22
The standard model of cosmology
where nB and ny are the present number densities of baryons and photons.
Before doing this, it is important to understand the origin of this number whose
explanation has been and remains a major topic of research. For this reason we
shall outline here how this number emerges from measurements of the present
abundances of the light elements, specifically deuterium (0), helium eHe and
4He) and lithium eLi). Light elements such as these and also tritium (T or 3H)
and beryllium eBe) were formed in a primordial nuclear reactor. We shall see
that the process begins towards the end of the 'first three minutes', as the era was
so memorably described by Weinberg [5]. The first step is the formation of the
A = 2 nucleus deuterium via the process
np-+ Oy
(1.130)
conventionally written by nuclear physicists as p(n, y)O. At earlier times, the
process goes in both directions. However, since there are more than 10 9 photons
for every nucleon in the universe at that time, any newly formed deuterium is
dissociated before it gets a chance to capture a neutron or proton and begin
building heavier nuclei. Thus, no appreciable deuterium density accumulates.
This 'deuterium bottleneck' persists until there are too few sufficiently energetic
photons to dissociate the deuterons before they can capture nucleons. The A = 3
nuclei 3He and 3H are then formed via
O(p, y)3He:
pD -+ 3Hey
(1.131)
D(D,n)3He :
DD -+ 3Hen
(1.132)
3He(n, p) 3H :
n 3He -+ 3Hp
(1.133)
and 4He via
T(D, n)4He:
DT -+ 4Hen
(1.134)
3He(0, p) 4He :
D 3 He -+ 4He p.
( 1.135)
Since there are no stable A = 5 nuclei, the synthesis of heavier nuclei requires
the 4He nuclei to interact with 0, 3H or 3He, all of which are positively charged.
The Coulomb repUlsion suppresses the reaction rates for such processes, thereby
ensuring that virtually all of the neutrons available for primordial nucleosynthesis
wind up in 4He, the most tightly bound of the light nuclei. Subsequently, the
processes T(4He, y) 1Li, 7Li(p, 4He)4He, 3He(4He, y) 7Be and 7Be(n, p) 1Li
form more 4He and also small amounts of lithium and beryllium.
The first process p(n, y)D is crucial, since an appreciable deuterium
abundance must be built up before the others can proceed; the neutron and proton
number densities are too low to allow the build-up of the other nuclear abundances
by direct many-body processes. Clearly, the original abundance of neutrons and
protons determines the light element abundances generated by these primordial
processes. However, light elements are also created and destroyed in stars,
supernovae and other astrophysical phenomena. Consequently, the light element
The standard model of cosmology
where nB and ny are the present number densities of baryons and photons.
Before doing this, it is important to understand the origin of this number whose
explanation has been and remains a major topic of research. For this reason we
shall outline here how this number emerges from measurements of the present
abundances of the light elements, specifically deuterium (0), helium eHe and
4He) and lithium eLi). Light elements such as these and also tritium (T or 3H)
and beryllium eBe) were formed in a primordial nuclear reactor. We shall see
that the process begins towards the end of the 'first three minutes', as the era was
so memorably described by Weinberg [5]. The first step is the formation of the
A = 2 nucleus deuterium via the process
np-+ Oy
(1.130)
conventionally written by nuclear physicists as p(n, y)O. At earlier times, the
process goes in both directions. However, since there are more than 10 9 photons
for every nucleon in the universe at that time, any newly formed deuterium is
dissociated before it gets a chance to capture a neutron or proton and begin
building heavier nuclei. Thus, no appreciable deuterium density accumulates.
This 'deuterium bottleneck' persists until there are too few sufficiently energetic
photons to dissociate the deuterons before they can capture nucleons. The A = 3
nuclei 3He and 3H are then formed via
O(p, y)3He:
pD -+ 3Hey
(1.131)
D(D,n)3He :
DD -+ 3Hen
(1.132)
3He(n, p) 3H :
n 3He -+ 3Hp
(1.133)
and 4He via
T(D, n)4He:
DT -+ 4Hen
(1.134)
3He(0, p) 4He :
D 3 He -+ 4He p.
( 1.135)
Since there are no stable A = 5 nuclei, the synthesis of heavier nuclei requires
the 4He nuclei to interact with 0, 3H or 3He, all of which are positively charged.
The Coulomb repUlsion suppresses the reaction rates for such processes, thereby
ensuring that virtually all of the neutrons available for primordial nucleosynthesis
wind up in 4He, the most tightly bound of the light nuclei. Subsequently, the
processes T(4He, y) 1Li, 7Li(p, 4He)4He, 3He(4He, y) 7Be and 7Be(n, p) 1Li
form more 4He and also small amounts of lithium and beryllium.
The first process p(n, y)D is crucial, since an appreciable deuterium
abundance must be built up before the others can proceed; the neutron and proton
number densities are too low to allow the build-up of the other nuclear abundances
by direct many-body processes. Clearly, the original abundance of neutrons and
protons determines the light element abundances generated by these primordial
processes. However, light elements are also created and destroyed in stars,
supernovae and other astrophysical phenomena. Consequently, the light element