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:


In the section on the Friedmann equations we introduced the energy conservation equation
(33.2) 


With the radiation equation of state we get the result:
(33.3) 


This equation integrates to give an expression for the way that the energy density varies with the scale factor. We get
(33.4) 


This expression can be used in the Friedmann equation involving the mass energy density:
(33.5) 


To investigate the simplest case we set and . The Friedmann equation then becomes:
(33.6) 


Substituting in the mass energy density in this case we arrive at the following evolution equation.
(33.7) 


This then leads to the following equation
(33.8)
This immediately integrates to the following relation:
(33.9) 


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.