Very Early Universe
In this situation we need to have the cosmological pressure nonzero. Since the universe is assumed to be radiation dominated in the very early universe we use an equation of state that is associated with radiation. This equation is written as follows:
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In the section on the Friedmann equations we introduced the energy conservation equation
(33.2) |
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With the radiation equation of state we get the result:
(33.3) |
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This equation integrates to give an expression for the way that the energy density varies with the scale factor. We get
(33.4) |
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This expression can be used in the Friedmann equation involving the mass energy density:
(33.5) |
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To investigate the simplest case we set and
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The Friedmann equation then becomes:
(33.6) |
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Substituting in the mass energy density in this case we arrive at the following evolution equation.
(33.7) |
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This then leads to the following equation
(33.8)
This immediately integrates to the following relation:
(33.9) |
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when we use the initial condition that .
This equation is assumed to be in effect in
the era called the ,
which lasts up until about 300,000 years after the Big Bang. Taking the
curvature constant
is consistent with the earlier stage having
to do with the Inflationary Universe Model since the exponential inflation
evolution wipes out the curvature term leaving the universe evolving as in the
above radiation dominated case at the end of the inflationary period. The time
of changeover from the radiation dominated universe model to the matter
dominated universe model is also called the Decoupling Era or the Recombination Era. Radiation is very
intensely involved with all interactions before this time since the matter
state present is that of plasma. There are no neutral structures present and
photons strongly interact with electrically charged particles and nuclei.
However about 300,000 years after the Big Bang the universe has expanded
sufficiently that the matter particles have cooled down. This means that less
kinetic energy destructive bombardment is present. Finally electrons can get
stably bound to nuclei and form simple atoms like Hydrogen and Helium. Since
the bombardment is still going on and the universe is still expanding rapidly
there is not sufficient time to form more complicated atoms than lithium and
beryllium. All other atoms have to come later when large stars cook up the
associated large nuclei in their cores over millions of years and splatter the
cooked up nuclei all over the place when they go supernova in their death.