_{1}

^{*}

We look at what may occur if Boltzmann equations, as presented by Murayama in 2007, Les Houches, are applied to graviton density in a pre-Planckian universe setting. Two restrictions are in order. First of all, we are assuming a graviton mass on the order of 10?62 grams, as if the pre-Planckian regime does not change the nature of Graviton mass, in its low end. Secondly, we are also assuming that a comparatively low temperature regime (far below the Planckian temperature) exists. Finally we are leaving unsaid what may happen if Gravitational waves enter the Planck regime of ultra-high temperature. With those three considerations, we proceed to examine a Graviton density value resulting from perturbation from low to higher temperatures. In the end an ultra- hot Pre big bang cosmology will yield essentially no early universe information transfer crossovers to our present cosmological system. This is not affected by the choice if we have a single repeating universe, or a multiverse. A cold pre inflationary state yields a very different situation. Initial frequencies of Gravitons, though, as outlined may be different in the multiverse case, as opposed to the single repeating universe case. We close with comments as to Bicep 2, and how this document has material as to how to avoid the BICEP 2 disaster. And about choosing between either the possibility of massless Scalar-Tensor Gravity as the correct theory of gravitation or conventional GR.

We will start off first, with the result of H. Murayama [^{−}^{62} grams [

We go on the assumptions, as follows that there are two givens as far as the initial thought experiment. First that

A suggestion written as by a reviewer as to allegedly refocusing this paper’s theme and allegedly proper reworking, Suggested title may be something like: “On exact numerical solution of Boltzmann equation, and its implications to relic density and dark matter prediction.” was turned down by the author for several explicit reasons. First of all, while Murayama is focused on the applications to Dark Matter, we chose this formalism because it does refer to bosons, and a graviton is a boson, and secondly the DM creation meme is not even relevant at the sub Planckian to Planckian regime of space-time physics. According to even [

We will not reference cyclic universes in this document as a main result, but in terms of an appendix entry, which we view as timely and in the spirit of the offered thought experiment. So for the time being we will be not citing a cyclic multiverse universe as the main result, but as a future project in the works, with tentative suggestions outlined to that effect. See the appendix entry for this with a summary of findings.

Debatable as this may be, the assumption will be that what H. Murayama postulated in [

Murayama also postulates [

The approximation we will use is that the right hand side of Equation (1) is almost zero, i.e.

Note that for the record, the

Will in part mean a rich interplay between Equation (3) and the inverse behavior of a scale factor, cubed which we will comment upon fully in the later part of this text. From here, we will fill in some would be parameters

First of all, assuming in Pre inflation mass (energy) and temperature a ratio of about, for what was given through [

This would imply for a pre-Planckian density, for a pre-Planckian bounce radii of one Planck length [

To start off with, we will be considering having [

The relevant quantity to consider here would be, then, with Equation (5), and [

This value for the initial time step would be probably lead to pre-Planckian time, i.e. smaller than 10^-43 seconds, which then leads us to consider, what would happen if a multi verse contributed to initial space-time conditions, then by [

Note that the values of E-V are discussed in Beckwith’s [

Recall that as of [^{−}^{55} grams, instead of the 10^{−62} grams as of the Planckian era, and also then, that due to the dominance of kinetic energy in the pre-Planckian space-time, that there would be a low value for the lower bound for the

See Appendix A for the multiverse construction. We then will have, if we follow Penrose

We first will start at the Penrose hypothesis for a cyclic conformal universe, starting with [

However, in the multiverse contribution to [

The end result in terms of GW frequencies to be parsed is

Please look at Appendix A as to details of how this second frequency is possible

First of all we will consider frequency, of relic “gravitons”, and next we will consider the impact of temperature, starting off first with frequency as to single repeating universe, then a multiverse.

The conclusions of Equation (13) are such that if we look at the value of h, i.e. strain, as given by Tong, Zhang Zhao, Liu, Zhao, and Yang [

In terms of the repeating single universe, we would have, say

In the case of Equations (15)-(16) there is no statistical averaging. It is the case of Equation (15) which we will be most concerned about. The contribution of the “strain”, in terms of the term

if

in the future, as far as research work initiated by the author to give more analogies along the line of [

Distinguishing between Equation (15) and Equation (16) should be our next task. It is unlikely that if there was just one universe, that it would be identical to N universes, statistically averaged, since it would be incredibly unlikely for the same frequency to be the resonant frequency in question from N (maybe almost infinite number of ) universes.

Next, the main event. What does temperature have to do with this business A strict inspection of Equation (3) yields the startling result that the higher the temperature is, the lower the value of the LHS of Equation (3) is, i.e. a hot Pre big bang cosmology will yield essentially no early universe information transfer crossovers to our present cosmological system. This is not affected by the choice if we have a single repeating universe, or a multiverse, i.e. the main thing being that the number, n, is inversely proportional to the initial scale factor, cubed, a detail, which is due to the structure of pre-Planckian cosmology, which the author things is behind the datum that the initial lower mass of the graviton was higher in the pre-Planckian state, than immediately afterwards.

As to Equation (15) and Equation (16), this issue is more important, than people appreciate in ascertaining distinguishing between either multiple sources, or a single spatial origin for gravitational waves. This is in lieu as to C. VAN DEN BROECK in [

“Omni-directional gravitational wave background radiation could arise from fundamental processes in the early Universe, or from the superposition of a large number of signals with a point-like origin. Examples of the former include parametric amplification of gravitational vacuum fluctuations during the inflationary era”

Distinguishing between Equation (15) and Equation (16) must be done in a way as to avoid the conundrum mentioned above. The multiple frequencies, averaged out, as given in Equation (15) are not the same as parametric amplification of gravitational vacuum during the inflationary era, and refining data picked up by instrumentation as to avoid any overlap of such pre big bang gravitational wave frequency mixing with parametric amplification of vacuum fluctuations will be supremely challenging. This though is not the only issue at hand. In a recently accepted by JPEPHC publication, [

“It is worth noting that Dr. Corda in [

We have in our situation that the third polarization issue may arise in Equation (15), for reasons as given in Dr. Corda’s reference according to [

“Thus, if advanced projects on the detection of GWs will improve their sensitivity allowing to perform a GWs astronomy (this is due because signals from GWs are quite weak) [

We are not done though, i.e. the final task is to avoid the Bicep 2 disaster. The overlay of dust as given in [

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

Andrew WalcottBeckwith, (2016) Gedanken Experiment for Using Boltzmann Equation for Relic Graviton Frequencies, in Pre-Planckian Physics and the Independence of Relic Graviton Density from Either Single Repeating Universe Models or Multiverses. Journal of High Energy Physics, Gravitation and Cosmology,02,83-91. doi: 10.4236/jhepgc.2016.21009

But, then if one is looking at a multiverse, we first will start at the Penrose hypothesis for a cyclic conformal universe, starting with [

However, in the multiverse contribution to [

So, does something like this hold? In a general sense? If N is the number of contributing multiverse single universes contributing to the beginning of space time, then we would be looking at [

Then the contribution of the multiverse to the beginning

And the graviton mass for a multiverse, would be then like

Then for multiverse there would be an energy density looking like, for all this

If so, there would then be a net Graviton based energy we would set up as given below which is a way to obtain, via a multiverse input to be as follows:

of the following equation which we will then lead to setting the graviton frequency as following, with N the number of universe contributions to the new universe, and the frequency, as averaged out by