There are now four main observations which validate the Big Bang theory: the expansion of the universe, the Planck spectrum of the Cosmic Microwave Background (CMB), the density fluctuations seen in the slight CMB anisotropy and in the local galaxy distribution, and BBN. Together, they show that the universe began hot and dense [2].
BBN occurs at the earliest times at which we have a
detailed understanding of physical processes. It makes
predictions which are relatively precise (10% - 0.1%), and which have been
verified with a variety of data.
It is critically important that the standard theory (SBBN) predicts the
abundances of several light nuclei (H, D, 3He,
4He, and 7Li) as
a function of a single cosmological parameter, the baryon to photon
ratio, 
nb /
n
[3].
The ratio of any two primordial abundances should give
, and
the measurement of the other three tests the theory.
The abundances of all the light elements have been measured
in a number of terrestrial and astrophysical environments.
Although it has often been hard to decide when these abundances
are close to primordial, it has been clear for decades
(e.g. [4],
[5])
that there is general agreement with the BBN predictions for all the
light nuclei.
The main development in recent years has been the increased accuracy of
measurement.
In 1995 a factor of three range in the baryon density was considered
b = 0.007 -
0.024. The low end of this range allowed no
significant dark baryonic matter. Now the new D/H measurements towards
quasars give
b = 0.019 ±
0.0024 (95%) - a 13% error, and there have been
improved measurements of the other nuclei.