In the context of the ``standard'' model (three families of massless,
or light, two-component neutrinos), the predictions of BBN (SBBN)
depend on only one free parameter, the nucleon-to-photon ratio
.
The key test of the standard, hot, big bang cosmology is to assess
if there exists a unique value or range of
for which the
predictions of the primordial abundances are consistent with the
light element abundances inferred from the observational data.
From a statistical point of view it might be preferrable to perform
a simultaneous fit of the inferred primordial abundances of D, 3He,
4He, and 7Li to the SBBN predictions. In this
manner the ``best
fit'' , along with
its probability distribution may be found,
and the ``goodness-of-fit'' assessed
[21].
However, since
systematic uncertainties most likely dominate observational errors
at present, the value of this approach is compromised. An alternate
approach is adopted here.
As emphasized earlier, deuterium is an ideal baryometer. As a first
step the primordial abundance of deuterium inferred from observations
at high redshift will be compared with the SBBN prediction to identify
a consistent range for
. Then, given this
range, the SBBN
abundances of 4He and 7Li are predicted and these
are compared to
the corresponding primordial abundances derived from the observational
data. The challenge is to see if the D-identified range for
leads to consistent predictions for 4He and 7Li.
Recall that due to
its complicated evolutionary history, it is difficult to use 3He to
test and constrain SBBN. Furthermore, another consistency test is to
compare the SBBN-inferred
range with the
present baryon density
derived from non-BBN observations and theory. Is our model for the
very early evolution of the Universe consistent with the present
Universe?
From the two well observed, high redshift absorption line systems with
``low-D'', the estimate adopted for the primordial-D abundance is:
(D/H)P = 2.9 - 4.0 x 10-5
(see Fig. 3). Also shown for
comparison in Figure 3 is the
allowed range of the primordial deuterium
abundance suggested by the ``high-D'' abundance inferred from observations
of one lower redshift absorption-line system. With allowance for the
~ 8% uncertainty in the theoretically predicted abundance, the
favored range (low-D) for
is quite narrow:
10 = 5.1
± 0.36. It is clear from
Figure 4 that for the baryon
abundance in this
range, the BBN-predicted lithium abundance is entirely consistent with
the Spite-plateau value, even if the plateau were raised by ~ 0.2 dex
to allow for modest stellar destruction/dilution or lowered by a similar
amount due to post-BBN production. For this narrow range in
the
predicted 4He mass fraction varies very little. For
10
5,
YP
0.010
/
, so that including the
error in the predicted abundance, YP = 0.247 ± 0.001.
As may be
verified from Figure 2, this is
within (albeit at the high end of) the
range allowed by the data from the low metallicity, extragalactic H II
regions. Given the current uncertainties in the primordial abundances,
SBBN is consistent with
``low-D/high-''.
The significance of this concordance cannot be underestimated. A glance
at Fig. 1 provides a reminder of
the enormous ranges for the predicted
primordial abundances. That the simplest hot, big bang cosmological
model can account for (``predict''!) 3 independent abundances (4 with
3He; although 3He hasn't been employed in this
comparison, its predicted
abundance is consistent with extant observational data) by adjusting
only one free parameter
() is a striking
success. The theory,
which is in principle falsifiable, has passed the test. It needn't
have. Indeed, future observational data coupled to better understanding
of systematic errors may provide new challenges. For example, if in the
future it should be determined that the primordial helium mass fraction
were lower than YP = 0.245, this would be inconsistent (within the
errors) with the
``low-D/high-'' range
derived above. Similarly,
if the best estimate for the D-determined
range changed, the
comparison performed above should be repeated. With this in mind,
what of the
``high-D/low-'' range
which has been set aside in the current comparison?
If, in contrast to the deuterium abundance adopted above, the true
value were higher, (D/H)P = 10 - 30 x 10-5, the
SBBN-favored range in
would be lower (see
Fig. 2). Accounting
for the ~ 8% uncertainty in the theoretically predicted abundance,
10 = 1.7
± 0.28. Inspection of
Figures 2 -
4 reveals that
as along as 10
1.1 - 1.3,
consistency with he and li
can be obtained. Hence, for ``high-D'' as well, the standard model
passes the key cosmological test.