ALFRED BENNUN, PH.D.

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ABSTRACTS

Astrophysics September 12, 2007

Changes in Space-time configuration of
CMB for a role in Vacuum fluctuations

_______________________________________________________________

Dr. Alfredo Bennun

Full Professor de Bioquímica (R)

Full Member Graduate Programs in the Molecular Biosciences

Rutgers, The State University of New Jersey

Abstract

Analysis, that introduces from relativity theory, originals relationships between radiation energy and its space coordinate. The latter, even for spontaneous process, shows changes of such magnitude, which could be correlated with the duality configuration photon-wavelength. Parametric Up Conversion, in which two photons generate one of half wavelength, may allow Cosmic Microwave Background (CMB) photons to shrink within their locus space-time configuration (Cassimir Effect). CMB Parametric Up and Down Conversions, could allow in vacuum, CMB wavelength fluctuations. These, could be difficult to detect because may occur within the range of its black body spectra (between 5 ´ 10^{-1 cm. to 2} ´ 10^{-1 cm.). The relic CMB photons, by number (411 cm3}), and by their very low energy (2.71 Kelvin), means a large space-time dimension may be, therefore, not only dimensioning the vacuum, but also generating its fluctuations.

Results

A simulation, by applying a wave function treatment to Planck energy limit, E_Pl, resulted in a Big-Bang description, in which, the evolution of the space-time, surges naturally as analogous to a continuum of decreasing frequency (n) (Fig. 1). The De Broglie duality concept, could be further enriched by parameters obtained from relativistic theory. These, like time of localization (t-loc), describe the duality in terms of space-time dimensional differences, suggesting two configurations of same energy. From this treatment, could be shown as demonstrated below, that electromagnetic radiation, yields different values for the localization of its energy, when dimensioning into a wavelength (l ) or photon (g).

Thus, applying to the Plank Energy Limit (E_Pl) = 1.22´10²² MeV

Equation 1: l / t-l-loc = velocity of light in vacuum (c) = 2.997´10¹⁰ cm/sec \

l / c = t-l-loc = 3.389´10^-43sec that also results from: 1 / n (n = frequency).

Equation 2: for a particle (t-p-loc) or g: 2r / t-g-loc = c and 2r / c =5.39121´10^-44 sec

Same value results from: (hG / 2pc⁵)^1/2 (G = gravitational constant).

For E_Pl: l / g = 3.389 ´10^-43sec / 5.39´10^-44 sec = 2p \ t-l-loc / 2p = t-g-loc

Replacing in equation 2: 2r / t-l-loc / 2p = c

Equation 3: the terms in equations 1 and 2 = c \ l / t-l-loc = 2r / t-l-loc / 2p

Under figure 1, is shown that a different value, Compton (l_c), defined by observation of the interaction between electron and photons, could be applied. The preceding, indicates that, t-l-loc and volume of localization (vol-l-loc), could be use to determine space-time changes in configuration for photons ⁽¹⁾.

Hence, allowing that the latter measurements, originated from relativistic theory, could be applied as a complementary description to the one originated from quantum mechanics. Thus, changes in the space-time configuration of photons, were applied into a relativistic continuum, surging from the description of energy evolution from E_Pl into relic Cosmic Microwave Background Radiation (CMB) (Fig 1). Relativity theory, predicts that, vacuum exists as and because is a locus of energy. Absence of matter in vacuum, does not mean absence of energy, because of the presence of CMB. Vacuum manifestations, should therefore, include the dynamics of CMB.

The inter-conversion of energy configuration of CMB, either by the duality or by Spontaneous Parametric Down Conversion (PDC) ^{(2, 3)}, could be expected to produce changes in t-l-loc and vol-l-loc. Therefore, CMB should be evaluated for a role in space-time modifications, which may include or not the presence of virtual or dark energy ⁽⁴⁾. Hence, experiments in CMB-free vacuum, may be required to exclude the possibility of CMB interference in the measuring of black or virtual energy. CMB capability to react in the direction of Parametric Up Conversion (PUpC), was estimated by the Casimir effect. The integration of two relic CMB photons into one with twice the energy, reduces initial volume by a large factor. As shown for a lc-volume (V_λc-loc = 2 ´ 10^-3 cm³ ´ 2 = 4 ´ 10^-3 cm³), would lead to attraction between the plates.

A system to evaluate phenomena in presence and absence of CMB, is suggested by the experimental conditions used to evaluate the Casimir effect.

The technique would consist in that, by joining two plates transparent to CMB, it would expected to have the effect of excluding CMB from within the plates. After, by attaching opaque plates to the transparent one, may prevent the reentering of CMB into the space delimited by the plates. This methodology, could be expected to obtain a CMB-free vacuum.

The control, would be that, by separating these plates, now it could be restarted the experiment in the absence of CMB and, therefore, measure if there is a remnant of energy capable to sustain again a Casimir effect of attraction between plates. Only if such is the case, could be assumed that the Casimir Effect is not due to CMB, but to either virtual or dark energy ⁽⁴⁾. Also, similar methodology, could be used to measure the velocity of propagation of light within a CMB-free vacuum.

The velocity of light changes when propagating through solvents and upon salt additions, and could be progressively decreased, up to reach its confinement ^{(6, 7, 8)}. According to equation 1, a decrease in the velocity of light, has to implicate a concomitant decrease of l, and / or an increase in t-l-loc. Since, a decrease in l, should be excluded, because it implicates energy increments, the dominant effect should be large increases in t-l-loc. Hence, the thermodynamic structure within the confinement locus, results in that the space-time and the energy parameters of the photons, becomes uncoupled allowing the delocalization of the energy from its locus, as photon into the confinement media.

The very low value, for the mean energy of the black body distribution of CMB photons, in the vacuum = 2,35 ´10 ^-4 eV , leads to predict minimum effects on atoms, but of the same order than that obtained, when measuring the vacuum effects on atoms ⁽⁹⁾. If found, that the dominant effect could be attributed to CMB. This raises the possibility that PDC and PUpC, by changing ng and the dimensional values of CMB, could be a source for vacuum fluctuations ⁽⁵⁾.

Discussion

Standard values, for the relic CMB photon number (ng) = 3.79 × 10⁸⁷, multiplied by their Vl_c-loc = 2.47 × 10^-03 cm³ = 9.3 × 10⁸⁴ cm³ or present universe volume. Accordingly, CMB photons, even representing only 0.04% of total cosmic energy, by their increasing volume and number, appear to be tightly filing and dimensioning the vacuum within the space-time. Hence, mass-less CMB by g-number increment and its l-elongation, as well as propagating as a radiation, not subject to gravity, would have antigravity effects similarly to that of dark energy. Thus, it could be proposed that CMB, could also be considered as leading or participating in the vacuum expansionary process, continually increasing the distance between galaxies.

Dark energy presently holds more than two thirds of total cosmic energy, and has been predicted as filling the space. However, in terms of the dimensioning of the cosmic vacuum, either by volume or by its quanta number, the presently detected 411 CMB photons per cm³, could have the dominant effect. It has been reported up to 160 times of spontaneous inter-conversions ^{(2, 3)}, between up and down parametric conversions.

If PDC reaches equilibrium of inter-conversion with PUpC, this may not affect significantly the black body energy distribution of CMB, but these wavelength fluctuations, may be detected as strong fluctuations in the vacuum structure of the space.

The down conversion increases number and volume of CMB photons ^{(2, 3)}, stretching space whereas the up-conversion would be contracting space. These space fluctuations, could be therefore detected without significant energy exchanges.

Fig. 1: Simulation of the unfolding of a self-contained universe by PDC.

Values used are approximations. Simulation table, annexed below.

Total cosmic energy = 1.7 × 10⁸² MeV divided by E_Pl = initial number of photon (ng_in) = 1.4 × 10⁶⁰.

Hence, E_Pl space-time coordinates (or initial) by Equation 1: l / t-l-loc or 1× 10^-32cm / 3.39 ´ 10^-43sec, by applying PDC ((ng_in ´ 2) × (2l_in)) ^n-1 allows, that a photon generates two of half energy, and also doubles their l and t-l-loc values, in order that a constant ratio equals c. An iterative treatment by PDC 106 times (stages), allows reaching the coordinates space-times values of relic CMB: 5.27 × 10^-01cm / 1.76 × 10^-11sec. A black body spectra of relic CMB, would be in a range from the latter values to les than 2´10^-01cm, this would may difficult to detect wavelength fluctuations. After separation of forces at t-l-loc= 1.456 ´ 10^-33sec., inflation ends at about 2.84 ´ 10¹² MeV. Photon transfer to the generation of dark energy, ordinary mater and dark energy, maintain constant ng from stages 56 to 70, increasing thereafter to present ng of CMB = 3.7 × 10⁸⁷. The Compton radius (r_c) of interaction of a photon with an electron (l_c) = l / 2p. Hence, l_c for l value of E_Pl = 1.016 ´ 10^-32 and divided by 2p = 1.616 ´ 10^-33cm or Planck length. The Compton volume, for l_c localization (Vl_{c loc}) = (4/3) p (l_c) ³ for E_Pl = 1.772 ´ 10^-98 cm³ which, multiply by ng_in 1.4 × 10⁶⁰ = 2.48 × 10^-38 cm³ or Big-Bang initial volume. Another simulation was based in that, the initial volume, corresponded to a single Planck locus. Hence, from an hypothetic hyper-space, the flow of energy, was delimited by each photon division, allowing a sixteen times increment of the space-time which sequential inflow of sixteen Planck photons, to reach a photon number ng_in 1.4 × 10⁶⁰ before have elapsed 1/1000 of the inflationary Era.

References

1. Bennun, A Model Dimensioning the Space-Time by Parametric Down Conversion, General Science Journal

2. Marshall et al., Journal of Modern Optics, Vol. 47, 1273 (2000)

3. Brida, G., Genovese, M., Novero, C., “Experimental limit on spontaneous parametric up conversion”,

Journal of Modern Optics, Vol. 50, N° 11, pp. 1757-1762 (6) (2003)

4. Djorgovski, S. and Gurzadyan, V., “Dark Energy from Vacuum Fluctuations”, in Cline, D. et al, Nuclear Physics B, (2006)

5. Padmanabhan, T., “Vacuum Fluctuations of Energy Density can Lead to the Observed Cosmological Constant”, arXiv:hep-th/0406060 v1, 7 Jun (2004)

6. Kramper, P., Kafesaki, M., Soukoulis, C., Birner, A., Müller, F., Gösele, U., Wehrspohn, R., Mylnek, J., Sandoghdar, V., “Near-field visualization of light confinement in a photonic crystal micro-resonator”, Optics Letters, Vol. 29, N° 2, pp. 174-176 (2004)

7. Cao, H., Xu, J., Zhang, D., Chang, S., Ho, S., Seelig, E., Liu, X., Chang, R., “Spatial Confinement of a Laser Light in Active Random Media”, Physical Review Letters, Vol. 84, N° 24, pp. 5584-5587 (2000)

8. Fedotov, A., Bugar, I., Naumov, A., Chorvat, D., Sidorov-Biryukov, D., Chorvat, D. and Zheltikov, A., “Light confinement and supercontinuum generation switching in photonic-molecule modes of a microstructure fiber”, JETP Letters, Vol 75, N° 7, pp. 304-308 (2002)

9. Barrow, John D. and Silk, Joseph, “The Left Hand of Creation”, London: J.M. Dent and Sons (1993)

Manuscript submitted to Nature Photonics Journal on March, 7^th 2007, unpublished.

Supporting Simulation Table by Alfred Bennun

The theoretical restriction of how small could be a particle, is delimited by the Planck length. However, this restriction not applies to a wavelength and, therefore, the model allows using simulations based in different values.

# of	Cosmic evolution	Energy of	Photon number	Time of γ	Compton
stage	Planck particle as a wave function	l or g	ET/Eg=nginitial	localization	Wavelength
(N)	tλ-loc/2π=tλc=tγ-loc	wavelength	ET=1.7E+82 MeV	tγ-loc	λc
	Particle: (-DE).(Dtγ-loc)=h/2π	Eλ=Eg	Eg=1.22E+22MeV		λc=λ/2π
[ ]	Wave: (-DE).(Dtl-loc)=h	Eg= initial*(1/2)^N	nγ= nγinitial´(2)^n	[s]	[cm]
	Expansion: -D(E)/2.D(tγ-loc),2=h/2π	[MeV]	[photons]	Factor:2	Factor:2
0	Planck Time: (tp) = 5,394E-44s	1.220E+22	1.400E+60	5.394E-44	1.617E-33
1	Planck Wave: tλ-loc=3.389E-43s	6.100E+21	2.800E+60	1.079E-43	3.233E-33
2		3.050E+21	5.600E+60	2.158E-43	6.467E-33
3		1.525E+21	1.120E+61	4.315E-43	1.293E-32
4		7.625E+20	2.240E+61	8.631E-43	2.587E-32
5		3.813E+20	4.480E+61	1.726E-42	5.173E-32
6		1.906E+20	8.960E+61	3.452E-42	1.035E-31
7	Electro-Strong-Weak force	9.531E+19	1.792E+62	6.905E-42	2.069E-31
8		4.766E+19	3.584E+62	1.381E-41	4.139E-31
9		2.383E+19	7.168E+62	2.762E-41	8.277E-31
10		1.191E+19	1.434E+63	5.524E-41	1.655E-30
11		5.957E+18	2.867E+63	1.105E-40	3.311E-30
12		2.979E+18	5.734E+63	2.210E-40	6.622E-30
13		1.489E+18	1.147E+64	4.419E-40	1.324E-29
14		7.446E+17	2.294E+64	8.838E-40	2.649E-29
15		3.723E+17	4.588E+64	1.768E-39	5.298E-29
16		1.862E+17	9.175E+64	3.535E-39	1.060E-28
17		9.308E+16	1.835E+65	7.070E-39	2.119E-28
18		4.654E+16	3.670E+65	1.414E-38	4.238E-28
19	Strong force dissociate	2.327E+16	7.340E+65	2.828E-38	8.476E-28
20		1.163E+16	1.468E+66	5.656E-38	1.695E-27
21		5.817E+15	2.936E+66	1.131E-37	3.390E-27
22		2.909E+15	5.872E+66	2.263E-37	6.781E-27
23		1.454E+15	1.174E+67	4.525E-37	1.356E-26
24		7.272E+14	2.349E+67	9.050E-37	2.712E-26
25		3.636E+14	4.698E+67	1.810E-36	5.425E-26
26		1.818E+14	9.395E+67	3.620E-36	1.085E-25
27		9.090E+13	1.879E+68	7.240E-36	2.170E-25
28		4.545E+13	3.758E+68	1.448E-35	4.340E-25
29		2.272E+13	7.516E+68	2.896E-35	8.679E-25
30		1.136E+13	1.503E+69	5.792E-35	1.736E-24
31		5.681E+12	3.006E+69	1.158E-34	3.472E-24
32		2.841E+12	6.013E+69	2.317E-34	6.944E-24
33	Weak force dissociate	1.420E+12	1.203E+70	4.634E-34	1.389E-23
34		7.101E+11	2.405E+70	5.823E-33	2.777E-23
35		3.551E+11	4.810E+70	1.165E-32	5.555E-23
36		1.775E+11	9.621E+70	2.329E-32	1.111E-22
37		8.877E+10	1.924E+71	4.658E-32	2.222E-22
38		4.438E+10	3.848E+71	9.317E-32	4.444E-22
39		2.219E+10	7.697E+71	1.863E-31	8.888E-22
40		1.110E+10	1.539E+72	3.727E-31	1.778E-21
41		5.548E+09	3.079E+72	7.453E-31	3.555E-21
42		2.774E+09	6.157E+72	1.491E-30	7.110E-21
43		1.387E+09	1.231E+73	2.981E-30	1.422E-20
44		6.935E+08	2.463E+73	5.963E-30	2.844E-20
45		3.467E+08	4.926E+73	1.193E-29	5.688E-20
46		1.734E+08	9.852E+73	2.385E-29	1.138E-19
47		8.669E+07	1.970E+74	4.770E-29	2.275E-19
48		4.334E+07	3.941E+74	9.540E-29	4.551E-19
49		2.167E+07	7.881E+74	1.908E-28	9.101E-19
50		1.084E+07	1.576E+75	3.816E-28	1.820E-18
51		5.418E+06	3.153E+75	7.632E-28	3.640E-18
52		2.709E+06	6.305E+75	1.526E-27	7.281E-18
53		1.354E+06	1.261E+76	3.053E-27	1.456E-17
# of	Cosmic evolution	Energy of	Photon number	Time of λγ	Compton
stage	Planck particle as a wave function	wavelength	ET/Eg=nginitial	localization	Wavelength
(N)	tλ-loc/2π=tλc=tγ-loc	(Eλ)	nγ	tγ-loc	λc
	Particle: (-DE).(Dtγ-loc)=h/2π	Eλ= initial*(1/2)^N	nγ= nγinitial´(2)^n	t=λγ/c	λc=λ/2π
[ ]	Wave: (-DE).(Dtl-loc)=h	[MeV]	[photons]	[s]	[cm]
	Expansion: -D(E)/2.D(tγ-loc),2=h/2π
54		6.772E+05	2.522E+76	6.106E-27	2.912E-17
55		3.386E+05	5.044E+76	1.221E-26	5.825E-17
56	Higgs boson	1.693E+05	?	2.442E-26	1.165E-16
57		8.465E+04	?	4.885E-26	2.330E-16
58		4.233E+04	?	9.769E-26	4.660E-16
59		2.116E+04	?	1.954E-25	9.319E-16
60		1.058E+04	?	3.908E-25	1.864E-15
61	Quarks: Charm	5.291E+03	?	7.815E-25	3.728E-15
62	Botton	2.645E+03	?	1.563E-24	7.456E-15
63	Proton	1.323E+03	?	3.126E-24	1.491E-14
64		6.614E+02	?	6.252E-24	2.982E-14
65		3.307E+02	?	1.250E-23	5.964E-14
66	Up, Down, Strage	1.653E+02	?	2.501E-23	1.193E-13
67	Pion	8.267E+01	?	5.002E-23	2.386E-13
68	(Strongly	4.134E+01	?	1.000E-22	4.772E-13
69	interactive particles)	2.067E+01	?	2.001E-22	9.543E-13
70		1.033E+01	?	4.001E-22	1.909E-12
71		5.167E+00	1.009E+77	8.003E-22	3.817E-12
72		2.583E+00	2.018E+77	1.601E-21	7.635E-12
73		1.292E+00	4.035E+77	3.201E-21	1.527E-11
74	Electron	6.459E-01	8.070E+77	6.402E-21	3.054E-11
75		3.229E-01	1.614E+78	1.280E-20	6.108E-11
76		1.615E-01	3.228E+78	2.561E-20	1.222E-10
77		8.073E-02	6.456E+78	5.122E-20	2.443E-10
78		4.037E-02	1.291E+79	1.024E-19	4.886E-10
79		2.018E-02	2.583E+79	2.049E-19	9.772E-10
80		1.009E-02	5.165E+79	4.097E-19	1.954E-09
81		5.046E-03	1.033E+80	8.195E-19	3.909E-09
82		2.523E-03	2.066E+80	1.639E-18	7.818E-09
83		1.261E-03	4.132E+80	3.278E-18	1.564E-08
84		6.307E-04	8.264E+80	6.556E-18	3.127E-08
85		3.154E-04	1.653E+81	1.311E-17	6.254E-08
86		1.577E-04	3.306E+81	2.622E-17	1.251E-07
87		7.884E-05	6.611E+81	5.245E-17	2.502E-07
88		3.942E-05	1.322E+82	1.049E-16	5.003E-07
89		1.971E-05	2.645E+82	2.098E-16	1.001E-06
90		9.855E-06	5.289E+82	4.196E-16	2.001E-06
91		4.928E-06	1.058E+83	8.392E-16	4.003E-06
92		2.464E-06	2.116E+83	1.678E-15	8.005E-06
93	Nuclei formation	1.232E-06	4.231E+83	3.357E-15	1.601E-05
94		6.159E-07	8.462E+83	6.713E-15	3.202E-05
95	Formation of Atoms	3.080E-07	1.692E+84	1.343E-14	6.404E-05
	Frontier of last dispersion	2.585E-07	3.440E+84	1.599E-14	7.629E-05
96		2.409E-07	3.691E+84	1.716E-14	8.187E-05
97		1.204E-07	7.383E+84	3.433E-14	1.637E-04
98		6.022E-08	1.477E+85	6.866E-14	3.275E-04
99		3.011E-08	2.953E+85	1.373E-13	6.550E-04
100		1.506E-08	5.906E+85	2.746E-13	1.310E-03
101		7.528E-09	1.181E+86	5.493E-13	2.620E-03
102		3.764E-09	2.363E+86	1.099E-12	5.240E-03
103		1.882E-09	4.725E+86	2.197E-12	1.048E-02
104		9.410E-10	9.450E+86	4.394E-12	2.096E-02
105		4.705E-10	1.890E+87	8.788E-12	4.192E-02
106	Present Era	2.353E-10	3.780E+87	1.758E-11	8.384E-02

# of	Volume of λc	Universe	Universe	Universe time	Space-time	Total Energy
stage	localization	Volume	radius		Ratio
(N)	Vλc	VU	rU	tU		(Et)
	Vλc=4/3´π´λc^3	VU=Vλc´nγ	rU=(VU´3/4π)^1/3	tU=rU/c	rU/tU=c
[ ]	[cm^3]	[cm^3]	[cm]	tU [s]	[cm/s]	[MeV]
	Factor: 8	Factor:16	Factor:2.52	Factor:2.5
0	1.770E-98	2.478E-38	1.809E-13	6.033E-24	3.00E+10	1.708E+82
1	1.416E-97	3.965E-37	4.557E-13	1.520E-23	3.00E+10	1.708E+82
2	1.133E-96	6.343E-36	1.148E-12	3.831E-23	3.00E+10	1.708E+82
3	9.062E-96	1.015E-34	2.894E-12	9.652E-23	3.00E+10	1.708E+82
4	7.250E-95	1.624E-33	7.292E-12	2.432E-22	3.00E+10	1.708E+82
5	5.800E-94	2.598E-32	1.837E-11	6.129E-22	3.00E+10	1.708E+82
6	4.640E-93	4.157E-31	4.630E-11	1.544E-21	3.00E+10	1.708E+82
7	3.712E-92	6.652E-30	1.167E-10	3.892E-21	3.00E+10	1.708E+82
8	2.969E-91	1.064E-28	2.940E-10	9.806E-21	3.00E+10	1.708E+82
9	2.376E-90	1.703E-27	7.408E-10	2.471E-20	3.00E+10	1.708E+82
10	1.900E-89	2.724E-26	1.867E-09	6.227E-20	3.00E+10	1.708E+82
11	1.520E-88	4.359E-25	4.704E-09	1.569E-19	3.00E+10	1.708E+82
12	1.216E-87	6.975E-24	1.185E-08	3.954E-19	3.00E+10	1.708E+82
13	9.730E-87	1.116E-22	2.987E-08	9.962E-19	3.00E+10	1.708E+82
14	7.784E-86	1.786E-21	7.526E-08	2.510E-18	3.00E+10	1.708E+82
15	6.227E-85	2.857E-20	1.896E-07	6.326E-18	3.00E+10	1.708E+82
16	4.982E-84	4.571E-19	4.779E-07	1.594E-17	3.00E+10	1.708E+82
17	3.986E-83	7.313E-18	1.204E-06	4.017E-17	3.00E+10	1.708E+82
18	3.188E-82	1.170E-16	3.034E-06	1.012E-16	3.00E+10	1.708E+82
19	2.551E-81	1.872E-15	7.646E-06	2.550E-16	3.00E+10	1.708E+82
20	2.041E-80	2.996E-14	1.927E-05	6.427E-16	3.00E+10	1.708E+82
21	1.632E-79	4.793E-13	4.855E-05	1.619E-15	3.00E+10	1.708E+82
22	1.306E-78	7.669E-12	1.223E-04	4.081E-15	3.00E+10	1.708E+82
23	1.045E-77	1.227E-10	3.083E-04	1.028E-14	3.00E+10	1.708E+82
24	8.358E-77	1.963E-09	7.768E-04	2.591E-14	3.00E+10	1.708E+82
25	6.687E-76	3.141E-08	1.957E-03	6.529E-14	3.00E+10	1.708E+82
26	5.349E-75	5.026E-07	4.932E-03	1.645E-13	3.00E+10	1.708E+82
27	4.279E-74	8.041E-06	1.243E-02	4.146E-13	3.00E+10	1.708E+82
28	3.424E-73	1.287E-04	3.132E-02	1.045E-12	3.00E+10	1.708E+82
29	2.739E-72	2.059E-03	7.891E-02	2.632E-12	3.00E+10	1.708E+82
30	2.191E-71	3.294E-02	1.989E-01	6.633E-12	3.00E+10	1.708E+82
31	1.753E-70	5.270E-01	5.011E-01	1.671E-11	3.00E+10	1.708E+82
32	1.402E-69	8.432E+00	1.263E+00	4.212E-11	3.00E+10	1.708E+82
33	1.122E-68	1.349E+02	3.182E+00	1.061E-10	3.00E+10	1.708E+82
34	8.975E-68	2.159E+03	8.017E+00	2.674E-10	3.00E+10	1.708E+82
35	7.180E-67	3.454E+04	2.020E+01	6.739E-10	3.00E+10	1.708E+82
36	5.744E-66	5.526E+05	5.091E+01	1.698E-09	3.00E+10	1.708E+82
37	4.595E-65	8.841E+06	1.283E+02	4.279E-09	3.00E+10	1.708E+82
38	3.676E-64	1.415E+08	3.232E+02	1.078E-08	3.00E+10	1.708E+82
39	2.941E-63	2.263E+09	8.145E+02	2.717E-08	3.00E+10	1.708E+82
40	2.353E-62	3.621E+10	2.052E+03	6.846E-08	3.00E+10	1.708E+82
41	1.882E-61	5.794E+11	5.172E+03	1.725E-07	3.00E+10	1.708E+82
42	1.506E-60	9.271E+12	1.303E+04	4.347E-07	3.00E+10	1.708E+82
43	1.205E-59	1.483E+14	3.284E+04	1.095E-06	3.00E+10	1.708E+82
44	9.636E-59	2.373E+15	8.275E+04	2.760E-06	3.00E+10	1.708E+82
45	7.709E-58	3.797E+16	2.085E+05	6.955E-06	3.00E+10	1.708E+82
46	6.167E-57	6.076E+17	5.254E+05	1.753E-05	3.00E+10	1.708E+82
47	4.934E-56	9.721E+18	1.324E+06	4.416E-05	3.00E+10	1.708E+82
48	3.947E-55	1.555E+20	3.336E+06	1.113E-04	3.00E+10	1.708E+82
49	3.158E-54	2.489E+21	8.407E+06	2.804E-04	3.00E+10	1.708E+82
50	2.526E-53	3.982E+22	2.118E+07	7.066E-04	3.00E+10	1.708E+82
51	2.021E-52	6.371E+23	5.338E+07	1.781E-03	3.00E+10	1.708E+82
52	1.617E-51	1.019E+25	1.345E+08	4.487E-03	3.00E+10	1.708E+82
53	1.293E-50	1.631E+26	3.389E+08	1.131E-02	3.00E+10	1.708E+82
# of	Volume of λc	Universe	Universe	Universe time	Space-time	Total Energy
stage	localization	Volume	radius		Ratio
(N)	Vλc	VU	rU	tU		(Et)
	Vλc=4/3´π´λc^3	VU=Vλc´nγ	rU=(VU´3/4π)^1/3	tU=rU/c	rU/tU=c
[ ]	[cm^3]	[cm^3]	[cm]	tU [s]	[cm/s]	[MeV]
54	1.035E-49	2.610E+27	8.541E+08	2.849E-02	3.00E+10	1.708E+82
55	8.278E-49	4.175E+28	2.152E+09	7.179E-02	3.00E+10	1.708E+82
56	6.622E-48	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
57	5.298E-47	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
58	4.238E-46	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
59	3.391E-45	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
60	2.712E-44	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
61	2.170E-43	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
62	1.736E-42	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
63	1.389E-41	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
64	1.111E-40	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
65	8.888E-40	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
66	7.110E-39	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
67	5.688E-38	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
68	4.551E-37	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
69	3.641E-36	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
70	2.912E-35	#¡VALOR!	#¡VALOR!	#¡VALOR!	#¡VALOR!	?
71	2.330E-34	2.350E+43	1.777E+14	5.927E+03	3.00E+10	5.212E+77
72	1.864E-33	3.761E+44	4.478E+14	1.494E+04	3.00E+10	5.212E+77
73	1.491E-32	6.017E+45	1.128E+15	3.764E+04	3.00E+10	5.212E+77
74	1.193E-31	9.627E+46	2.843E+15	9.484E+04	3.00E+10	5.212E+77
75	9.543E-31	1.540E+48	7.164E+15	2.390E+05	3.00E+10	5.212E+77
76	7.635E-30	2.465E+49	1.805E+16	6.022E+05	3.00E+10	5.212E+77
77	6.108E-29	3.943E+50	4.549E+16	1.517E+06	3.00E+10	5.212E+77
78	4.886E-28	6.309E+51	1.146E+17	3.824E+06	3.00E+10	5.212E+77
79	3.909E-27	1.010E+53	2.889E+17	9.635E+06	3.00E+10	5.212E+77
80	3.127E-26	1.615E+54	7.279E+17	2.428E+07	3.00E+10	5.212E+77
81	2.502E-25	2.584E+55	1.834E+18	6.118E+07	3.00E+10	5.212E+77
82	2.001E-24	4.135E+56	4.622E+18	1.542E+08	3.00E+10	5.212E+77
83	1.601E-23	6.616E+57	1.165E+19	3.885E+08	3.00E+10	5.212E+77
84	1.281E-22	1.059E+59	2.935E+19	9.789E+08	3.00E+10	5.212E+77
85	1.025E-21	1.694E+60	7.395E+19	2.467E+09	3.00E+10	5.212E+77
86	8.198E-21	2.710E+61	1.863E+20	6.215E+09	3.00E+10	5.212E+77
87	6.558E-20	4.336E+62	4.695E+20	1.566E+10	3.00E+10	5.212E+77
88	5.247E-19	6.937E+63	1.183E+21	3.947E+10	3.00E+10	5.212E+77
89	4.197E-18	1.110E+65	2.981E+21	9.945E+10	3.00E+10	5.212E+77
90	3.358E-17	1.776E+66	7.512E+21	2.506E+11	3.00E+10	5.212E+77
91	2.686E-16	2.842E+67	1.893E+22	6.314E+11	3.00E+10	5.212E+77
92	2.149E-15	4.546E+68	4.770E+22	1.591E+12	3.00E+10	5.212E+77
93	1.719E-14	7.274E+69	1.202E+23	4.009E+12	3.00E+10	5.212E+77
94	1.375E-13	1.164E+71	3.029E+23	1.010E+13	3.00E+10	5.212E+77
95	1.100E-12	1.862E+72	7.632E+23	2.546E+13	3.00E+10	5.212E+77
	1.860E-12	6.399E+72	1.152E+24	3.842E+13	3.00E+10	8.893E+77
96	2.299E-12	8.486E+72	1.265E+24	4.221E+13	3.00E+10	8.893E+77
97	1.839E-11	1.358E+74	3.188E+24	1.064E+14	3.00E+10	8.893E+77
98	1.471E-10	2.172E+75	8.034E+24	2.680E+14	3.00E+10	8.893E+77
99	1.177E-09	3.476E+76	2.025E+25	6.753E+14	3.00E+10	8.893E+77
100	9.416E-09	5.562E+77	5.102E+25	1.702E+15	3.00E+10	8.893E+77
101	7.533E-08	8.899E+78	1.286E+26	4.288E+15	3.00E+10	8.893E+77
102	6.027E-07	1.424E+80	3.239E+26	1.081E+16	3.00E+10	8.893E+77
103	4.821E-06	2.278E+81	8.163E+26	2.723E+16	3.00E+10	8.893E+77
104	3.857E-05	3.645E+82	2.057E+27	6.861E+16	3.00E+10	8.893E+77
105	3.086E-04	5.832E+83	5.183E+27	1.729E+17	3.00E+10	8.893E+77
106	2.468E-03	9.331E+84	1.306E+28	4.356E+17	3.00E+10	8.893E+77