20. Big-Bang nucleosynthesis
1
20. BIG-BANG NUCLEOSYNTHESIS
Revised August 2009 by B.D. Fields (Univ. of Illinois) and S. Sarkar (Univ. of Oxford).
Big-Bang nucleosynthesis (BBN) o±ers the deepest reliable probe of the early Universe,
being based on well-understood Standard Model physics [1–5].
Predictions of the
abundances of the light elements, D,
3
He,
4
He, and
7
Li, synthesized at the end of the ‘²rst
three minutes’, are in good overall agreement with the primordial abundances inferred
from observational data, thus validating the standard hot Big-Bang cosmology (see [6] for
a review). This is particularly impressive given that these abundances span nine orders of
magnitude – from
4
He
/
H
∼
0
.
08 down to
7
Li
/
H
∼
10
−
10
(ratios by number). Thus BBN
provides powerful constraints on possible deviations from the standard cosmology [2],
and on new physics beyond the Standard Model [3,4].
20.1. Theory
The synthesis of the light elements is sensitive to physical conditions in the early
radiation-dominated era at a temperature
T
∼
1 MeV, corresponding to an age
t
∼
1s. At
higher temperatures, weak interactions were in thermal equilibrium, thus ²xing the ratio
of the neutron and proton number densities to be
n/p
=e
−
Q/T
,where
Q
=1
.
293 MeV
is the neutron-proton mass di±erence. As the temperature dropped, the neutron-proton
inter-conversion rate, Γ
n
↔
p
∼
G
2
F
T
5
, fell faster than the Hubble expansion rate,
H
∼
√
g
∗
G
N
T
2
g
∗
counts the number of relativistic particle species determining
the energy density in radiation (see ‘Big Bang Cosmology’ review). This resulted in
departure from chemical equilibrium (‘freeze-out’) at
T
fr
∼
(
g
∗
G
N
/G
4
F
)
1
/
6
±
1M
eV
.
The neutron fraction at this time,
n/p
−
Q/T
fr
±
1
/
6, is thus sensitive to every
known physical interaction, since
Q
is determined by both strong and electromagnetic
interactions while
T
fr
depends on the weak as well as gravitational interactions. Moreover,
the sensitivity to the Hubble expansion rate a±ords a probe of
e.g.,
the number of
relativistic neutrino species [7].
After freeze-out, the neutrons were free to
β
-decay,
so the neutron fraction dropped to
n/p
±
1
/
7 by the time nuclear reactions began. A
simpli²ed analytic model of freeze-out yields the
n/p
ratio to an accuracy of
∼
1% [8,9].
The rates of these reactions depend on the density of baryons (strictly speaking,
nucleons), which is usually expressed normalized to the relic blackbody photon density as
η
≡
n
b
/n
γ
. As we shall see, all the light-element abundances can be explained with
η
10
≡
η
×
10
10
in the range 5
.
1–6
.
5 (95% CL). With
n
γ
²xed by the present CMB temperature
2.725 K (see ‘Cosmic Microwave Background’ review), this can be stated as the allowed
range for the baryon mass density today,
ρ
b
=(3
.
5–4
.
5)
×
10
−
31
gcm
−
3
,o
ra
sth
e
baryonic fraction of the critical density, Ω
b
=
ρ
b
/ρ
crit
±
η
10
h
−
2
/
274 = (0
.
019–0
.
024)
h
−
2
,
where
h
≡
H
0
/
100 km s
−
1
Mpc
−
1
=0
.
72
²
0
.
08 is the present Hubble parameter (see
Cosmological Parameters review).