We now outline the generalization for Penrose CCC(Cosmology) before inflation which we state we are extending Penrose’s suggestion of cyclic universes, black hole evaporation, and the embedding structure our universe is contained within, This multiverse has BHs and may resolve what appears to be an impossible dichotomy. The following is largely from [13] and has serious relevance to the final part of the conclusion. That there are N universes undergoing Penrose ‘infinite expansion’ (Penrose) [18] contained in a mega universe structure. Furthermore, each of the N universes has black hole evaporation, which is with Hawking radiation from decaying black holes. If each of the N universes is defined by a partition function, called { Ξ i } i ≡ 1 i ≡ N , then there exists an information ensemble of mixed minimum information correlated about 10⁷ - 10⁸ bits of information per partition function in the set { Ξ i } i ≡ 1 i ≡ N | before , so minimum information is conserved between a set of partition functions per universe [13]

However, there is non-uniqueness of information put into individual partition function { Ξ i } i ≡ 1 i ≡ N . Also Hawking radiation from black holes is collated via a strange attractor collection in the mega universe structure to form a new inflationary regime for each of the N universes represented.

We use what is known as CCC cosmology [13][18], which can be thought of as the following. First. Have a big bang (initial expansion) for the universe which is represented by { Ξ i } i ≡ 1 i ≡ N . Verification of this mega structure compression and expansion of information with stated non-uniqueness of information placed in each of the N universes favors ergodic mixing of initial values for each of N universes expanding from a singularity beginning. The n f stated value, will be using (Ng, 2008) S entropy ~ n f [20]. How to tie in this energy expression, as in Equation (12) will be to look at the formation of a nontrivial gravitational measure as a new big bang for each of the N universes as by n ( E i ) the density of states at energy E i for partition function [13][14].

Each of E identified with Equation (3) above, are with the iteration for N universes [13], and [18] (Penrose, 2006) Then the following holds, by asserting the following claim to the universe, as a mixed state, with black holes playing a major part, i.e.

Claim1

See the below [13] representation of mixing for assorted N partition functions per CCC cycle

For N number of universes, with each Ξ j | j   before nucleation regime for j = 1 to N being the partition function of each universe just before the blend into the RHS of Equation (4) above for our present universe. Also, each independent universe as given by Ξ j | j   before nucleation regime is constructed by the absorption of one to ten million black holes taking inenergy,i.e.(Penrose).

Furthermore, the main point is done in [13] in terms of general ergodic mixing [21]-[23].

Claim2

What is done inClaims1and2 [13] is to come up as to how a multi dimensional representation of black hole physics enables continual mixing of spacetime [13][18][22][24] largely as a way to avoid the Anthropic principle [13][25], as to a preferred set of initial conditions

We argue this modification is mandated byhaving the initial DE wavefunction set as

After having set this in place we will be comparing this method to the Klauder argument.

We use the Padmanabhan 1^st integral [26] of the form, with the third entry of Equation (1) having a Ricci scalar defined via [27][28]and usually the curvature ℵ [13] set as extremely small, with the general relativity [13][28] action of

We are going to go to page 78 by Klauder [8][13] of what he calls on page 78 a restricted Quantum action principle which he writes as: where we write a 1-1 equivalence as in [8][13], which is

Our assumption is that Λ is a constant [13], hence we assume then use the approximation, from [8], and [13]

Our innovation is to then equate q = q 0 ± p 0 t ~ ϕ and to assume small time step values. Then [13]

If we assume that Equation (10) was formed within a cosmic bubble of space-time [12]

Here, we have that ρ is a space-time density function, whereas σ is the tension of a space-time bubble presumably of the order of a Planck radius. Also, within the bubble of space-time a ¨ a ≈ ε + ≃ 0 and a ( t ) = a min t γ at the surface of the space-time bubble. Hence

c 1 is to be determined, whereas the inflaton [13][26].

And what we will use the “inflaton potential” we write as [13][26]

Also

Λ ≈ − [ V 0 3 γ − 1 + 2 N ˜ + γ ( 3 γ − 1 ) 8 π G t P l a n c k ] 1 κ ∫ − g d 3 x + c 1 16 π M P 2 ⋅ ( ρ − ρ 2 2 | σ | ) ⇔ ρ D E = Λ 8 π G ⇔ Λ ≈ ℏ ⋅ 8 π G ⋅ ( 2 π ) 4 λ D E 4 | λ D E ≈ 10 30 ℓ P l a n c k ≡ 8 π ⋅ ( 2 π ) 4 λ D E 4 | λ D E ≈ 10 30 (31)

To compare these twovalueswe can state that within the bubble,that just before the bubble boundary,we have N ˜ = 0 ,hence we look at,initially

Λ ≈ − [ V 0 3 γ − 1 + γ ( 3 γ − 1 ) 8 π G t Planck ] 1 κ ∫ − g d 3 x + c 1 16 π M P 2 ⋅ ( ρ − ρ 2 2 | σ | ) ⇔ Λ ≈ ℏ ⋅ 8 π G ⋅ ( 2 π ) 4 λ D E 4 | λ D E ≈ 10 30 ℓ Planck ≡ 8 π ⋅ ( 2 π ) 4 λ D E 4 | λ D E ≈ 10 30 (32)

i.e. we pick c 1 so that the two are equivalent in value.

Note this is just before a very large value set to N ˜ at the boundary of the initial space-time bubble. Hence,we also would be looking at

Λ ≈ γ ⋅ t 2 + 8 π V 0 ⋅ { 8 π V 0 γ ( 3 γ − 1 ) ⋅ t } γ 4 π − 8 π γ | t ≈ t Planck = 1 ≈ − [ V 0 3 γ − 1 + γ ( 3 γ − 1 ) 8 π ] 1 κ ∫ − g d 3 x + c 1 16 π M P 2 ⋅ ( ρ − ρ 2 2 | σ | ) ≈ ℏ ⋅ 8 π G ⋅ ( 2 π ) 4 λ D E 4 | λ D E ≈ 10 30 ℓ Planck = 8 π ⋅ ( 2 π ) 4 λ D E 4 | λ D E ≈ 10 30 (33)

InEquation(31)we will also make the following identification

ρ ≈ ρ D E ≈ ℏ ⋅ ( 2 π ) 4 λ D E 4 | λ D E ≈ 10 30 .

I.e. just before the bubble,we will factor in a very large bubble tension, σ .

Doing so would be to have an optimal c 1 value,and that this choice of c 1 would allow us to make the identification of the choice of wavefunction for our model which would according to theEquation(28)model have a quantum flavor,while at the same time in adherence be similar to theEquation(31)values of Dark Energy density.

First of all,as noted by Kieffer,the wavefunction inEquation(28)vanishes if r=0.We avoid having a vanishing wavefunction by asserting that we will be making an evaluation of it in the neighborhood of a Planck Length. Secondly in making this assumption we are at least proceeding in a direction where we can ditch the Anthropic principle,which I consider a MAJOR blight on cosmology. I also too though this this procedure as outline is experimentally verifiable,once we understand what may constitute embedding of Quantum Mechanics within a deterministic structure. The entire referral of this problem can be contrasted with the solution given in[19]by Rosen,which is in the mode of Quantum mechanics for a single particle in an isotropicuniverse.

The primary difference between the Rosen approach, [19]and what is done in this document is that the mass of a graviton,is proportional to the square of the Cosmological constant,an assumption which Rosen does not make. In addition the Rosen document assumes that “The situation is somewhat analogous to the quantum mechanics of a single particle as compared to quantum field theory” and assumes an isotropic background.

We do not confine ourselves to Isotropic backgrounds. We also do sharewith Rosen {19] a procedure as torendition a linkage between classical to quantum mechanical treatment of our problem,but our work is more in tune with using what Powell and Craseman in their book on quantum mechanics used,which is similar to a limiting case of geometric optics.

I wish to thank Christian Corda as to alerting me to the Rosen article which is also applicable to a Dust Cosmology. I also wish to thank Fangyu Li,Wen Hao,and others for alerting me as to the crucial role of polarization. As it is,I presented part of this idea in Zeldovich4,in the ICRANET on line conferences(a small part of it)and found that the audience and the reviewers didnot understand the Klauder treatment of the cosmological constant via Klauder Enhanced quantization.

Hence this expanded treatment whereas the Rosen treatment as Corda outlined is most effective for quantum black holes.

( 1 + z initial era ) ≡ a today a initial era ≈ ( ω Earth orbit ω initial era ) − 1 ⇒ ( 1 + z initial era ) ω Earth orbit ≈ 10 25 ω Earth orbit ≈ ω initial era (34)

Equation (34) can be seen in [35] as well as [36].

Whereas we postulate that we specify an initial era frequency via use of simple dimensional analysis which is slightly modified by Maggiore for the speed of a graviton [35] whereas

and that dimensional comparison with initially having a temperature built up so as

where T universe ≈ T Plank temerature = 1.22 × 10 19   GeV . If so then the Planck era we would have temperature would be extremely high leading to a change in temperature from the Pre Planckian conditions to Planck era leading to

In doing so, be assuming

Where we would be assuming ω initial era ≈ c ℓ planck ≤ 1.8549 × 10 43   Hz so then we would be looking at frequencies on Earth from gravitons of mass m(graviton) less than of equal to

And this partly due to the transference of cosmological ‘information’ as given in [13] for a phantom bounce type of construction .Further point that since we have that gravitons travel at nearly the speed of light [36], that gravitons are formed from the surface of a bubble of space-time up to the electroweak era that mass values of the order of 10^-65 grams (rest mass of relic gravitons) would increase due to extremely high velocity would lead to enormous Δ E ≈ ℏ ω initial era values per graviton, which would make the conflation of ultrahigh temperatures with gravitons traveling at nearly the speed of light as given in Equation(39) as compared with Δ E ≈ ℏ ω initial era . We can in future work compare this with the Rosen [19] value of energy for a mini universe of (from a Schrodinger equation) with ground state mass of m = π M Planck and an energy of

E n ^ = − G m 5 2 π 2 ℏ 2 n ^ 2 (40)

Our preliminary supposition is thatEquation(40)could represent the initial energy of a Pre Planckian Universe and thatEquation(37)be the thermal energy dumped in due to the use of Cyclic Conformal cosmology(maybe in multiverse form)so that if there is a buildup of energy greater thanEquation(40)due to thermal buildup of temperature due to in fall of matter-energy,we have a release of Gravitons in great number which would commence as a domain wall broke down about in the Planckian era with a temperature of the magnitude of Planck Energy for a volume of radius of the order of Plank Length. This will be investigated in detailed future calculations. All this should be in fidelity,in experimental limits to[37],as well as looking at ideas about Quantum tunneling we may gain from[38]as to understand the transition from Pre Planckian to Planckian physics[39][40].