_{1}

^{*}

Could a causal discontinuity lead to an explanation of fluctuations in the CMBR radiation spectrum? Is this argument valid if there is some third choice of set structure (for instance do self-referential sets fall into one category or another)? The answer to this question may lie in (entangled) vortex structure of space time, along the lines of structure similar to that generate in the laboratory by Ruutu. Self-referential sets may be part of the generated vortex structure, and we will endeavor to find if this can be experimentally investigated. If the causal set argument and its violation via this procedure holds, we have the view that what we see a space time “drum” effect with the causal discontinuity forming the head of a “drum” for a region of about 10
^{10} bits of “information” before our present universe up to the instant of the big bang itself for a time region less than t~10
^{-44 }seconds in duration, with a region of increasing bits of “information” going up to 10
^{120} due to vortex filament condensed matter style forming through a symmetry breaking phase transition. We address the issue of what this has to do with Bicep 2, the question of scalar-tensor gravity versus general relativity, how to avoid the detection of dust generated Gravity wave signals as what ruined the Bicep 2 experiment and some issues information flow and causal structure has for our CMBR data as seen in an overall summary of these issues in Appendix X, of this document. Appendix XI mentions how to differentiate between scalar-tensor gravity, and general relativity whereas Appendix XII, discusses how to avoid the Bicep 2 mistake again. While Appendix VIII gives us a simple data for a graviton power burst which we find instructive. We stress again, the importance of obtaining clean data sets so as to help us in the eventual detection of gravitational waves which we regard as decisively important and which we think by 2025 or so which will be an important test to discriminate in a full experimental sense the choice of general relativity and other gravity theories, for the evolution of cosmology. Finally, Appendix VII brings up a model for production for gravitons, which is extremely simple. Based upon a formula given in a reference, by Weinberg, in 1971, we chose it due to its illustrative convenience and ties in with Bosonic particles.

We start, as stated earlier, by appealing to work done by Ruutu [

The causal discontinuity condition is in [

This has real and imaginary components to the scalar field which can be identified as of the form

J.J. Blainco-Pillado et al. [

If one has no coupling of terms as in an expanding universe metric of the form [

Then the Christoffel symbols take the form given by

The implications for the scalar evolution equation are that we have

If we can write as follows, i.e. say that we have

On the other hand,

Otherwise, taking into account the causal discontinuity expression, we claim that we will be working with

For very short time duration, and looking at the case for chaotic inflation, we would be working with, in this situation

If

This would lead to, if provided

Similarly, for

Upshot is that for

Racetrack models of inflation, assuming far more detail than what is given in this simplistic treatment provide a power spectrum for the scalar field given by

This is assuming a slow roll parameter treatment with

Now, how does this tie in with the lumpiness seen in the CMBR spectra? In an e mail communication, Sarkar summarized the situation up as follows [

“Quasi-DeSitter space-time during inflation has no ‘lumpiness’―it is necessarily very smooth. Nevertheless one can generate structure in the spectrum of quantum fluctuations originating from inflation by disturbing the slow-roll of the inflaton―in our model this happens because other fields to which the inflation couples through gravity undergo symmetry breaking phase transitions as the universe cools during inflation”.

If we use what is in Appendix I, namely the non flat space generalization of the flat space De Alembertian leading to, for a quartic potential as given in Appendix I

The mass being referred to fades out if there is a temperature increase. So happens that there is one. And this due to the worm hole transfer of thermal heat and the like from a prior universe. This is done and can be made far more complex if the De Alembertian has off diagonal terms in it

i.e. if one does not insist upon simple Euclidian space, the Laplacian takes the form [

We claim that the generalization for Equation (17) and Equation (18) will lead in the case of cooling for a scalar field system in the aftermath of immediate rapid expansion of the scalar field a very different, and far more complicated dynamic than is given by Equation (18)

Recall what is given in modeling the pure Dilatonic potential, i.e. as given by Lalak, Ross, and Sakar [

This is assuming that we are having

Point which is to be made here, is that the richer the structure with respect to Equation (20), and its race track version which has real and imaginary components to a scalar field, the less tenable the simple Equation (17) pictures of simply rising and falling scalar potentials are. So the following claim is made.

CLAIM 1: In the initial phase of expansion in an inflationary sense, the period of time

CLAIM 2: In the cool down period before the re heating period after inflation, we have additional structure put in, enough so, so that multiple minima and fluctuations exist which would give far more definition as to local scalar power spectra. I.e. we are looking at

Provided that we have a nonzero minimum if we set

We can use the criteria of Appendix III, which gives realistic data input parameters as to the variance of the CMBR spectra. In particular, we can take Equation (3) of Appendix III and splicing that in on a new derivation as to

Here we can make the following assertion. Especially with regards to Gravitational waves. This is from Durrer [

i.e.

We can appeal to simplified models as to how to come up with

are working directly with Equation (12) in part, and at the regime of at least partial causal discontinuity [

In addition to this treatment of how to get a CMBR reconstruction of gravitational tensor fluctuations, we can also look at observational efforts to confirm, or falsify different models of

entropy varies will be in its own way will affect the power spectra, which in turn affects confirming or falsify-

ing the spectral index

follow through on elementary calculations of how P varies due to choices of potential system we are examining. I.e. recall Sarkar’s 2001 investigation of a simple choice of variant of the standard chaotic inflationary potential given by [

Sarkar treated the inflaton as having a varying effective mass, with an initial value of effective mass of

This is, when Sarkar did it, with

dex value, and it also would be a way to consider an increase in inflation based entropy. The only drawback to this phenomenological treatment is that it in itself does not address the formation of an instanton in the very beginning of inflation, a serious draw back since this does not also give an entry into the formation of the layers of complexity which we think is more accurately reflected in the transferal of state from a growing value of the magnitude of the scalar field as given by Equation (17) and Equation (18) as temperature flux flows in from a prior universe, to the cooling off period we think is necessary for the formation of a complex scalar field and its analogies in the race track style models, as in Equation (20), and Appendix I below. Equation (72) with its treatment of tensorial contributions to the CMBR has its counterpart, an implied release in relic gravitons which may, or may not be amendable to observational techniques. We would most likely imply their existence indirectly via use of Equation (22) and seeing if they can be linked to the behavior of the inflation generating a new burst of entropy at the onset of inflation. Appendix VI shows what we may wish to consider as to relic graviton production which is linkable to the worm hole, and causal discontinuity discussion we have brought up, with regards to early universe entropy generation. We also will make reference that this has been linked to brane theory via Appendix VII material.

In a colloquium presentation done by Dr. Smoot in Paris [

1) Physically observable bits of information possibly in present Universe-0^{180}.

2) Holographic principle allowed states in the evolution/development of the Universe-10^{120}.

3) Initially available states given to us to work with at the onset of the inflationary era-10^{10}.

4) Observable bits of information present due to quantum/statistical fluctuations-10^{8}.

Our guess is as follows. The thermal flux so implied by the existence of a worm hole accounts for perhaps 10^{10} bits of information. These could be transferred via a worm hole solution from a prior universe to our present, and that there could be, perhaps 10^{120} minus 10^{10} bytes of information temporarily suppressed during the initial bozonification phase of matter right at the onset of the big bang itself.

Then after the degrees of freedom dramatically drops during the beginning of the descent of temperature from about

To [

Whichever model we can come up with that does this is the one we need to follow, experimentally. And it gives us hope in confirming if or not we can eventually analyze the growth of structure in the initial phases of quantum nucleation of emergent space time [

The race track models, after the inflation begins to decline will be ideal in getting the couplings, and the symmetry breaking. We will refer to this topic in a future publication. We can make a few observations though about the coupling so assumed. First, there is a question of if or not there is a finite or infinite fifth dimension. String theorists have argued for a brane-world with a warped, infinite extra dimension allowing for the inflation to decay into the bulk so that after inflation, the effective dark energy disappears from our brane. This is achieved by shifting away the decay products into the infinity of the 5th dimension [

What if we do not have an infinite fifth dimension? What if it is compactified only? We then have to change our analysis.

Another thing. We place limits on inflationary models; for example, a minimally coupled

matter of information flow, in terms of details on information theory and the like and also Dowker causal structure, and how it may tie into the subject of our inquiry as stated in the title and abstract. Appendix X is a re statement of the basic summary points of this paper with regards to causal structure and discontinuity and re iterates what is scattered through this document for a quick read. Appendix XI addresses the issue of what may relate this to the question of if Scalar-tensor gravity is favored, or General relativity, and Appendix XII discusses the tie in with differentiating our inquiry from problems which destroyed the fidelity of Bicep 2’s measurements, due to dust generated GW signals which is what we wish to avoid at all costs in this inquiry. Our conclusion is that we need, especially, to consider fully the issues raised in Appendix X, which will then allow us, to if we are careful to distinguish between scalar-tensor gravity in Appendix XI, and GR as a foundational construction in cosmology. Clean data sets, and observational platforms as brought up in Appendix XII, will commence, if done rigorously, to enhance the probability of relic GW being measured instead of the chaos multi source generation of gravitational waves, created by dust. Note Appendix X, has 2 sub sessions and they are meant to be a focus of this document upon the information flow aspect of this paper. The entire document Appendix X is meant to summarize the theme of information flow and causal discontinuity as it may affect the CMBR in this very long document. For convenience.

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

Andrew Walcott Beckwith, (2016) Open Question: Could a Causal Discontinuity Explain Fluctuations in the CMBR Radiation Spectrum?. Journal of High Energy Physics, Gravitation and Cosmology,02,186-208. doi: 10.4236/jhepgc.2016.22018

We begin with the D’Albertain operator as part of an equation of motion for an emergent scalar field. We refer to the Penrose potential ( with an initial assumption of Euclidian flat space for computational simplicity) to account for, in a high temperature regime an emergent non zero value for the scalar field

When the mass approaches far lower values, it, a non zero scalar field re appears.

Leading to

Let us now begin to initiate how to model the Penrose quintessence scalar field evolution equation. To begin, look at the flat space version of the evolution equation

This is, in the Friedman-Walker metric using the following as a potential system to work with, namely:

This is pre supposing

That means

We find the following as far as basic phenomenology, namely

The difference is due to the behavior of

P. Brax, A. Davis et al. [

This has scalar fields

This ultra simple version of the race track potential is chosen so that the following conditions may be applied.

1) Exist a minimum at

2) We set a cosmological constant equal to zero with

3) We have a flat saddle at

4) We re-cale the potential via

Doing all this though frequently leads to the odd situation that

Then the spectral index of the inflation is consistent with WMAP data. I.e. if we have the number of e foldings

These sorts of restrictions on the spectral index will start to help us retrieve information as to possible inflation models which may be congruent with at least one layer of WMAP data. This model says nothing about if or not the model starts to fit in the data issues Sarkar identified in is Pune, India lecture in 2007.

Begin first of all looking at

This leads to consider what to do with

Samtleben et al. [

i.e. Contributions to

Durrer [

and

Here we are interpreting A = amplitude of metric perturbations at horizon scale, and we set

Then for

We get for tensor fluctuation, i.e. gravity waves, and a scale invariant spectrum with

Start with Padamadans’s formulas [

If

Both regimes as specified by Equation (2) above lead to zero values for a quintessence scalar field. But it does not stop there. We will show later that in actuality, the scalar field likely damps out far before the CMBR barrier value of expansion when Z = 1100, about 380,000 to 400,000 years after the big bang.

We show this by noting that in Equation (2), the time derivative of

Sub point to claim 1: The existence of two zero values of the scalar field

If we have a non infinite but huge negative value of the cosmological vacuum energy in the wormhole, then we have 10^{10} bits of computing information. When we leave the wormhole, we have 10^{120} bits of computing information. We specify a transition between the two regions in terms of a causal discontinuity regime created by a(t) chaotic behavior due initially to the initially very large value of thermal vacuum energy transmitted.

Details, and many more of them are needed to bridge this transition to the problem of structure formation and a drop of temperature. If we look at Ruutu’s [

1) Do the filaments in any shape or form have an analogy to the cosmic strings so hypothesized by String theorists? My guess is a flat MAYBE but one cannot be certain of this. This deserves to be analyzed fully. If they have an analogy to cosmic strings, then what is the phase transition from a maximally entangled space time continuum, with a soliton type behavior for temperatures of the order of

2) What is the mechanism for the actual transition from the initial “soliton” at high temperatures to the symmetry breaking phase transition? This is trickier than people think. Many theorists consider that, in tandem with Ruutu’s [

3) One of the models considered as a super fluid candidate for this model has been the di quark one. This however was advanced by Zhitinisky [

4) Do the formation of such initial conditions permit us to allow optimal conditions for graviton production? If so, can this be transferred to engineering prototypes? How can this be modeled appropriately?

Here is a very simplified model as to what we may be able to expect if there is actual relic graviton production. I.e. Detecting gravitons as spin 2 objects with available technology. To briefly review what we can say now about standard graviton detection schemes, Rothman [

Here,

This has

If this is the case, then what can we do to see how relic gravitons may emerge if we have a worm hole transferred burst of thermal/ vacuum energy? [

Time | Thermal Inputs | Dynamics of Axion | Graviton Eq. |
---|---|---|---|

Time | Use of quantum gravity to give thermal input via quantum bounce from prior universe collapse to singularity. Brane theory predicts beginning of graviton production. | Axion wall dominant feature of pre inflation conditions, due to jeans inequality with enhanced g ravitational field, quintessence scalar equation of motion valid for short time interval | Weinberg formula for relic graviton production beginning to produce gravitons due to sharp rise in temperatures. |

Time | End of thermal input from quantum gravity due to prior universe quantum bounce. Brane theory predicts massive relic graviton production | Axion wall is in process of disappearing due to mark rise in temperatures. Quintessence valid for short time interval | Weinberg formula for relic graviton production produces massive spike gravitons due to sharp rise in temperatures |

Time | Relic graviton production largely tapering off, due to thermal input rising above a preferred level, via brane theory calculations. Beginning of regime where the | Axion wall disappears, and beginning of Guth style inflation. Quintessence scalar equations are valid. Beginning of regime for | Weinberg formula for relic graviton production leading to few relic gravitons being produced. |

Also, one can expect a difference in the upper limit of Park’s four dimensional inflation [

A minimum value of

This is in contrast to the nearly infinite value of the Planck’s constant as given by Park (2003) [

As opposed to a minimum value as given by Park (2003) [

As is well known, a good statement about the number of gravitons per unit volume with frequencies between

The hypothesis presented here is that input thermal energy (given by the prior universe) inputted into an initial cavity/region (dominated by an initially configured low temperature Axion domain wall) would be thermally excited to reach the regime of temperature excitation. This would permit an order-of-magnitude drop of Axion

density

Time | Time | Time | Time |
---|---|---|---|

To do this, one needs to refer to a power spectrum value that can be associated with the emission of a graviton. Fortunately, the literature contains a working expression of power generation for a graviton produced for a rod spinning at a frequency per second

The contribution of frequency here needs to be understood as a mechanical analogue to the brute mechanics of graviton production. The frequency

And then one can set a normalized “energy input” as

Here, N1 refers to a net graviton numerical production value as given by Equation (9). There is a distinct power spike of thermal energy that is congruent with a relic graviton burst.

We use our bound to the cosmological constant to obtain a conditional escape of gravitons from an early universe brane. To begin, we present using the paper written by Leach et al. on conditions for graviton production [^{ }

Also there exists an “impact parameter”

This leads to, practically, a condition of “accessibility” via PP R so defined is with respect to “bulk dimensions”^{ }

Here, k = 0 for flat space, k = −1 for hyperbolic three space, and k = 1 for a three sphere, while an radius of curvature

Numerical values of graviton production | Scaled power values |
---|---|

Power = 0 | |

Power = 0 | |

Power = | |

Power @ very small value | |

Power= 0 |

Here, we have that we are given

Park et al. note that if we have a “horizon” temperature term

We can define a quantity

Then there exists a relationship between a four-dimensional version of the

So

In working with these values, one should pay attention to how

Here, I am defining

Here we are looking at how the initial vacuum energy ‘cosmological constant’ parameter may be effected by a change in the potential system with the

This, for potential,

Sarkar treated the inflation as having a varying effective mass, with an initial value of effective mass of

Either this potential can be used, or we just use a variant of a transition to the race track potential given by

This with a version of the scalar field in part be minimized. This is assuming that we are having

This paper uses a special metric that is congruent with the Wheeler-De Witt equation, which can be explained as follows. If one rewrites the Friedmann equation using Classical mechanics, we can obtain a Hamiltonian, using typical values of

in Dalarsson (2005) [

the same flavor as a pseudo-WKB approximation to the Schrodinger equation. This, with some refinements, constitutes what we used for forming a “wormhole” bridge.

We referenced the Reissner-Nordstrom metric. This is a metric that is similar to the space-time metric used for black hole physics, i.e., black holes with a charge. With some modifications, this is the metric that Crowell (2005) [

passes through a thin shell separating two space-times. The radius of the shell,

times is of length

This has:

Note that Equation (2) referenced above is a way to link this metric to space-times via the following model of energy density equation, linked to a so called “membrane” model of two universes separated by a small “rescaled distance”

Frequently, this is simplified with the term,

This is a wave functional solution to a Wheeler De Witt equation bridging two space-times. The solution bridging two space-times is similar to one made by Crowell (2005) [

This equation has

It is asserted here that a thermal bridge in wormhole form exists as a bridge between a prior and present universe. Furthermore, it is asserted that the existence of this bridge is part of a necessary condition for thermal energy transfer between a prior and present universe. The prior universe shrinks to a singularity at the time that thermal energy is transferred to our present universe, thereby helping to initiate cosmological inflation. dominated. This is due in part to the absolute value of the five-dimensional “vacuum state” parameter varying with temperature T, as Beckwith (2007) [

This contrasts with the more traditional four-dimensional version of the same, without the minus sign of the brane world theory version (i.e., the four-dimensional cosmological constant grows large and is a positive valued expression at the same time that the five-dimensional vacuum energy expression shrinks in value and has a negative value). The five-dimensional version is based on brane theory and higher dimensions, whereas the four-dimensional version is linked to more traditional De Sitter space-time geometry, as given by Park (2002):

Looking at the range of allowed upper bounds of the cosmological constant, one can note the difference between what Park (2002) predicted (a nearly infinite four-dimensional cosmological constant) and Barvinsky (2006), who specified an upper limit of 360 times the square of Planck’s mass m. This indicates that a phase transition is occurring within a Planck interval of time.. This allows for a brief interlude of quintessence. This assumes that a release of gravitons occurs, which leads to a removal of graviton energy stored contributions to this cosmological parameter, with m_{P} as the Planck mass, i.e. the mass of a black hole of “radius” on the order of magnitude of Planck length l_{P} ~ 10^{-35} m. This leads to Planck’s mass

Right after the gravitons are released, there is still a drop off of temperature contributions to the cosmological constant. For a small time value,

the 32nd power Kelvin, this difference is the ratio of the value of the four-dimensional version of the cosmological constant divided by the absolute value of the five dimensional cosmological constant, which is equal to 1 plus 1/n, where n is a positive integer. This assumes Beckwith’s (2007) [

The absolute value of the brane world vacuum energy expression becomes identical in value to the four-di- mensional cosmological constant at time t (Planck) interval when the matter-energy exits the wormhole. In other words, t (Planck), or 10 to the minus 44 seconds after exiting the wormhole mouth, there are approximately equal values of the four- and five-dimensional cosmological parameters, i.e., the magnitude of the brane world vacuum energy increases as the four-dimensional cosmological constant shrinks with decreasing temperature.

This huge drop in temperature occurs because energy is removed due to the release of relic gravitons during a phase transition from a nearly infinite thermally based Park value of the cosmological constant to Barvinsky’s [

The transition outlined in Equation (7) above has a starting point with extremely high temperatures given by a vacuum energy transferal between a prior universe and our present universe, as outlined by Equation (3) and Equation (4) above; whereas the regime where there is an upper bound to vacuum energy in four dimensions is outlined in Equation (9) above. So eventually, we can model the behavior of scalar fields as transformed from cyclic behavior, with an imaginary component, to a purely real-valued scalar equation, as given by the argument in the next sections. The paper concludes with a proof of the short-term behavior of this quintessence scalar field, making reference to both Equation (7) and Equation (8) above. This wormhole solution is a necessary and sufficient condition for thermal transfer of heat from that prior universe to allow for graviton production under relic inflationary conditions.

CLAIM 1: The following are equivalent (In a space-time evolution sense? Definitely yes).

1) There exists a Reisnner-Nordstrom Metric with -F(r) dt^{2} dominated by a cosmological vacuum energy term,

2) A solution for a pseudo-time dependent version of the Wheeler De Witt equation exists, with a wave function

3) The heat flux-dominated vacuum energy value given by

The proof of claim 1 is referenced via an article in arXIV, Beckwith (2007) [

Begin first by presenting a version of the Friedmann equation given by Frampton (2007) [

The existence of such a nonlinear equation for early universe scale factor evolution introduces a de facto “information” barrier between a prior universe, which can only include thermal bounce input to the new nucleation phase of our present universe. To see this, refer to Dowker’s (2005) [

(1) If

(2) If

(3) For any pair of fixed elements x and zof elements in C, the set

Items (1) and (2) show that C is a partially ordered set, and the third statement permits local finiteness. Stated as a model for how the universe evolves via a scale factor equation permits us to write, after we substitute

model of Equation (5) leads to the existence of a de facto causal discontinuity in the arrow of time and blockage of information flow, once the scale factor evolution leads to a break in the causal set construction written above.

CLAIM 2: The Friedmann equation for the evolution of a scale factor

set evolution of the scale factor with evolving time, thereby implying a causal discontinuity. The validity of this formalism is established by rewriting the Friedman equation as follows:

So in the initial phases of the big bang, with a very large vacuum energy, the following relation, which violates (signal) causality, is obtained for any given fluctuation of time in the “positive” direction:

The existence of such a violation of a causal set arrangement in the evolution of a scale factor argues for a break in information propagation from a prior universe to our present universe. This has just proved non-par- tially ordered set evolution, by deriving a contradiction from the partially ordered set assumption. The easiest way to show this discontinuity is to use Equation (12) to show that in the evolution of the scale factor is in certain time steps either partly reversed, or in a chaotic mode. This shows up in a breakage in causal evolution of “information” transmitted via the medium, where Equation (12) shows an information exchange/flow with a linear progression in time. There is a causal break, since information flow is not linear in time if the scale factor is unexpectedly made chaotic in its time evolution.

One valid area of inquiry that will be investigated in the future is the following: Is this argument valid if there is some third choice of set structure (for instance, do self-referential sets fall into one category or another)? The answer to this, it is suggested, lies in (entangled?) vortex structure of space-time, along the lines of structure similar to that generated in the laboratory by Ruutu (1996) [^{10} bits of “information” before our present universe, up to the instant of the big bang itself, for a time region less than ^{120}due to vortex filament condensed matter forming through a symmetry breaking phase transition.

Many people would not understand why computational models of the universe would be important to either cosmology or to propulsion. What we establish though this model is a way to explain why the dominant contribution to gravity waves from a wormhole transferal of vacuum energy to our present universe is tilted toward a dominant high-frequency spectrum. This allows us to understand what sort of initial conditions would be favored for graviton production, which it is claimed, is the way to go for an advanced propulsion system in spacecraft design. One can make use of the formula given by Seth Lloyd (2002) [

The second limit is the number of operations, which is linked to entropy, due to limits to memory space, as Lloyd [

The third limit, based on a matter-dominated universe, relates the number of allowed computations/operations within a volume for the alleged space of a universe. This makes the identification of this space-time volume as

If

Lloyd further refines this to read as follows:

It is assumed that

Furthermore, if based on the assumption that the temperature is within the given range of

Lloyd (2002) defines a horizon parameter as:

And an early universe:

Then:

CLAIM 3: The number of allowed operations in the evolution of the universe specifies a relationship between an evaluated volume for space-time, and upper limits of released relic graviton frequencies. This is proved by appealing to Equation (22) above. Next, the existence of certain symmetries in the scalar field itself are examined.

CLAIM 4: Without the frequency in Equation (21) becoming large, the number of operations could effectively go to 10^{1000} or higher. How can this be shown? One would need to have a very large gravitational frequency

range, with high-frequency gravity waves, in order to brake the effects of a tiny Planck time interval

in the number of operations. So that instead of Equation (22) bounded by 10^{120}, as the volume increased, one could have the number of degrees of operations become almost infinite.

This last claim combined with the discussion right after Equation (11) above (the initial “drum head” model for a bounded region of space bracketed by causal discontinuity regions) constitutes a working model of an information-based model of cosmology that the author expects will yield falsifiable experimental criteria.

Appendix Xb: Smoot’S Information Theory/Cosmology ConclusionsAt the “D. Chalonge” school presentation Dr. Smoot (2007) [

1) Physically observable bits of information possibly generated in the universe: 10^{180}.

2) Holographic principle allowed bits (states) in the evolution/development of the universe: 10^{120}.

3) Initially available bits (states) given to us to work with at the onset of the inflationary era: 10^{10}.

4) Observable bits of information present due to quantum/statistical fluctuations: 10^{8}.

The author’s speculation is that the thermal flux implied by the existence of a wormhole accounts for perhaps 10^{10} bits of information. These bits could be transferred via a wormhole solution from a prior universe to our present, as alluded to by Equation (4) above, and that there could be perhaps 10^{120} minus 10^{10 }bits of information temporarily suppressed during the initial bozonification phase of matter right at the onset of the big bang itself. Then, the degrees of freedom dramatically dropped during the beginning of the descent of temperature from about

Quoting from [

Quote

“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) [

End of quote

What we are doing is to try to create conditions in which we will have enough data to determine if a third polarization is necessary. If it is not necessary, due to data analysis, then it is pretty clear that General relativity is the preferred cosmological theory.

The purpose of this appendix is to bring up the essential question. Is GR the preferred theory, on the basis of the quote given by [

We argue that a third polarization in Gravitational waves from the early universe may be detected, if there is proof positive that in the pre Planckian regime that the Corda conjecture [

Quote from [

“The case of massless Scalar-Tensor Gravity has been discussed in [

End of quote: This ends our recap of the section given in [

What we are arguing for is that the choice of the vacuum energy as given by Equation (2) may give conclusive proof as to satisfy the Corda conjecture and his supposition as to the existence of an additional polarization [

The main agenda would be in utilization of Equation (1) to help nail down a range of admissible frequencies, as given by [

Then we are looking at

Here,

Picking an optimal choice for Equation (2) and Equation (3) frequencies and behavior would be enough, via use of [

An optimal frequency pick which would be to avoid [