72 The hot universe
Problem 3.3Dark energy with equation of statew=− 1 /3 leads to a term∝ 1 /a^2
in the Friedmann equation (1.67). How can we nevertheless distinguish it from the
spatial curvature term,k/a^2 ,in an open universe?
3.2 Brief thermal history
The temperature of the cosmic radiation decreases as the universe expands. It is
unambiguously related to the redshift,
Tγ(z)=Tγ 0 (1+z), (3.4)and can be used as an alternative to time or redshift to parameterize the history of
the universe. To obtain an estimate for the temperature expressed in MeV, at the
timetmeasured in seconds, we can use the formula
TMeVO( 1 )
√
tsec,
which is valid during the radiation-dominated epoch (see Section 3.4.2).
Below we briefly summarize the sequence of main events constituting the history
of our universe (in reverse chronological order):
∼ 1016 – 1017 s Galaxies and their clusters are formed from small initial inhomogeneities as
a result of gravitational instability. Structure formation can be described using Newtonian
gravity. However, it is still a very complicated nonlinear problem, which can only be
solved numerically and it is likely to remain an active field of research for a long time.
One of the main unresolved fundamental issues regarding this period is the nature of dark
matter and dark energy.
∼ 1012 – 1013 s At this time nearly all free electrons and protons recombine and form neu-
tral hydrogen. The universe becomes transparent to the background radiation. The CMB
temperature fluctuations, induced by the slightly inhomogeneous matter distribution at
recombination, survive to the present day and deliver direct information about the state
of the universe at the last scattering surface. Helium, which constitutes about 25% of the
baryonic matter, has recombined and become neutral before this time. After helium re-
combination there remain many free electrons and the universe is still opaque to radiation.
Helium recombination, therefore, is not a very dramatic event, though we must take it
properly into account when calculating the microwave background fluctuations because
it influences the speed of sound.
∼ 1011 s(T∼eV) This time corresponds to matter–radiation equality which separates
the radiation-dominated epoch from the matter-dominated epoch. The exact value of the
cosmological time at equality depends on the constituents of the dark component and,
therefore, is known at present only up to a numerical factor of order unity.
∼ 200 – 300 s(T∼ 0 .05 MeV) Nuclear reactions become efficient at this temperature. As
a result, free protons and neutrons form helium and other light elements. The abundances