Authors: Andrew Beckwith
The following document attempts to answer the role additional degrees of freedom have as to initial inflationary cosmology. I.e. the idea is to cut down on the number of independent variables to get as simple an emergent space time structure of entropy and its generation as possible. One parameter being initial degrees of freedom, the second the minimum allowed grid size in space time, and the final parameter being emergent space time temperature. In order to initiate this inquiry, a comparison is made to two representations of a scale evolutionary Friedman equation, with one of the equations based upon LQG, and another involving an initial Hubble expansion parameter with initial temperature TPlanck ~ 10^19 GeV used as an input into T4 times N(T). Initial assumptions as to the number of degrees of freedom has for TPlanck ~ 10^19 GeV a maximum value of N(T) ~ 103 . Making that upper end approximation for the value of permissible degrees of freedom is dependent upon a minimum grid size length as of about lPlanck ~ 10^-33 centimeters. Should the minimum uncertainty grid size for space time be higher than lPlanck ~ 10^-33 centimeters, then top value degrees of freedom of phase space as given by a value N(T) ~ 10^3 drops. In addition, the issue of bits, i.e. information is shown to not only have temperature dependence, but to be affected by minimum 'grid size' as well. A bifurcation diagram argument involving Hemoltz free energy as a 'driver' to push through a transition from a prior universe to the present universe, with classical physics behavior down to a grid size of lPlanck ~ 10^-33 centimeters ( i.e. start of quantum gravity effects) is employed to invoke use of classical physics down to lPlanck ~ 10^-33 centimeters. Subsequent chaotic dynamics during the expansion phase driven by Helmholtz free energy leads to up to N(T) ~ 103 degrees of freedom at the start of the inflationary regime. The possibility this semi classical argument for increase of the degrees of freedom up to N(T) ~ 10^3 is tied in with the possible emergence of space time E8 embedding is included as a speculative bonus. This is akin to Bogolyubov "spontaneous" particle creation arguments outlined in the article.
Comments: 7 Pages. Fixed several typos. Also re configured to be sent into a journal for analysis
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