Cosmic microwave background radiation (CMBR)
21
With h given by (1.66) and 00 by (1.42), we have
Teq::::3eV.
(1.125)
This justifies the original assumption that the only relativistic particles are the
photon and three neutrinos.
1.10 Cosmic microwave background radiation (CMBR)
During the radiation-dominated era, the photons were in thennal equilibrium
with matter (at the same temperature) because of interaction with the charge
of the electrons and protons. We are making the approximation here that all
baryons in the universe at this time are in the fonn of protons. However,
eventually the electrons and protons combine into neutral atoms. (This is referred
to as 'recombination'.) Thereafter, photons decouple from matter and evolve
at a temperature different from matter. In this way. black-body radiation at
the recombination temperature develops into black-body radiation in the present
universe at a lower temperature, because the temperature is proportional to the
mean photon energy and the energy of the photons has redshifted with the
expansion of the universe. Thus. for the photons,
T '" R(I)-I.
(1.126)
The recombination temperature T rec may be estimated to be
Tree = 3575 K = 0.31 eV.
(1.127)
Here, recombination has been defined as the point at which 90% of electrons
have combined with protons. (See, for example, section 3.5 of Kolb and Turner
in the general references.) We may calculate the time of recombination tm; from
(1.116), noting that the universe has been matter dominated from the time of
recombination until the present by comparing (1.127) with (1.125). Using (1.42),
(1.65) and (1.66), with To = 2.73 K, gives
Im; :::: 1.89 x 10 5 yr.
(1.128)
1.11 Big-bang nucleosynthesis
In chapter 4 we shall discuss possible explanations of the 'observed baryon
asymmetry of the universe':
nB
TJ '= - ~ 6.4 x 10- 10
(1.l29)
ny
21
With h given by (1.66) and 00 by (1.42), we have
Teq::::3eV.
(1.125)
This justifies the original assumption that the only relativistic particles are the
photon and three neutrinos.
1.10 Cosmic microwave background radiation (CMBR)
During the radiation-dominated era, the photons were in thennal equilibrium
with matter (at the same temperature) because of interaction with the charge
of the electrons and protons. We are making the approximation here that all
baryons in the universe at this time are in the fonn of protons. However,
eventually the electrons and protons combine into neutral atoms. (This is referred
to as 'recombination'.) Thereafter, photons decouple from matter and evolve
at a temperature different from matter. In this way. black-body radiation at
the recombination temperature develops into black-body radiation in the present
universe at a lower temperature, because the temperature is proportional to the
mean photon energy and the energy of the photons has redshifted with the
expansion of the universe. Thus. for the photons,
T '" R(I)-I.
(1.126)
The recombination temperature T rec may be estimated to be
Tree = 3575 K = 0.31 eV.
(1.127)
Here, recombination has been defined as the point at which 90% of electrons
have combined with protons. (See, for example, section 3.5 of Kolb and Turner
in the general references.) We may calculate the time of recombination tm; from
(1.116), noting that the universe has been matter dominated from the time of
recombination until the present by comparing (1.127) with (1.125). Using (1.42),
(1.65) and (1.66), with To = 2.73 K, gives
Im; :::: 1.89 x 10 5 yr.
(1.128)
1.11 Big-bang nucleosynthesis
In chapter 4 we shall discuss possible explanations of the 'observed baryon
asymmetry of the universe':
nB
TJ '= - ~ 6.4 x 10- 10
(1.l29)
ny