1.1.11. The Hot Big Bang Model
On the basis of two observations, 1) the Universe is currently in a state of uniform expansion and 2) the Universe is filled with photons that come from background radiation at a temperature of 2.74 K, we can construct our generic cosmological model known as the Hot Big Bang model. This model is but a mere 30 years old so we should not expect it to be a complete description of what we observe and indeed it is not. What the model can explain well is the following:
The Origin of the CMB: From
its initially extremely hot
and dense state, the CMB arises due to
photon production from matter-anti-matter annihilation. Once
the photon background is produced it simply cools with the expansion
of the Universe, in the thermodynamic manner first specified by
Gamow. The observed entropy of the Universe, S, which is measured
by the ratio of baryons to photons is
5 x 10-10. Essentially
this means for every 5 billion anti-quarks, there was 5 billion +1
quarks. The residue of this tiny mass asymmetry has produced the
observed stars and galaxies in the Universe.
The Uniform Expansion of the
Universe: By simple
extrapolation to very small times, the currently observed expansion law,
V = HD, must produce a situation where all the matter is concentrated
into a small volume. At some point in this small volume, unknown physics
initiated the expansion. Since the observed expansion today shows no
preferred direction then the expansion became isotropic very early on.
The Abundance of Light
Elements: The Universe at expansion
age of about one second was a hot and dense mixture of electrons, protons,
neutrons, neutrinos and photons. The ratio of protons to neutrons
at this time was unity as interactions with neutrinos mediated the
neutron to proton and proton to neutron conversion. However, at
expansion age of 2 seconds, the Universe had cooled to the point where
it became transparent to neutrinos and this mediation was gone.
Since free neutrons decay with 1/2 life of
900 seconds, the
proton-to-neutron (p / n)ratio began to increase. As the Universe
continued
to expand, it cooled to the point where some the nucleons could fuse
into light elements such as Deuterium and Helium through the same series
of fusion reactions that are presently occurring in our Sun. At the
time of this hydrogen to helium fusion p / n was 7. Thus for every
14 protons there were 2 neutrons. Since the proton-proton chain ultimately
binds two protons to two neutrons so that 4He is produced, then 12
protons plus 1 4He nucleus results. Since the mass of 1
4He is
very nearly equal to the mass of 4 protons (Hydrogen atoms), then an
initial p / n of 7 makes a definite prediction about the 4He
baryonic
mass fraction of the Universe. Since the total baryonic mass of the
Universe is essentially the mass in Hydrogen plus the mass in Helium
then the Helium mass fraction is: (Mass of Helium) / (Mass of Hydrogen +
Helium)
or, in units of the proton mass, (4) / (4+12) = 1/4. The observed abundances
of Deuterium, 3He and 4He are all quite consistent
with simple
predictions based on the theoretical conditions of the Universe at time
1-2 seconds (see Kernin and Sarkar 1996).
These three observations really form the observation foundation of the Hot Big Bang model. A fourth observation, that the Universe is filled with galaxies that are arranged in a complex structure, can not easily be accounted for in this model. While the general idea that structure formation via gravitational instability should produce observable anisotropies in the CMB is consistent with our observations, the overall complexity of the observed distribution of galaxies is not well understood yet. We will examine this issue in great detail in later chapters.