3 The hot universe
In the previous chapters we studied the geometrical properties of the universe.
Now we turn to its thermal history. This history can be subdivided into several
periods. Here we focus mainly on the period between neutrino decoupling and
recombination. This period is characterized by a sequence of important departures
from thermal and chemical equilibrium that shaped the present state of the universe.
We begin with an overview of the main thermal events and then turn to their
detailed description. In particular, in this chapter we study the decoupling of neu-
trinos, primordial nucleosynthesis and recombination. Our considerations are based
on well understood and tested laws of particle, nuclear and atomic physics below a
few MeV and, as such, are not likely to be a rich source of future research. How-
ever, this is important background material which underlies the concept of the hot
expanding universe.
3.1 The composition of the universe
According to the Friedmann equations, the expansion rate of the universe is de-
termined by the energy density and equation of state of its constituents. The main
components of the matter composition that played an important role at tempera-
tures below a few MeV are primordial radiation, baryons, electrons, neutrinos, dark
matter and dark energy.
Primordial radiationThe cosmic microwave background (CMB) radiation has
temperatureTγ 0 2 .73 K. Its current energy density is aboutεγ 0 10 −^34 gcm−^3
and constitutes only 10−^5 of the total energy density. The radiation has a perfect
Planckian spectrum and appears to have been present in the very early universe
at energies well above a GeV. Since the temperature of radiation scales in inverse
proportion to the scale factor, it must have been very high in the past.
Baryonic matterThis is the material out of which the planets, stars, clouds of
gas and possibly “dark” stars of low mass are made; some of it could also form
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