Supplying Conditions for Having up to 1000 Degrees of Freedom in the Onset of Inflation , Instead of 2 to 3 Degrees of Freedom , Today , in Space-Time

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 19 Planck ~ 10 GeV T used as an input into T times N(T). Initial assumptions as to the number of degrees of freedom have for 19 Planck ~ 10 GeV T a maximum value of N(T) ~ 10. Making that upper end approximation for the value of permissible degrees of freedom is dependent upon a minimum grid size length as of about 33 Planck ~ 10 l − centimeters. Should the minimum uncertainty grid size for space time be higher than 33 Planck ~ 10 l − centimeters, then top value degrees of freedom of phase space as given by a value N(T) ~ 10 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.

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 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.

Introduction
Recently, a big bounce has been proposed1 as an alternative to singularity conditions that Hawkings, Ellis [1], and others use.A quantum bounce, with a non zero but finite initial radius inevitably will lead to questions as to relic particle production, and of the amount of information bits surviving the big bounce, from a prior universe.This paper intends to find ways to configure scaling procedures to answer the question as to what would be optimal conditions for initial entropy production and byte of information "production" initially.To begin this inquiry we can start with examining candidates for the initial configuration of the normalized energy density.The normalized energy density of gravitational waves, as given by Maggiore [2] is where n ν is a frequency-based count of gravitons per unit cell of phase space.Equation (1.1) leads to, as given to Figure 1, candidates as to early universe models which should be investigated experimentally.
The author, Beckwith, wishes to determine inputs into n ν above, in terms of frequency, and also initial temperature.Doing so will, if one gets inputs into Equation (1.  ( ) The consequence of Equation (1.5) would be to set conditions for which the following could be true.
( ) If we take a dimensional re scaling of Equation (1.6), with One can then obtain an algebraic equation to the effect that as reported by Kolb and Turner, 1991 [8], which is the usual value for degrees of freedom for the case of the electro weak era.

First Principle Evaluation of Initial Bits of Information, as Opposed to Numerical Counting, and Entropy
A consequence of Verlinde's [9] generalization of this technique as far as entropy, and the number of "bits" yields the following consideration, which will be put here for startling effect.Namely, if a net acceleration is such that accel 2π B a k cT =  as mentioned by Verlinde [9] as an Unruth result, and that the number of "bits" is ( ) This Equation (1.9) has a T 2 temperature dependence for information bits, as opposed to [10] ( ) The situation for which one has [8] even if one has very high temperatures.Note that for WIMPS a situation as Y. J.

Ng has it that [10] [11]
Particle-Count The problem, though, is that there may be more than one graviton per information bit as given by Beckwith's calculations for entropy, and also energy carried per graviton.As given by Beckwith, in DICE 2010, Beckwith has made the following estimate, i.e. [10].Note that J. Y. Ng uses the following [11], i.e. for DM, S n, but this is for DM particles, presumably of the order of mass of a WIMP, i.e.The author will later on attempt to prove that the 10 38 factor so recorded is an artifact of Equation (1.9), i.e. that the scaling so implied in Equation (1.9) with the square of temperature, divided by grid size length means that for very light particles, the influence of high levels temperature will make the 10 38 factor inevitable.
Still though, it would be important to come up with criteria as to how one can obtain a temperature and a mass of a "particle" regime for which S N work may be solvable via making the Ng."Entropy" linkable to particle count.AND bits of information at the same time.To do so may entail introducing a new concept, that of "configurational entropy", as introduced below.

Does SC as "Configurational Entropy" Serve as a Way to Make a One to One Connection between a Particle Count Algorithm of Entropy, and Bits of Information? No
Matter What the "Mass" of a Particle and the Initial Background Temperature?
The author has been advised that Rubi et al., 2008 [12] has a net temperature, as given by the following, namely for non equilibrium processes, one can look at T  as an effective temperature, and C S as "configurational entropy", and (1.17) In the case that the graviton has a very slight rest mass, one can, if [13] we pick E to be the rest energy, and graviton m the almost nonexistent rest mass of a graviton in four dimensions ( ) The net temperature may be considered to be a calculated function of a rise in temperature from almost nonexistent status, up to nearly Planck temperature, and the author is convinced, that one would have to, given different geometries, reconstruct the configurational entropy, once an idea of a minimum to the peak temperature, T, for Plank temperature values is obtained.
By doing so, the author hopes to obtain an evolution of C S with different values of the temperature, in order to come up with an emergent structure with . This should be done while paying attention to t' Hooft's idea that an emergent structure would by necessity likely engage more than 100 dimensions, i.e. as Beckwith wrote about in [10], so how one defines Equation (1.17) may, with a proper definition of effective temperature, may force the adaptation of additional degrees of freedom.

Conclusions. Extensions of This Thought Experiment, and Comparison with Entropy of Photons
Recently, the author has been fortunate enough to obtain Leff's [14] entropy of photons per unit volume paper where for a phase space volume, V, and temperature T, This should be compared with Beckwith's derived "graviton clumping" entropy result [10] per unit volume of phase space as given by What the author supposes, is that fine tuning the inter play between these two formulas, from the onset of inflation when there was likely coupling between gravitons, clumps of gravitons, and photons, may permit experimental measurements permitting investigation if there is an interplay between E & M and gravity, and also modifications of gravity theory along the lines brought up by Sidharth [15], i.e. if Equation (1.10), Equation (1.17) and Equation (1.19) are representations of a joint phenomenon as is suggested by Sidarth's (which incidentally is for E and M radiation characterized by a given "carrier wave" frequency) where A µ can be identified with the electromagnetic four potential.The idea, as Beckwith sees it would be to determine if there could be coupling between E & M effects, and gravitation along the lines of employing the Quantum (coupled) oscillator frequency relationship for coherent "state" oscillation as given by Sidarth [15] via and gravitational waves in early universe conditions.Also , the author hopes that examining a potential inter play of Equation (1.10) to Equation (1.21) that the datum that the 10 38 coherent gravitons [10] to form coherent clumps to obtain GW is necessary derivation will also, allow for explaining further the inter play between the choice of minimum length and momentum, as given by Planck p l P φ ∆ ≈ =  and the supposition of more initial degrees of freedom than is usually supposed by conventional cosmology, of the sort presented by Kolb And Turner's book on cosmology.Finally, once this task is done, the author thinks that L. Glinka's formula [16] could be investigated as being part of the bridge between phenomenology of both photon gases, and their entropy, as well as a modified treatment of L. Glinka's graviton gas [16] [17], with suitable inputs into the frequencies allowed for both "gases".
It is well worth noting that tests concerning the alleged Graviton gas should be tested against the predictions given in [18] by Dr. Corda, i.e. note this quote "it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity.In this essay we show that, if advanced projects on the detection of Gravitational Waves (GWs) will improve their sensitivity, allowing to perform a GWs astronomy, accurate angular and frequency dependent response functions of interferometers for GWs arising from various Theories of Gravity, i.e.General Relativity and Extended Theories of Gravity, will be the definitive test for General Relativity".
Formula (1.22) as well would be useful in determining the would be existence of frequency response functions as far as a would be experimental datum for analysis, and also of falsifiable tests of alternatives to General Relativity as far as the foundation of gravity itself.
Finally, we should note as to the existence of positive identification of Gravitational waves.As seen in [19] and [20] there have been confirmation of GW,.
Which afterwards is lending credibility to the would be frequency issue brought up in Equation (1.22) as well as testing of the criteria raised in [18] by Dr. Corda.
T used as an input into T 4 times N(T).Initial assumptions as to the number of degrees of freedom have for 19 Planck ~10 GeV T a maximum value of N(T) ~ 10 3 .Making that upper end approximation for the value of permissible degrees of freedom is dependent upon a minimum grid size length as of about

8 )
Journal of High Energy Physics, Gravitation and CosmologyThis above approximation would be assuming that temperature.The other assumption is that the starting point for Planck expansion, has initial 1 a = with an enormous value for a in the present era as opposed to another scaling convention that have the red shift with values at the onset of inflation of the order of 25 initial ~10 z at the start of inflation, and CMBR ~1100 1000 z − at the moment of CMBR photon radiation "turn on" with Today 0 z = in the present era.Examining what happens if one substitutes in for Planck l the following holds, i.e.
of magnitude minimum grid size hold, then conceivably when T ~ 1019 GeV m ≈ electron volts, as opposed to a relic graviton mass-energy relationship[10]: the relic graviton mass-energy relationship is: one is looking at the mass of a graviton a billion years ago, with .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 obtain WIMP level energy-mass values, congruent with Y. Jack Ng's S counting algorithm[10] [11].What the author is suggesting, as he brought up in DICE 2010 is that the extra degrees of freedom may be necessary for obtaining clumps of 10 38 gravitons to form coherent clumps to obtain GW of sufficient semi classical initial conditions, to obtain conditions, initially to have the S N counting algorithm work.
.21) This would be to come up with a realistic way to talk about clumps of gravitons which may have coherent oscillatory behavior and to use this to make sense of the structure of up to 10 38 coherent gravitons to form coherent clumps to obtain GW of sufficient semi classical initial conditions, to obtain conditions, initially to have the S N counting algorithm work for gravitons as coherent clumps, allegedly in a structure defined by Equation (1.21).Then, after employing Equation (1.21) to next examine the limits of, and interexchange of effects given in Equation (1.14) and Equation (1.15) to determine from there to what degree is Equation (1.16) is giving us joint linkage of E&M

Consequences If There Are up to 1000 Degrees of Freedom, i.e. What If There Are Regimes of Space Time When Bits of Information Count Is Very Different from Particle Count for Entropy?
[10], if the additional degrees of freedom are warranted, comes the question of what are measurable protocols which may confirm/falsify this supposition.The following discussion will in part recap and extend a discussion which the author, Beckwith has presented in DICE 2010, in Italy[10].
[11]Note that Y. Jack Ng[10][11]has Matter, with a much higher mass than what is observed with any accounting for Journal of High Energy Physics, Gravitation and Cosmology ticles as of up to 100 GeV.4.