The relic abundances of D, 3He, and 7Li are rate limited, determined by the competition between the early Universe expansion rate and the nucleon density. Any of these three nuclides is, therefore, a potential baryometer; see Figure 1.
 |
Figure 1. The SBBN-predicted abundances of
D, 3He, and 7Li by number with respect to
hydrogen, and the 4He mass fraction YP, as
a function of the nucleon (baryon) abundance parameter
|
In contrast to the synthesis of the other light nuclides, once BBN begins
(T 
80
keV) the reactions building 4He are so rapid that its relic
abundance is not rate limited. The primordial abundance of
4He is limited
by the availability of neutrons. To a very good approximation, its relic
abundance is set by the neutron abundance at the beginning of BBN. As a
result, the primordial mass fraction of 4He, YP,
while being a relatively insensitive baryometer (see
Figure 1), is
an excellent, early-Universe chronometer.
The qualitative effects of a nonstandard expansion rate on the relic
abundances of the light nuclides may be understood with reference to
Figure 1. For the baryon abundance range of
interest the relic abundances of D and 3He are decreasing
functions of
; in this
range, D and 3He are being destroyed to build 4He.
A faster than standard expansion (S > 1) provides less time
for this destruction so that more D and 3He will survive. The
same behavior occurs for 7Li at low values of
, where its
abundance is a decreasing function of
. However, at
higher values of ,
the BBN-predicted 7Li abundance increases with
, so that
less time available results in less production and a smaller
7Li relic abundance. Except for dramatic changes to the
early-Universe expansion rate, these effects on the relic abundances of
D, 3He, and 7Li are subdominant to their
variations with the baryon density. Not so for 4He, whose
relic abundance is very weakly (logarithmically)
dependent on the baryon density, but very strongly dependent on the
early-Universe expansion rate. A faster expansion leaves more neutrons
available to build 4He; to a good approximation
Y
0.16 (S -
1). It is clear then that if 4He is paired with any of
the other light nuclides, together they can constrain the baryon
density ( or
B
h2 
B) and the
early-Universe expansion rate (S or
N
).
As noted above in Section 2, the
neutron-proton ratio at BBN can
also be modified from its standard value in the presence of a significant
electron-neutrino asymmetry
(
e
0.01). As a
result, YP is
also sensitive to any neutrino asymmetry. More
e than
e drives
the neutron-to-proton ratio down (see Eq. 1),
leaving fewer neutrons available to build 4He; to a good
approximation Y
-0.23
e
(Kneller &
Steigman 2003).
In contrast, the relic abundances of D, 3He, and
7Li are very insensitive to
e
0, so that when paired with
4He, they can simultaneously constrain
the baryon density and the electron-neutrino asymmetry. Notice that if
both S and
e are
allowed to be free parameters, another
observational constraint is needed to simultaneously constrain
,
S, and
e.
While neither 3He nor 7Li can provide the needed
constraint, the CBR temperature anisotropy spectrum, which is sensitive
to and
S, but not to
e, can
(see
Barger et
al. 2003b).
This review will concentrate on combining constraints from the CBR and
SBBN (S = 1,
e = 0)
and also for S 1
(e = 0).
For the influence of and constraints on electron neutrino asymmetry, see
[Barger et
al. (2003b)]
and further references therein.
) in
the BBN predictions.