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Units, Constants and Useful Formulas

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Big Bang Model
--------------

The chronology of the Big Bang model is as follows:

Planck Epoch:       0 s - 10-43 s
T = 1032 K.
No theories.

Grand Unification:  10-43 s - 10-36 s
epoch               Gravity separates.

Electroweak epoch:  10-36 s - 10-32 s
T = 1028 K.
Strong Force separates.

Inflationary epoch: 10-36 - 10-32 s
Rapid expansion.
Universe become filled with a uniform quark–gluon plasma.

Quark epoch:        10-12 s - 10-6 s
Weak and electromagnetic forces separate.
Quarks continue to appear but cannot bind.
Appearance of the Higgs Field - elementary particles
get mass.

Hadron epoch:       10-6 s - 1 s
Quarks combine and hadrons, including baryons such
as protons and neutrons form.

Lepton epoch:       1 s - 10 s
leptons and anti-leptons to dominate the mass of the
universe.

Photon epoch:       10 s - 380,000 years
Leptons and anti-leptons annihilate each other leaving
photons to dominate the mass of the universe.

Nucleosynthesis:    3 mins - 20 mins
Protons (hydrogen ions) and neutrons begin to combine
into atomic nuclei in the process of nuclear fusion.  All
neutrons are absorbed into Helium nuclei. Ratio of H to

Matter domination:  70,000 years +
Matter dominates, allowing for gravitational collapse to
amplify the inhomogeneities left by cosmic inflation,
making dense regions denser and rarefied regions more
rarefied.

Recombination:      377,000 years
(decoupling)        Electrons get captured by the H and He ions, forming
electrically neutral H and He atoms. Most of the protons
are now bound up in these neutral atoms leaving photons
to travel freely.  These are the photons that we see in the
Cosmic Background Radiation after being greatly cooled
by the expansion of the universe.  The universe becomes
transparent.   Baryogenesis occurs.

According to this model the universe at early times was a nearly uniform
expanding collection of high energy, high temperature particles.  As it
expanded and cooled, small inhomogeneities were amplified by gravity
and collapsed to form the structures we see today.

The big bang model is in perfect agreement with general relativity.  which
predicts that a homogeneous universe would expand and cool in exactly
this way. In addition, there have been many observational confirmations
of the model. These include the apparent motions of distant objects relative
to us and the cosmic microwave background radiation.

It is tempting to try and extrapolate the big bang model all the way back
to the time of the actual big bang.  This iimplies that we could run the
equations of general relativity backwards to earlier times and higher
densities.  Unfortunately, there is a problem.  When we try and describe
regions of spacetime whose density exceeds the Planck density of roughy
1093 g/cm3, which correspnds to a Planck time of approximately 10-43,
quantum fluctuations in spacetime become important and quantum mechanics
and general relativity start to disagree and we have no solid theories to
describe this situation.

As successful as the Big Bang theory is at explaining the universe from
the time after the Planck density, there are certain drawbacks.  While
on a 'local' scale the universe is 'lumpy' and we need Einstein's General
Theory to explain things, on a grand scale, the universe is measured to
be homogeneous, isotropic and almost flat.  However, under Big Bang
cosmology, for a closed (positive curvature) universe,  curvature grows
with time.  Recall from the FRW equation:

H2 = 8πGρ/3 - k/a2

Rearranging we get:

k/a2 = 8πGρ/3 - H2

As time progreses, the H2 term get smaller and smaller and at some point
will become zero.  The expansion stops and the universe begins to
contract.  Up until that point, however, k/a2 will grow.

Another issue is that distant regions of space in opposite directions are
so far apart that they could never have been in contact because the light
travel time between them exceeds the age of the universe.  Yet the
uniformity of the cosmic microwave background radiation (WMAP) tells
us that these regions must have been in contact with each other in the
past.  This is referred to as the 'horizon' problem.

Current theories of particle physics predict that in the extraordinary hot
and dense conditions that existed during the earliest stages of the
universe, various kinds of 'relic' particles such as magnetic monopoles
would be produced.  Big Bang cosmology predicts that we should be able
to see these particles.  However, magnetic monopoles have never been
observed in nature.

Finally, to get us to the present day, the Big Bang model would require
that the curvature of the universe at the time of the Planck density
could not exceed one part in 1059.  If it were slightly more curved
than this (closed), it would have recollapsed long ago.  If it were
slightly less (open), it would have flown apart so quickly galaxies
would never have formed. The probability that the curvature was exactly
right for the universe to survive to later times is considered to be
highly improbable

To see how these things might be resolved it is necessary to introduce
the INFLATION THEORY.