Editing Appendix/Ramblings/StrongNuclearForce (section)

==Insert Dependence on (Energy) Density==

The QGP is a regime where the interaction between quarks and gluons is dominated by the ''Coulomb-like'' term in the interaction potential.  The particles interact with one another as though they are not confined; this is the so-called ''asymptotically free'' regime.  Generally speaking, a QGP is achieved in a very high energy-density environment.

We can mimic this behavior in our modified cosmology by assuming that the coefficient on the <math>1/r</math> term in the gravitational acceleration varies with the energy-density of the fluid.  (More simply, let's have it vary with the ''mass''-dentiy.)  We want to kill off the <math>1/r</math> term when the density climbs above some threshold, <math>\rho_H</math>.  Let's try &hellip;
<table border="0" align="center" cellpadding="5">
<tr>
  <td align="right"><math>\ddot{R}</math></td>
  <td align="center"><math>=</math></td>
  <td align="left">
<math>- \frac{GM}{R^2} \biggl\{ 1 + \biggl[\frac{\rho}{\rho_H} - 1\biggr]^{-2} \frac{R}{a_T} \biggr\} \, .</math>
  </td>
</tr>
</table>
Note that the <math>~R-</math>dependent potential from which this expression for the acceleration is derived is,
<table border="0" align="center" cellpadding="5">
<tr>
  <td align="right"><math>~\Phi(R)</math></td>
  <td align="center"><math>=</math></td>
  <td align="left">
<math>+ \frac{GM}{R}  - \frac{GM_r}{a_T} \biggl[\frac{\rho}{\rho_H} - 1\biggr]^{-2} \ln \biggl(\frac{R}{a_T}\biggr)  \, .</math>
  </td>
</tr>
</table>

This expression for the gravitational acceleration has the desired properties:
<ul>
<li>
In the early universe, when <math>\rho/\rho_H \gg 1</math>, the density-dependent coefficient of the second (confining) term goes to zero; we have an ''asymptotically free regime'' in which a Coulomb-like potential dominates throughout the universe.
</li>
<li>
As the universe expands, the density will steadily drop.  For <math>\rho/\rho_H \ll 1</math>, the density-dependent coefficient of the confining term approaches unity and we retrieve our originally proposed, modified cosmology; that is, the potential is dominated by a logarithmic term for all distances greater than <math>~a_T</math>.
</li>
</ul>