^{*}

We first of all consider what if the initial inflaton was nearly zero instead of proportional to a Planck mass, in a SUSY type potential. Using the construction of Padmanabhan about general inflaton physics and the conditions of what are usual constituent slow roll requirements for inflation, and also of Kolb, Pi and Raby about a SUSY potential, we come up with the counter intuitive formulation of how usual tests for slow roll give the standard answers even if the inflaton in the SUSY potential as given by Kolb, Pi, and Raby is initially zero. The result gives support to a formulation of VEV conditions used right after a Planck instant of time. As it is, we will from first principles examine what adding acceleration does as to the HUP previously derived. In doing so we will be tying it in our discussion with the earlier work done on the HUP. The HUP results, so modified are appropriate for the Pre-Planckian results and may explain why the slow roll formulation as given by Padmanabhan holds where there is the phenomenon of for Pre-Planckian space-time. This leads to a very paradoxical result that in Pre-Planckian physics the traditional slow roll formulas are satisfied even if . But it also puts in extremely tight restrictions upon the formulation of the degree of freedom problem, as given in Equation (26) in this document.

In this introduction, we use the results of how we set the state for a modified Pre-Planckian physics HUP. This will be leading to initial conditions which will lead to, later

As stated in [

Namely we will be working with [

i.e. the fluctuation

In short, we would require an enormous “inflaton” style

Here, [

We will be looking at the likelihood of recovery of the usual Heisenberg uncertainty principle as would be seen if [

In short, we would require an enormous “inflaton” style

Going to Kolb, Pi, and Raby, [

With [ ] a minimum value for Equation (23) according to the first derivative,

Were this followed, we would also would have a defined mass, for the scalar field which is given in [ ] by the following

With a minimization of a SUSY style Equation (7), and Equation (9) below if

i.e. this is still, with some tweaking a commonly accepted SUSY VeV model, with a minimum if

So,

We will be looking at the value of Equation (10) if

If we use the following, from the Roberson-Walker metric [

Following Unruth [

Then, the surviving version of Equation (7) and Equation (8) is, then, if

This Equation (14) is such that we can extract, up to a point the HUP principle for uncertainty in time and energy, with one very large caveat added, namely if we use the fluid approximation of space-time [

Then [

Then,

How likely is

To begin this process, we will break it down into the following co ordinates. In the rr,

If as an example, we have negative pressure, with

1) Working with Equation (10) as a link to

The key equation is to look at the following expression for the Hubble parameter, which is [

Here, we will be having

2) Working with Slow Roll If we are using Equation (20) if

From using Padmanabhan [

Then, if

Note that this is commensurate with this K.E. as proportional to have the left side of Equation (22) almost infinite in value and in turn that also relates to

Which due to [

Then by Equation (23) and Equation (24)

If we are in a very small Pre-Planckian regime of space-time, we could, then write Equation (24) as then proportional to

As given by Kolb and Turner, the projected degrees of freedom max out about 110, while unorthodox treatment of the same problem lead to an upper bound of about 1000. Needless to say though, the given Equation (26) only works if there is an extremely small, almost zero inflaton value, as given by the following:

We think the only explanation is that even if Equation (21) and Equation (22) are not satisfied with an almost zero inflaton magnitude, the only explanation we have is of a causal discontinuity which would effectively wipe out a good deal of the information and structure from Pre-Plankian to Planckian space time, even if the behavior of Equation (21) and Equation (22) is commensurate with the Planckian slow roll conditions. We will write more of this in a subsequent publication. This will complete our full development of an extension of [

This work is supported in part by National Nature Science Foundation of China Grant No. 11375279.

Beckwith, A.W. (2017) Gedanken Experiment for Initial Expansion of the Universe and Effects of a Nearly Zero Inflaton in Pre-Planckian Physics Space-Time Satisfying Traditional Slow Roll Formulas Which Happens in Pre-Planckian Regimes Even If . Journal of High Energy Physics, Gravitation and Cosmology, 3, 360-367. https://doi.org/10.4236/jhepgc.2017.32030