Could Gravitons from a Prior Universe Survive a (LQG Inspired) “Quantum Bounce” to Re-Appear in Our Present Universe?

We ask the question if a formula for entropy, as given by S E T ≡ with a usual value ascribed of initial entropy 5 ~ 10 S of the onset of inflation can allow an order of magnitude resolution of the question of if there could be a survival of a graviton from a prior to the present universe, using typical Planckian peak temperature values of 19 ~10 GeV T . We obtain values consistent with up to 10 38 gravitons contributing to an energy value of 24 ~10 GeV E if we assume a relic energy contribution based upon each graviton initially exhibiting a frequency spike of 10 10 Hz. The value of 24 ~10 GeV E is picked from looking at the aftermath of what happens if there exists a quantum bounce with a peak density value of planck ~ 2.07 ρ [1] in a regime of LQG bounce regime radii of the order of magnitude of 35 ~10 λ − meters. The author, in making estimates spe-cifically avoids using [ S E − , by setting the chemical potential 0 µ≡ for ultra high temperatures for reasons which will be brought up in the conclusion.

T . We obtain values consistent with up to 10 38 gravitons contributing to an energy value of 24 10 GeV E if we assume a relic energy contribution based upon each graviton initially exhibiting a frequency spike of 10 10 Hz. The value of 24 10 GeV

Introduction
Recently, a big bounce has been proposed 1 as an alternative to singularity conditions that Hawking's, Ellis [2], and others use. The 1 st problem is that there appears to exist no fundamental argument presented in either traditional Friedman 1 metric GR or LQG for preservation of the same value for Planck's constant or the fine structure constant from prior universes (before ours) and the present universe. Ashtekar [3], in conversations with the author in the inaugural opening of the Penn State gravity center (2007) told the author that the universe preserves most of its "memory" in cosmological cycles, but the proof of this assertion does not show up in Rovelli's [4] reference on Quantum Gravity. The driving force for this present investigation is due to a conversation the author had with Steinhardt and 'tHooft at the meeting "Fundamental Frontiers of Physics" in a parallel session about LQG, and new developments in it.

What Are Necessary First Principles to Consider in Graviton/GW Detection?
Modeling how much information may be carried by an individual graviton can be achieved by measuring the graviton via instrumentation. Normalized energy density of gravitational waves, as given by Maggiore [5] is where n ν is a frequency-based count of gravitons per unit cell of phase space? Is Equation (1.1) above fundamental physics? And what is the significance of the n ν and ν terms with regards to if gravitons could have been cycled from a prior to the present universe? The rest of the document will attempt to answer the question of what ultra high frequency inputs into the n ν as well as ν term are relevant to, assuming that the quantum bounce model of a "recycled" universe is in part, correct.

Onset of Creation
As suggested earlier by Beckwith [6], gravitons may have contributed to the re-acceleration of the universe one billion years ago. When q becomes negative, the rate of acceleration of the universe is actually increasing, rather than slowing down [6] [7]. The suggestion Beckwith made for implementing re acceleration involves correct use of the de celebration parameter, and also looking at the behavior of gravitons. The use of Equation (1.2) below to have re acceleration in the application Beckwith made is dependent upon "heavy gravity" and the rest mass of gravitons in four dimensions having a small mass term.
We wish next to consider what happens not a billion years ago, but at the onset of creation itself. If a correct understanding of initial graviton conditions is presented, it may add more credence to the idea of a small graviton mass, in a  10 10 Hz~10 GeV 10 Having said that, the

5) with S ñ Used by Y. Jack Ng for DM Particles in His Entropy/Particle Counting Algorithm?
Note that J. Y. Ng uses the following. [9] i.e. for DM, S n , but this is for DM particles, presumably of the order of mass of a WIMP, i.e.
If one drops the effective energy contribution to 0 10~1 Hz ν ≈ , as has been suggested, then the relic graviton mass-energy relationship is: Finally, if one is looking at the mass of a graviton a billion years ago, with ( ) i.e., if one is looking at the mass of a graviton, in terms of its possible value as of a billion years ago, one gets the factor of needing to multiply by 10 38 in order to counting algorithm, i.e., the equivalence relationship for entropy and "particle count" may work out well for the WIMP sized DM candidates, and may break down for the graviton mass-energy problem.

The Electro Weak Generation Regime of Space Time for Entropy and Early Universe Graviton Production before Eletro Weak Transitions
A typical value and relationship between an inflation potential [ ]   [10] and denotes that the electro weak transition was a "strongly first order phase transition") then one can write, by conventional theory that Here, the factor put in, of g *  is the number of degrees of freedom. Kolb and Turner [11] put a ceiling of about 100 -120 Should the degrees of freedom hold, for temperatures much greater than T * , and with 1000 g * ≈  at the onset of inflation, for temperatures, rising up to, say T-10 19 GeV, from initially a very low level, pre inflation, then this may be enough to explain how and why certain particle may arise in a nucleated state, without necessarily being transferred from a prior to a present universe.
I.e. the suggestion being presented is that a more standard thermodynamic dependence of entropy upon temperature, i.e. S T ∝ when 1000 g * ≈  or even higher even if 19 10 GeV 19 10 GeV T T *  , and assuming that 1000 g * ≠  , i.e. that an upper limit of 100 -110 g * ≈  in degrees of freedom is all that is permitted.
Furthermore, if one assumes that 3 S T ∝ [11] when 1000 g * ≈  or even higher even if 19 10 GeV T T *  , then there is the possibility that The Mukhanov et al. argument leads to an exercise which Mukhanov et.al. [12] claims is solutions to the exercise yields an increase in number count, as can be given by first setting the oscillator in the ground state with  10 Hz Ω ∝ , then Equation (1.12), and Equation (1.14) plus its generalization as given in Equation (1.15) may be a way to imply either vacuum nucleation, or transport of gravitons from a prior to the present universe. Having said that, the problem of Heavy Gravity raises its ugly head in the following field theory example.

Massive Graviton Field Theories and the Limit
The mismatch between these two equations, when graviton 0 m → is largely due  between a prior to the present universe, provided that there was no cosmic singularity and that the LQG quantum bounce hypothesis has some validity., Note that the author has been informed by J. Dickau of research by [16] de Rham and Gabadadze which in the authors opinion clears up the problem of ghosts and heavy gravity (massive Gravitons). However, the issue of if a graviton could survive a quantum bounce in LQG [1] stands alone as a problem which the author believes has been removed from being impossible to entertain, to one which cannot be ruled out.

Conclusions
A way to obtain traces of information exchange, from prior to present universe cycles is finding a linkage between information and entropy. If such a parameterization can be found and analyzed, then Seth Lloyd's [17] shorthand for entropy, [ ]

Further Research Questions for Investigative Inquiry and How to Link Our Inquiry to the Overall Geometry of the Universe
The problem of reconciling the existence of a graviton mass with quantum mechanics, in spin two particles usually having zero mass appears to be resolvable, and may imply a linkage between DE and DM [6] Furthermore, the radius of the universe problem, as presented by Roos [18], will yield rich applications of the Specifically, the author is convinced that analyzing Equation (1.19) will be tied in, with appropriate analysis of the following Figure 1.

The relation between
g Ω and the spectrum ( )  and also attempting to make sense of if there is a way to distinguish between the criteria given in Section 2 of this document.
Note that Appendix A below summarizes some of the methods used by the author in terms of counting of gravitons and initial entropy assumed in this document. The reader should also review [23] as well which places the idea of infinite quantum statistics in context.
In addition, in Appendix B, the author gives a summary as to some emerging trends in gravitational wave astronomy which are extremely important. References [24], [25] and [26] are extraordinarily relevant to the ideas brought up and shared here, i.e. that Corda in [26] has outlined protocol as to the emerging issues concerning interferometry and the tests for the nature of gravity is undeniably relevant to our manuscript, and not to mention the speculations on extra dimensions in [27].