Editing Appendix/Ramblings/StrongNuclearForce (section)

==Standard Presentation==
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Derivation of the [[SSC/Dynamics/FreeFall#Relationship_to_Relativistic_Cosmologies|Friedmann Equations]] in the context of our discussion of ''Newtonian'' free-fall collapse.

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Newtonian Description of Pressure-Free Collapse
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<math>~\biggl( \frac{\dot{R}}{R} \biggr)^2</math>
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<math>~=</math>
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<math>~\frac{8}{3}\pi G \rho - \frac{k(R_i, v_i)}{R^2} \, ,</math>
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<math>~\frac{\ddot{R}}{R}</math>
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<math>~=</math>
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<math>~- \frac{4}{3}\pi G \rho \, ,</math>
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where, &nbsp; &nbsp; <math>~k(R_i,v_i)</math>
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<math>~=</math>
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<math>~\frac{8}{3}\pi G \rho_i R_i^2 - v_i^2 \, .</math>
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[http://www.astro.caltech.edu/~george/ay21/readings/Friemanetal_DE_ARAA.pdf Frieman, Turner &amp; Huterer (2008, ARAA, 46, 385 - 432)] provide an excellent, very readable review of dark matter and dark energy in the context of various cosmologies; see also, chapter 29 of [https://www.scribd.com/doc/301615425/An-Introduction-to-Modern-Astrophysics Carroll &amp; Ostlie (2007, 2<sup>nd</sup> Edition)].  Their equations (2) and (3) are written in the following table &#8212; with factors of <math>~c^2</math> inserted to explicitly clarify how the dimensional units are the same for every term in each equation.  

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Friedmann equations:<br />
''Field equations of GR applied to the FRW metric''
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<math>~H^2 = \biggl( \frac{\dot{a}}{a} \biggr)^2</math>
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<math>~=</math>
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<math>~\frac{8}{3}\pi G \rho - \frac{k}{a^2} + \frac{\Lambda c^2}{3}\, ,</math>
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<math>~\frac{\ddot{a}}{a}</math>
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<math>~=</math>
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<math>~- \frac{4}{3}\pi G \biggl[\rho + \frac{3p}{c^2} \biggr] + \frac{\Lambda c^2}{3} \, .</math>
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