determine primordial abundance of baryonic
matter that has remained in its primordial condition for the ~ 13.7 billion years
since the nucleosyntheis epoch.
Burles et al. (1999b) noted that, the predicted abundances of the light elements
have been used to test the consistency of the hot big bang model at very early times (t ~0.01200sec). Fields et al. (1996) pointed out that the abundances of 4He and 7Li alone are su cient to probe and test the theoryphoton ratio
.Successes of the Standard Model
The assumptions that the standard model is based on are the laws of physics, which have been verifi ed at the present time by experiments, are also valid in the early universe. The cosmological principle described above holds. The temperature at early time t1 is greater than
and contents of the universe are in thermal equilibrium.It is suggested that (t1) is very close to 1. A baryon asymmetry is consistent with
observed radiation density. It is assumed also that the initial density fluctuations gave rise to later formation of structures. The standard cosmology model nonetheless achieved success.
Close connections have been developed between theory and observations for Standard Big Bang Nucleosynthesis (SBBN), and observations are more and more reliable now. The BBN model leads to a deeper understanding of the creation of primordial elements and the predictions of the CMB. The most important of all is predicting abundances of
and explaining it through a single free parameter . The value of baryon density 
agrees with other estimated values. Astrophysicists up to now used SBBN predictions and measured abundances to successfully estimate best values for cosmological parameters of baryon density and baryon to photon ratio . Generally one uses the low D/H ratio as the decent estimator for find for the baryon density. The next chapter will show that, the observed abundances of elements D, 4He and 7Li are close to the primordial abundances predicted by SBBN.References:
1.E. M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle. Synthesis of
the elements in stars. Rev. Mod. Phys., 29:547{650, Oct 1957. doi: 10.1103/
RevModPhys.29.547. URL http://link.aps.org/doi/10.1103/RevModPhys.
29.547.
2. S. Burles, K. M. Nollett, J. W. Truran, and M. S. Turner. Sharpening the predictions of big-bang nucleosynthesis. Physical Review Letters, 82:4176{4179, May 1999b. doi: 10.1103/PhysRevLett.82.4176.
3. B. D. Fields, K. Kainulainen, K. A. Olive, and D. Thomas. Model independent
predictions of big bang nucleosynthesis from ^4He and ^7Li: consistency and
implications. New A, 1:77{96, July 1996. doi: 10.1016/S1384-1076(96)00007-3.
