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20. BigBang nucleosynthesis
1
20. BIGBANG NUCLEOSYNTHESIS
Revised October 2005 by B.D. Fields (Univ. of Illinois) and S. Sarkar (Univ. of Oxford).
Bigbang nucleosynthesis (BBN) o±ers the deepest reliable probe of the early universe,
being based on wellunderstood Standard Model physics
[1–4].
Predictions of the
abundances of the light elements, D,
3
He,
4
He, and
7
Li, synthesized at the end of the
“ﬁrst three minutes” are in good overall agreement with the primordial abundances
inferred from observational data, thus validating the standard hot bigbang cosmology
(see [5] 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].
20.1.
Theory
The synthesis of the light elements is sensitive to physical conditions in the early
radiationdominated era at temperatures
T
<
∼
1 MeV, corresponding to an age
t
>
∼
1 s.
At higher temperatures,
weak interactions were in thermal equilibrium, thus ﬁxing
the ratio of the neutron and proton number densities to be
n/p
= e

Q/T
,
where
Q
= 1
.
293 MeV is the neutronproton mass di±erence. As the temperature dropped,
the neutronproton interconversion rate, Γ
n
↔
p
∼
G
2
F
T
5
, fell faster than the Hubble
expansion rate,
H
∼
√
g
*
G
N
T
2
, where
g
*
counts the number of relativistic particle
species determining the energy density in radiation. This resulted in departure from
chemical equilibrium (“freezeout”) at
T
fr
∼
(
g
*
G
N
/G
4
F
)
1
/
6
±
1 MeV. The neutron
fraction at this time,
n/p
= e

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 [6].
After freezeout the neutrons were free to
β
decay so the neutron fraction
dropped to
±
1
/
7 by the time nuclear reactions began. A simpliﬁed analytic model of
freezeout yields the
n/p
ratio to an accuracy of
∼
1% [7,8].
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 lightelement abundances can be explained with
η
10
≡
η
×
10
10
in the range 4
.
7–6
.
5 (95% CL). With
n
γ
ﬁxed 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
.
2–4
.
5)
×
10

31
g cm

3
, or as the
baryonic fraction of the critical density, Ω
B
=
ρ
B
/ρ
crit
±
η
10
h

2
/
274 = (0
.
017–0
.
024)
h

2
,
where
h
≡
H
0
/
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This note was uploaded on 08/01/2008 for the course ASTRO 228 taught by Professor Chungpeima during the Fall '06 term at University of California, Berkeley.
 Fall '06
 CHUNGPEIMA
 Cosmology

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