Physical Foundations of Cosmology

3.4 Lepton era 95

Converting from Planckian units, we can rewrite this relation in the following useful
form:

tsec=tPl

(

3

32 πκ

) 1 / 2 (

TPl

T

) 2

 1. 39 κ−^1 /^2

1

TMeV^2

, (3.88)

where the cosmological time and temperature are measured in seconds and MeV
respectively.
When the temperature decreases to a few MeV,that is, about a second after the big
bang, weak interactions become inefficient. These interactions are important in two
respects. First, they keep neutrinos in thermal contact with each other and with the
other particles, and second, they maintain the chemical equilibrium between protons
and neutrons. The two events, namely, the thermal decoupling of neutrinos and the
chemical decoupling of baryons, are somewhat separated in time. The first happens
when the temperature is about 1.5 MeV,while the second occurs atT 0 .8 MeV.
The chemical decoupling of the baryons is essential for nucleosynthesis and it will
be considered in detail in the next section. Here we concentrate on the thermal
decoupling of neutrinos.
The main reactions responsible for the coupling of the electron neutrinos to the
relativistic electron–positron plasma, and hence to radiation, are

e++e−
νe+ν ̄e, e±+νe→e±+νe, e±+ν ̄e→e±+ν ̄e. (3.89)

Some diagrams describing these interactions in electroweak theory (see next chap-
ter) are shown in Figure 3.4. Both chargedW±-bosons and the neutralZ-boson
contribute to these processes. At energies much smaller than the masses of the in-
termediate bosons the propagators of theZ- andW-bosons reduce to 1/MW^2 ,Zand
Fermi theory can be used to estimate the cross sections. For relativistic electrons

Z 0

Z^0 W−

e+ νe

νe

νe

νe νe

e− ν ̃e

e− e−

e−

e−

Fig. 3.4.