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The quarks (u d t) and magnetic monopoles them-selves pairs production by the Schwinger effect atthe end of inflation at the origin of CMB B curlpattern matter creation and of the Higgs field

id2881937 pdfMachine by Broadgun Software - a great PDF writer - a great PDF creator - httpwwwpdfmachinecom httpwwwbroadguncom


Stefan Mehedinteanu

CITON Center of Technology andEngineering for Nuclear Projects StrAtomistilor No 409 BOP-5204-MG-4 Oras Magurele Ilfov (ROMANIA)E-mail mehedintzyahoocom

In present work is established a correlation with Inflation Dynamics especially at the reheat-ing era when the Inflaton field is sufficiently strong and the energy of the vacuum can belowered in order to create by Schwinger effect pairs of quarks (u d t) gluons bosons (W)gluons (monopoles) the magnetic monopoles themselves (of spin 1) Also in the work iscalculated the Inflation Dynamics putting in evidence all the epochs (quarks hadrons leptons)That ours permitting to observe that the potential nears the end of reheating (at quarks epoch) isvery much reduced thus at smH end 0030][10 61

the potential becomes V

end = 100GeV at

confinement smH end 33][1091 V = 100MeV and the quarks pairs created by Schwinger effectget 26MeV Therefore apparently is not any trace of an external residual field like of Higgsfield In others words the Inflation can not explains the Higgs field only if we consider that the

top (t) and antitop ( t ) quarks pairs also produced by Schwinger effect they form a bound statethat is a composite Higgs boson field as in the frame of Topcolor model This is a model ofdynamical electroweak symmetry breaking in which the top quark and anti-top quark form atop quark condensate and act effectively like the Higgs boson This is analogous to the phe-nomenon of superconductivity These theories will ultimately be tested at the LHC in its Run-II commencing in 2015 In our present model the things are similarly an equivalence of mymodel with that of the Standard Model is given in previously author works Thus in mymodel the Inflaton potential by Schwinger effect during the reheating period generates allkinds of particles gluons magnetic monopoles themselves and fermions (quarks top quarks)In the model theses gluon-gluon interactions constrain color fields to string-like objects calledflux tubes which exert constant force when stretched The difference with Standard Modelis that it results a probability 1 (or a continuously production rates) for gluons and a numberof 1090 quarks Finally at all the gluons are being captured by all 3 flux_tubes generated by eequarks ( 1090) pairs together forming nucleons of an incredibly exactly number 1090 which is theknown number of particles in Universe Since the reheating potential continues to diminish atapproximately V 01[GeV]-that corresponding to confinement the production of gluons(monopoles) quarks stops But a near e field it was created inside nucleons as was found inpreviously authors works This field makes possible the beta decay of free neutrons and later ofisotopes Also this field creates a Lorenz force between quarks flux tube and gluons (in structuresof gauge monopoles type current) that is found to explain the gravity of nucleons (mass) Thereare found the number and mass of top quarks pairs locked in Higgs field and its decay Also isdiscovered the exact origin of primordial magnetic field (PMF) which can B-imprints CMBnamely the magnetic flux of magnetic (anti)monopole coupled in strings and generated by a thesame Schwinger effect Thus at the end of CMB time all (1090) of magnetic monopoles pairsproduced are already bounded in strings and the light of B curl type imprinted is due of theirsmagnetic field resulted to be B

PMF = B

CMB 15 1012[T] either as itself or by Faraday rotation

of 0051rad 295 that gives l = 68 for a frequency of 41GHz Therefore the monopoles pairssuppression by bounding its in strings that explains the magnetic monopoles absence mentionedin Iflation works Also in order to pass the plasma period as to be formed by particles it needsto preserve the magnetic field in some way like in theses strings till CMB That it is not the casewith gravitational field which it is not affected by this plasma

Abstract

Full Paper

Corresponding authorsName amp Address

Stefan MehedinteanuCITON Center of Technology andEngineering for Nuclear Projects StrAtomistilor No 409 BOP-5204-MG-4 Oras Magurele Ilfov (ROMANIA)E-mail mehedintzyahoocom

Key WordsInflation Reheating Wave number BICEP2-B-curl pattern Quarks Gluons MonopolesHiggs field Epochs

Manuscript Num JOPA_325Journal Name Journal of Physics amp AstronomyManuscript Title The Quarks and Magnetic Monopoles Themselves Pairs Production by theSchwinger Effect at the End of Inflation at the Origin of Pattern Matter Creation and of the HiggsFieldArticle Type Full PaperCorresponding Author stefan

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INTRODUCTION

Recently were reported the results from theBICEP2 experiment a Cosmic Microwave Background(CMB) polarimeter specifically designed to search forthe signal of inflationary gravitational waves in the B-mode power spectrum around l 80[1]

Because of the Universe high conductivity twoimportant quantities are almost conserved during Uni-verse evolution the magnetic flux and the magnetichelicity

A near similarly pattern could be obtained if isconsidered a Primordial Magnetic Flux (PMF)

During the inflationary era the physical wavelengthof any given mode will grow with the scale factor a(t)and hence will grow exponentially The Hubble lengthH1 however is approximately constant during infla-tion

The modes of interest will start at wavelengths farless than H1 and will grow during inflation to be per-haps 20 orders of magnitude larger than H1

The Hubble length aaH 1 will grow linearlywith t so eventually the Hubble length will overtakethe wavelength and the wave will come back insidethe Hubble length

During inflation[2] aH[m1] increases with timeand a commoving scale ak is said to leave the horizonwhen aHk = 1 After inflation aH decreases and thecommoving scale is said to enter the horizon whenaHk = 1

The scale leaving the horizon at a given epoch isdirectly related to the number N() of e-folds of slow-roll inflation that occur after the epoch of horizonexit Indeed since H is slowly varying we have d ln k= d(ln(aH)) d ln a = Ht From the definition Eq(38) of[2] this gives d ln k = shydN() as of eq(46) from[2]and therefore ln(k

endk) = N() or k

end = keN[m] where

kend

is the scale leaving the horizon at the end of slow-roll inflation or usually ][11 mkk

end

the correct equa-tion being k = k

endeN [m1]

For a flat universe eq (162) of[12]

GH3

8(1)

= 1090 1092 gcm3 or = 1e87[kgm3] = 127 1039 [s1] or results H = 737 1038 [s1] orl = Hc = 4 1031 [m1]

Inflation ended when the inflaton field decayed intoordinary particles in a process called reheating at whichpoint ordinary Big Bang expansion began

When the wavelength (k1 [m]) is large comparedto the Hubble length (H1 [m]) the distance that lightcan travel in a Hubble time becomes small compared

to the wavelength and hence all motion is very slowand the pattern is essentially frozen in

Reheating occurs promptly at the end of inflationIn the simple models that we have explored this meansthat the reheat temperature is at least 1011 GeV

If the scalar field falls below inst

before the endof inflation the false vacuum is destabilized and thereis a possibility of a second-order phase transition of akind quite different from the usual thermal phase tran-sition

The cosmological significance of this different evo-lution depends on when the defects form If they formafter cosmologically interesting scales leave the hori-zon (50 or 60 Hubble times before the end of infla-tion) the scaling solution has been established by thetime that these scales enter the horizon If they formbefore their typical spacing is still much bigger thanthe horizon size and we presumably see no defectsFinally if they form at about the same time the con-figuration of the defects will differ from the scalingsolution that being the case of structure forming gaugestrings

A commoving scale ak is said to be outside thehorizon when it is bigger than H1

When inflation ends the scalar field begins to os-cillate near the minimum of V() As any rapidly oscil-lating classical field it looses its energy by creating pairsof elementary particles These particles interact with eachother and come to a state of thermal equilibrium withsome temperature T

r

It is known that as the temperature decreases to T T

c1 1014 1015 GeV a phase transition (or several)

takes place generating a classical scalar field 1015

GeV which breaks the symmetry between the strongand electroweak interactions[3a] When the temperaturedrops to T

c2 200GeV the symmetry between the

weak and electromagnetic interactions breaks Finallyat T = 102 MeV there should be a phase transition (ortwo separate transitions) which breaks the chiral in-variance of the theory of strong interactions and leadsto the coalescence of quarks into hadrons (confinement)

Without a solution of the baryogenesis problem theinflationary universe scenario would be impossible sincethe density of baryons that exist at the earliest stages ofevolution of the universe becomes exponentially smallafter inflation Or in others words if it is not generateda new field (the initial one vanishing till today) theuniverse is collapsed

This field could be assimilated with Higgs field asbeing described by the same formula (chaotic inflatonpotential) see Linde[3a] It needs to understand whichis the provenience of the Higgs field that generatesHiggs particles in Standard Model

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Also it is known that the QCD-monopole has anintrinsic structure relating to a large amount of off-diagonal gluons around its center similar to the tHooft-Polyakov monopole At a large scale where thisstructure becomes invisible QCD-monopoles can beregarded as point-like Dirac monopoles[6]

In[3b] where is explained how the matter is cre-ated is shown that if the particles produced by thedecaying inflaton field interact with each other stronglyenough then the thermodynamic equilibrium sets inquickly after the decay of the inflaton field and thematter acquires a temperature T

r Creation of particles

leads to the several effects which can change the dy-namics of the system In particular it terminates thebroad resonance particle production First the energyfrom the homogeneous field (t) is transferred to thecreated particles The amplitude of the classical oscilla-tions

0 is therefore decreasing faster than it would

decrease due to the expansion of the universe only Itis found in[3b] that the decay of the inflaton field typi-cally begins with the explosive production of particlesduring the stage of preheating in the regime of a broadparametric During the second stage the inflaton fielddecays further in the regime of the narrow resonanceand particles produced at this stage decay into otherparticles and self-interacting The third stage is the ther-malization

The inflationary paradigm invokes quantum ef-fects in highly curved spacetime at energies near 1016

GeV and timescales less than 1032 s[3a]The detection of B-mode polarization of the CMB

at large angular scales would provide a unique confir-mation of inflation and a probe of its energy scaleNotice that the BICEP2 result at 1 060

050160

r [5] cor-

responds to the range V(0) = (18 22) 1016 GeV

and to HI = (08 12) 1014 GeV

In the present work are verified all theses knownresults and supplementary is discovered an alternativeof B-mode polarization of the CMB as due of the pri-mordial magnetic field (PMF) of magnetic(anti)monopole pairs generated by a Schwingereffect[4a4b6] due of an external field E as the above sca-lar potential V equally initially with the Inflation Po-tential at the reheating of V 4 1012 GeV

THE ANALYSIS OF UNIVERSE EVOLUTION

In[7] is explained how Inflation worksThus is shows that the time constant 1 of the

exponential expansion would be about 1038 and thatthe corresponding Hubble length would be about H

1 = 1030 [m] and H is the time-dependent Hubble pa-rameter given by (in natural units)

43

42

)(3

8

3

8

cc

GVGVH

Here we introduce the following our derivationThus from[8] the Ricci scalar curvature is aa(6

)22 aa which reduces to 2

22

6a

ac or

432

4

2

2

2 )(3

6

ccM

cV

a

a

c Plank

(2)

][61 2

2

2

2

m

c

H

R with the potential when

leaves the horizon at the slow-roll end of inflation eraV = 1011 GeV results H1 = 14 1027 [m]

Remember the equations derived in[17] which re-late the gravitation constant with Planck mass

2

PlanckM

cG

(3)

This relation derives from the equality between

Schwarzschild radius 2

2

c

GM with either Compton

length Mc

lCompton

or with Planck length 3c

GlPlanck

when M = MPlanck

and the Lorenz force exercised onthe surface either of 2

Pl or of Compton length orSchwarzschild radius finally as being given as F

L =

ecBWhere

22

3

4242

1

4

8

4

82

ec

cec

G

c

c

G

l

F

c

G

R P

L

(4)

Now we have

eB

G

ecBc

c

G

R

2

4

82 3

42

(5)

or with Schwarzschild radius of an object

GM

ecB

GM

ecBc

c

G

Reraction

2

int

22

4

42 8

82

(6)

R being the object radius and Bint

eraction

= Bpair

N

particles

In case of Earth the interacting field between nucle-ons is B

pair = 1015 [T] N = 1051 the object number of

particles M = 6 1024 [Kg][8] it results R 65 106 [m]

Or ][6 2

22 m

eBcH

(61)

that means the Hubble length is given by the magneticfield of gluons (monopoles)

That with GeVVTBGeV

1137

111010][1071 re-

sults ][10721 252

2

m

R or H = 5 1035 [s] or H1 =

6 1024 [m] the same value as above

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If B22GeV

= 88 1015 [T] at Confinement it re-sults H1 = 27 1016 [m]

If we use ][102 42

1510TB

GeV H1 = 15 1029 [m]

the value obtained in Inflationary models[3a] In otherswords it is found a equivalence between the gravita-tional potential and the electromagnetic potential dueof magnetic monopoles themselves

For inflation to achieve its goals this patch hasto expand exponentially for at least 65e-foldings butthe amount of inflation could be much larger thanthis Eventually however the inflaton field at anygiven location will roll off the hill ending inflationWhen it does the energy density that has been lockedin the inflaton field is released Because of the cou-pling of the inflaton to other fields that energy be-comes thermalized to produce a hot soup of particleswhich is exactly what had always been taken as thestarting point of the standard big bang theory beforeinflation was introduced Note that while inflationwas originally developed in the context of grand uni-fied theories the only real requirements on the par-ticle physics are the existence of a false vacuum stateand the possibility of creating the net baryon num-ber of the universe after inflation

First of all we know that the universe is incred-ibly large the visible part of the universe contains about1090 particles

The cosmic background radiation was releasedabout 400000 years after the big bang after the uni-verse cooled enough so that the opaque plasma neu-tralized into a transparent gas The cosmic backgroundradiation photons have mostly been traveling onstraight lines since then so they provide an image ofwhat the universe looked like at 400000 years afterthe big bang

In some works[3a] it is mentioned the absence ofmagnetic monopoles even all grand unified theoriespredict that there should be in the spectrum of pos-sible particles extremely massive particles carrying anet magnetic charge

In present work is re-introduced a such ideamainly based on the production of gluons (monopoles)and of magnetic monopoles themselves pairs and ofelectrons (quarks) due of the Schwinger effect Thishappens when the field is sufficiently strong and theenergy of the vacuum can be lowered by creating anelectron-positron ( ee ) which form the quarks (u d t)gluons bosons (W) gluons (monopoles) the magneticmonopoles themselves (of spin 1) pairs The field whichmakes the vacuum unstable is just considered theInflaton potential in the reheating period The absenceof monopoles it will be shown to be due of theirsbounding in the neutral dumbbell strings for CMB B-

imprints and for dark matter

The calculation of spacetime windows for electro-magnetic-waves (EMW) generation and of mattercreation

We have calculated the horizon-crossingwavenumbers for different important epochs (quarkshadrons leptons)

Thus if it is considered a re-entry in horizon atreheating when from k

leave = k

endeN results

kend_M1

= kleave_M1

eN (7)

or )(10][101052 211

1_

51

1_ CMBMpcmHk MendMend

the scale factor being aend

Hend

kend

= 1 and aleave

= 1

for ][10871 271

1_ mrH monopole

ComptonMleave

with N = 51 re-

sults kleave_M1

= 7 102 [m] and 21

4

_ 10

1093

end

endCMBend H

ka

= 39 see the TABLE 1In case of magnetic monopoles the value of field

at end of CMB era respectively at ][10 211 mH CMB is given

as[910]

2

_

2

0_

2

0

1)(

)(

)()()(

CMBend

leave

CMBend

leaveleave

PMF

endCMB atB

ta

tatBBtB (8)

With the above magnetic field at leave horizon Vleave

4 1012 GeV is

][1066)(

)( 47

2

0

22 CNE

c

VE

e

C

leave

(9)

Bleave

(t) = Ec = 22 1039 [T] that results BPMF

=B

CMB = 15 1012 [T] 15nGs see Figure 1 near that

it was obtained in[910]If the wavelength is 151 1052

CMBend Hkl

][1021][1033][10 131221 sCMBsm time we cansee these imprints as B-curl type due of Faraday rota-tion (see below) at CMB time

Also if we consider the primordial moment whenthe re-entry in horizon is at ][1081 271 mH end

theleave of horizon being at ][10871 351 mH leave

with N

= 7 that results ][102 321 mkend

or inside horizon at

the end of aend

= 87 104 results B = 282 1025 [T]and with the value of the potential as V = 11 1019

[GeV] that means a mass of thesis monopoles (viewedas micro(babies) -blackhole) considered for V

monopol =

1019 [GeV] mass = 178 108 [kg] rSchwarzschild

= lp =

18 1035 [m] the number of monopoles pairs (seebelow the formula) becomes N 39 1016 that webelieve to be the seeds of the blackholes

THE MATTER CREATION

We shall be defining horizon crossing at a given

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epoch as k = aH We can thus give the horizon-cross-ing wavenumbers for these different important epochsIf reheating is prompt we learn that in most modelsthe observable universe leaves the horizon about 62e-folds before the end of inflation If reheating is longdelayed N could be considerably reduced being equalto 32 for the most extreme possibility of GeVV reh 100041

(corresponding to reheating just before the electroweaktransition which is presumably the last opportunityfor baryogenesis) For most purposes however oneneeds only the order of magnitude of N

The matter creation is due mostly to reheating atabout V = 1012 100GeV T = 1015 K also at nearthe end this field is being locked in the Higgs field viabounded top quarks ( tt ) as in Topcolor theory (whichneeds developments) and appearing as V = e =247GeV The top quark is the heaviest known elemen-tary particle which makes it an excellent candidate fornew physics searches Origin of its mass might be dif-ferent from that of other quarks and leptons a topquark condensate ( tt ) for example could be re-sponsible for at least part of the mechanism ofelectroweak symmetry breaking (EWSB) An interest-

ing model involving a role for the top quark in dy-namical EWSB is known as the topcolor-assistedtechnicolor (T C2) model Topcolor scenario also pre-dicts the existence of the top-Higgs 0

th which is the ttbound state[21]

Again we have )()ln( 11

Nkk entryreCMB N

entryreCMB ekk 11

kCMB

= kre-entry

eN N() = 51Or k

re-entryk

CMB = eN

The results of calculations are presented in TABLE1 and Figure 1

The same approach as for inflation and reheatingis applied to calculate the evolution of the field lock-ing in the top quarks pairs see the calculations resultsin TABLE 2 and Figure 1

Thus today this scaled field becomes Vtoday

=V

lockeda

end = 274208 = 119GeV with N = 39

Or today the value of the field becomes 119GeVnear Higgs value

In other words theses fields after the reentries donot contribute to the imprint of CMB that are pro-duced by the primordial field (B

PMF) of the magnetic

monopoles as been locked in stringsTherefore the Faraday rotation (see chapter 5)

Figure 1 The evolution of universe correlated with pairs production and matter creation

TABLE 1

H_end_1[m] k_end[m] a_end H_1[m] Va[GeV] k_1[m] a a_endH_end[m] B_PMF[T]

100E-02 250E-05 390 180E-27 100E+10 110E-15 250E-03 256E-05 142E+34

100E+05 250E-05 390E+09 180E-27 100E+03 700E-18 250E-10 256E-05 142E+20

100E+06 260E-05 380E+10 180E-27 100E+02 700E-17 260E-11 153E+18

100E+09 260E-05 370E+13 180E-27 100E-01 700E-14 260E-14 153E+12

100E+15 250E-05 390E+19 180E-27 100E-07 700E-08 250E-20 256E-05 142E+00

100E+21 250E-05 390E+25 180E-27 100E-13 700E-02 250E-26 142E-12

180E+25 250E-05 700E+29 180E-27 560E-18 120E+03 140E-30 430E-21

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due of BPMF

at CMB time is

0

2

0

3

02952][0510

8

3

rad

Bc

eF CMB

(10)

Here the frequency being 0 = 41GHz is taken

from[11] where are derived current constraints on themagnetic field energy density B from the WMAP 7-year polarization data by comparing magnetic fieldinduced theoretical CMB B-mode power spectrum BB

lC

as given by Eq (65) of[11] with the WMAP observedB-mode power spectrum using the 2 statistics

Roughly speaking the multipole moments TT

LC

measure the mean-square temperature difference be-tween two points separated by an angle(1) 200lor that means that l = 70 a result mentioned also in allarticles[3a910] but without explaining the provenienceof PMF that is done in this work

Therefore with 0 = 41GHz l = 68 like the

results of gravitational waves[173a]

The pairs creation at the end of Inflation bySchwinger effect at origin of matter creation

In the following as based on the values of the po-tential at different evolution eras are calculated the pairsproduction for spin 1 particles and for spin 12 byapplying separately the Schwinger formulas

(a) The gluons (monopoles) and magnetic mono-poles themselves pairs production

In[4a6] eq (44) the following result was obtainedfor the probability of gluon pair production from ar-bitrary time dependent chromo-electric field Ea(t) in = 1 gauge via Schwinger mechanism

)()2(

3

1323

)(

1 1ln)(4

1)(

tjgTp

jj

T

gg

T etgpxddtd

dWCpf (11)

)(cos12

)(12

1 ttC

)(

3cos1

2

)(12

32 ttC

The results of calculations from[6] are given in Fig-ure 2 where we can see for example in the case of ppcollision at LHC which correspond with our InflatonPotential (at the end of the reheating) V

end 104 the

probability of gluon pair production from arbitrarytime f(p

T = 3 C

1 = 72GTeV4) 012 which in

fact it was happen at LHCThat means a near continuously rate production

during the reheating periodNext we have calculated the magnetic monopoles

(themselves) pairs production rate For that we con-sider the initial results of Sauter Heisenberg and Eulerand Weisskopf where in a seminal work Schwingerderived a central result of strong-field quantum elec-trodynamics namely the rate per unit volume of paircreation R in a constant and uniform electric field ofstrength E of leading order behavior

R = (EEcr)2 (c4)(83)1 exp(E

crE) (12)

for EEcr 1 positron charge e mass m Compton

wave-length mc and so-called critical electricfield

ecmEcr32 (13)

TABLE 2

H_end_1_H[m] k_end_H[m] a_end_H H_1_H[m] Va_H[GeV] k_1_H[m] a_H B_PMF_H[T]

100E+09 860E+08 115E+00 100E-08 214E+02 115E-08 860E-01 399E+18

180E+14 860E+14 280E-01 100E-02 510E+01 200E-03 481E+00 129E+17

180E+21 130E+21 139E+00 180E+04 178E+02 200E+04 720E-01 156E+18

180E+25 860E+24 208E+00 100E+08 119E+02 200E+08 480E-01 692E+17

Figure 2 The evolution of probability of gluonquarks pairsproduction for different collision energies

If we use the zone of reheating for matter creationof Hubble length ][10 41 mH end

when all the kinds ofparticles could be created (quarks gluons bosons glu-ons (monopoles) and top quark which gives Higgsfield) the mass of the first top quarks created is m =46 1025 [kg] that resulting from the external poten-tial after scaling with a

end see TABLE 1 V a

end = 4

1012 26 109 = 104 [GeV] and the top quarks hav-ing the mass V

monopol a

end = 1011 26 109 = 262GeV

see TABLE 1 and the Compton length being)(3 cV CCCompton

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The Compton volume is VCompton

= 85 1082 [m3

s] where C = 71 1019 [m]

Here is supposed that the vector potential or theInflaton V

end = 4 1012 [GeV] 169 106 [J] gener-

ates an electric field E which polarizes the (false)vacuum that creating the primordial pairs of magneticmonopoles ( MM )

To note the fundamental equations or how passfrom the potential (scalar) to the electrical field

B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38

1029 [NC] e = 16 1019 [C] ][10041 34 Js V-isthe electromagnetic potential

With theses result RV = 55 1080 that forV

Compton results RV V

Compton 047 1 pair

To note that in[4a4b] V[GeV] is the energy of avortex

The process continues in cascade during the re-heating when is a re-entry in horizon in the electroweakperiod Thus by using the same formula for reheatingperiod till confinement are obtained the number ofmagnetic monopoles which are locked in strings tillCMB as following

pairsVRN matter

ew

MMpairs

9080 10551055 wherethe volume is given by

The pairs production volume is][10)( 31031 smaHV endendmatter (16)

where the Hubble radius at the matter creation is][10 41 mH matter

aend

= 38 108 after that the field trans-fer to nucleons see Figure 1 The process time is

106 1[s] the necessary volume is 3 Cpairsnecessary NV

][102)107(10 33631990 m and the available vol-

ume is ][1045)( 33731 maHV endmatteravailable that it is avery good result

In the Electroweak symmetry breaking and thequark epoch which is between 1012 106 [s] secondafter the Big Bang when as the universes temperaturefalls below a certain very high energy level it is be-lieved that in the frame of Standard Model the Higgsfield spontaneously acquires a vacuum expectation value(V = 247GeV) which breaks electroweak gauge sym-metry Via the Higgs mechanism all elementary par-ticles interacting with the Higgs field become massivehaving been massless at higher energy levels To notethat the Hadron epoch is between 106 [s] and 1[s] afterthe Big Bang when the quarkgluon plasma that com-

poses the universe cools until hadrons including bary-ons such as protons and neutrons can form

But following the Inflation Dynamics the poten-tial nears the end of reheating (quarks-gluons epoch) isvery much reduced thus at smH

end0030][1061 the

potential becomes Vend

= 100GeV Therefore appar-ently is not any trace of an external residual field likeof Higgs field In others words the Inflation does notexplains the Higgs field Only if we consider that thetop (t) and antitop ( t ) quarks form a bound state thatis a composite Higgs boson field

In physics a bound state describes a system wherea particle is subject to a potential such that the particlehas a tendency to remain localized in one or more re-gions of space The potential may be either an externalpotential (in our case the Inflaton (at reheating) Poten-tial) or may be the result of the presence of anotherparticle

In teorethical physics Topcolor is a model ofdynamical electroweak symmetry breaking in whichthe top quark and anti-top quark form a top quarkcondensate and act effectively like the Higgs bosonThis is analogous to the phenomenon of superconduc-tivity These theories will ultimately be tested at theLHC in its Run-II commencing in 2015

Therefore the as formed nucleons embed gluonsinto some structures of gauge tHooft monopoles) andof quarks pairs (u d) as was shown in[4a]

In the present model the things are similarly formore see the equivalence of my model with that ofthe Standard Model respectively the eq (23) of AppA of[4a] Thus in my model the Inflaton potential bySchwinger effect during the reheating period gener-ates all kinds of particles in our cases gluons with struc-ture of monopoles magnetic monopoles themselvesand fermions (quarks top quarks) In the model thesegluon-gluon interactions constrain color fields tostring-like objects called flux tubes which exert con-stant force when stretched The difference with Stan-dard Model is that all gluons (monopoles) are cap-tured by all 3 flux_tubes generated by ee quarks pairs( 1090) by the same Schwinger effect as will resultbellow

(b) Fermions production

The fermions (quark s u d t) pairs production bySchwinger effect

An interesting aspect of virtual particles (invacuum) both theoretically and experimentally is thepossibility that they can become real by the effect ofexternal fields In this case real particles are excitedout of the vacuum In the framework of quantummechanics by Klein Sauter Euler and Heisenberg who

FP 9

Full Paper

studied the behavior of the Dirac vacuum in a strongexternal electric field If the field is sufficiently strongthe energy of the vacuum can be lowered by creatingan electron-positron pairs ee (later bounded in quarks)This makes the vacuum unstable

Te first ee pair seems to be created in the same E asused above for magnetic monopoles ( MM ) creationand with the contribution of the magnetic field gener-ated by thesis magnetic monopole as calculated aboveB

monopol also both viewed as external magnetic fields

The next ee and MM are created in the reheating pe-riod (V = 4 1012 GeV with V

cr = 1011 GeV) at the

end of inflationThen the 4-potential is given by V

= (Ez0 Bx0)

that copy very well with our new understanding whenthe electric field E and B is the magnetic field compo-nent

In[4a4b612] eq (73) is obtained the pair-productionrate for fermions as

E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)

for spin 12 particle

where = 1137 V[m3 s] and 04 to convert cgs

SI JWKB meaning (Jeffreys-Wentzel-Kramers-Brillouin) model

The effect of magnetic field is the same as shiftingthe effective mass )12(24242

jcqBcmcm e for fer-mions for each Landau level

The Compton space-time volume of an electronhas the size

][1049)( 3803 smcV CCCompton

where ][1032 18 mcmC

(18)

the effective mass is2242 ccqBcmm monopole

(19)

the critical field ][1053 2832

CNEe

cmEc

as from

eq(A40) of[4a4b] that results m = 14 1025 [kg] in

place of me = 9 1031 [kg]

The potential B being the same as for monopolespairs V = 104 [GeV] 16 106 [J]

][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)

Reheating occurs promptly at the end of inflationIn the simple models that we have explored this meansthat the reheat temperature begins at least 1011 GeVB

monop E

monopolc = 15 1022 [JAm2]

And the external field is

3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)

So it results the same value as above E = 14 1030 [NC]

With these values it results the number of quarks

pairs ( ee ) created as smpairseeVJWKB

378 _1049 If the pairs production volume is 31 )(

endendmatter aHV

][10 310 sm JWKB

= 94 1088 where the Hubble ra-dius at the matter creation is ][10 41 mH matter

after thatin case of top quarks the field transfers to Higgs fieldsee Figure 1 The process time is 106 1[s] the

necessary volume is 7(1049 883

Cpairsnecessary NV

][1043)10 334319 m and the available volume is

][1045)( 33731 maHVendmatteravailable

that it is a very

good resultOr if we consider V

Compton it result a rate

JWKB

VCompton

09[e pairs] that means a continuously pro-cess which ends at quarks epoch or when both thescaled values of V and V

cr (for each known mass-to-

day) becomes V Vcr

In other words at very early time inside the Infla-tion Volume are available only pairs of massive elec-tron-positron-quarks (u d) which will later form Cou-lomb flux tubes and of top quarks )( tt which createHiggs field all that has been created by the conjuga-tion of the field E(V) and of the magnetic field B

monopole

already generated only by the Schwinger effect basedonly on the field E(V)

Immediately at confinement the quarks formsCoulomb flux tubes thesis capturing gluons organizedin monopole type structures (hedgehog) as is explainedin[4a4b4c] in order to form a primordial massive vor-texes 13 nucleon

Finally theses pairs together form nucleons of anincredibly exactly number 1090 which is the knownnumber of particles in Universe Since the potentialcontinues to diminish thus at approximately V 01[GeV]-that corresponding to confinement (10s 20min utes) see Figure 1 then the production of gluons(monopoles) stops But the a near a value of e fieldit was also created inside nucleons as was found inthe frame of Dual Ginsburg-Landau theory[4a4b4c] thatdue of the interaction between the three vortexes whichcompose the nucleons see eq (42) (45) (46) (47) (66)(69) of my model[4a] This field is sufficient to createnew pairs of W Z ee by the same Schwinger effectthat makes possible the beta decay of free neutronsand later of isotopes As a consequence it follows thatEq(315) of[19b] does not depend on n

max and the n p

conversion grows linearly with the field strength aboveB

c In the absence of other effects the consequence of

the amplification of n p

due to the magnetic fieldwould be to decrease the relic abundance of 4He A

FP 10

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such result it was found in[4a]Also this field creates a Lorenz force between

quarks flux tube and gluons (monopoles) current thatis found to explain the gravity of nucleons (mass) as itwas already found before

THE SPECTRUM AT CMB

Here it is defined an effective magnetic fieldB

eff in terms of the total energy density in the mag-

netic field

8

2

0

effB(22)


LC

measure the mean-square temperature difference be-tween two points separated by an angle(1) 200l

At this surface an angle degrees subtends a com-moving distance x 200Mpc

For a dipole cEk with eq(21) E = 4 1036

[J] BPMF

and distance along the tube between twomagnetic monopoles d = 67 = 2 1016 [m] asfrom[8] resulting k = 43 1011 [m1] = kc = 13 102 [s1]

For example to describe the electromagnetic po-tential V from a source in a small region near theorigin the coefficients may be written as

0

)()()(l

l

lm

ml

ml YrCrV (23)

From[13] it results that before recombinationThomson scattering between photons and electronsalong with Coulomb interactions between electronsand baryons were sufficiently rapid that the photon-baryon system behaved as a single tightly coupled fluid

Since the trajectory of plasma particles is bent byLorentz forces in a magnetic field photons are indi-rectly influenced by the magnetic field throughThomson scattering Let us consider the PMF createdat some moment during the radiation-dominated ep-och

The energy momentum tensor for electromagne-tism is

6

200

][ 8 a

BT EM

(24)

We assume that the PMF B0 is statistically homo-

geneous isotropic and random For such a magneticfield as result from[13] the fluctuation power spectrumcan be taken as a power-law BnkkBkBkS

)()()(where n

B is the power-law spectral index of the PMF

Although possible origins of the PMF have beenstudied by many authors[19a19b] there is no consensusas to how the PMF correlates with the primordial den-

sity fluctuations Nonetheless almost all previousworks have assumed that there is no correlation be-tween them In order to study the possible effects of aPMF in a more general manner in[13] is considered apossible correlations between the PMF and the primor-dial density and tensor fluctuations

Based on fundamental works then it is describeda connection between electroweak strings and primor-dial magnetic fields The basic idea is that as the Higgsfield acquires a vacuum expectation value currents areproduced that lead to a magnetic field[19b] Once mag-netic fields are generated they can be imprinted in thehighly conductive medium and eventually survive

The first generalized definition of the electromag-netic field in the presence of a non-trivial Higgs back-ground was given by tHooft ref [150] of[19b] in theseminal paper where he introduced magnetic mono-poles in a SO(3) Georgi-Glashow model In this casesingular points (monopoles) or lines (strings) where

a

= 0 appear which the source of magnetic fields be-come tHooft result provides an existence proof ofmagnetic fields produced by non-trivial vacuum con-figurations model A possible generalization of thedefinition (421) of[19b] for the Weinberg-Salam modelwas given by Vachaspati ref [106] of[19b] The eq (423)was used by Vachaspati[19b] to argue that magnetic fieldsshould have been produced during the electroweakphase transition (EWPT) Since here on dimensionalgrounds D

where is the Higgs field vacuum

expectation value Vachaspati concluded that magneticfields (electric fields were supposed to be screened bythe plasma) should have been produced at the EWPTwith strength ][1010sin 19232 TGgTB cw Here theHubble radius at the EWPT is of the order of 1cmwhereas = (eT

c)1 1016 cm where T

c 100GeV is

the critical temperature at which the phase transitionoccurs The both values are confirmed in the presentwork

In the present work I have discovered which couldbe the exact origin of PMF namely the magnetic fluxof magnetic (anti)monopole as been generated by aSchwinger effect due of an external electrical field dur-ing the inflation

In the work[13] are implemented a numericalmethod to evaluate the PMF source power spectrumUsing this method they are able to quantitativelyevolve the cut off scale and thereby reliably calculatethe effects of the PMF on the observed CMB powerspectrum

Also in[13] are explored the effects of a PMF on theCMB for the allowed PMF parameters (ie B

lt 10nGs

and nB lt 24)

In theirs model the BB mode from the PMF can

FP 11

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dominate for l 200 if B 20nGs A potential prob-

lem in attempting to detect this signal on such angularscales therefore is the contamination from gravita-tional lensing which converts the dominant EE powerinto the BB mode Since our results on value of B

PMF

= 15 1012 [T] 15[nGs] are near identically all theconclusions of the works[13] remaining the same

We also point out that the observed power spec-trum of temperature fluctuations in the CMB is likelyto depend on frequency Such dependence is theoreti-cally expected to originate from foreground effectssuch as the Sunyaev-Zeldovich effect at highermultipoles In contrast the effects of a PMF are fre-quency-independent because the PMF affects the pri-mary CMB as a background Therefore the correla-tion between the PMF and other foreground effectsshould be weak Because of this one should be able toeventually distinguish the PMF from foreground ef-fects by using more than two observational data sets atdifferent frequencies

In the context of anisotropies induced by densityperturbations velocity gradients in the photon-baryonfluid are responsible for the quadrupole that generatespolarization[14]

FARADAY ROTATION CORRELATORS

In physics the Faraday effect or Faraday rotationis a magneto-optical phenomenon that is an interac-tion between light and a magnetic field in a mediumsee Figure 3 The Faraday Effect causes a rotation ofthe plane of polarization which is linearly proportionalto the component of the magnetic field in the direc-tion of propagation Formally it is a special case ofgyroelectromagnetism obtained when the dielectricpermittivity tensor is diagonal

Let us notice however that the lensing signal aswell as that generated by gravitational waves are

independent of the frequency while F scales as 2

0

thus multi-frequency measurements should easily dis-tinguish the Faraday rotation contribution

From[1115] the CMB is linearly polarized and anintervening magnetic field will rotate the polarizationvector at a rate given by

2

0

0

28

3

B

eF (25)

The coefficient F represents the average Faradayrotation (in radians) between Thomson scatterings[8]

0 is the CMB frequency observed today B

= B(t

) is

the strength of the primordial magnetic field at a red-shift z

= 1000 around the time of decoupling of

matter and radiation Current bounds suggest that amagnetic field pervading cosmological distances if itexists should have a present strength below B

0 109

Gauss It is conceivable that the large scale magneticfields observed in galaxies and clusters have their ori-gin in a primordial field and several theoretical specu-lations exist about its possible origin[16] like the inter-galactic dust As it was shown above the primordialmagnetic field is expected to scale as B(t) = B(t

0) a2 (t

0)

a2 (t) where a(t) is the Robertson-Walker scale factordefined above

Finally at the end of CMB when the Hubble lengtharrives at ][10 211 mH CMB

all (1090) of magnetic mono-poles pairs produced are already bounded in stringsand the light of B curl type imprinted is due of theirsmagnetic field B

PMF = B

CMB 15 1012 [T]

A near the same number of magnetic monopolespairs are coupled in neutral dumbbell strings as darkmater particles[18] that at the decoupling time

Also in classical optics a light ray can be bent ifthere is a gradient in the refractive index However inQED it is possible by the vacuum polarization thatallows the photon to exist as a virtual e e+-pair viawhich the external field can couple Thus the totalbending angle due of thesis dark matter particles canbe obtained by Kims formula[7817]

Therefore only in this way we can explain theboth processes the monopoles pairs suppression bybounding its in strings that explains the magnetic mono-poles absence mentioned in[20] Also as an magneticfield can pass the plasma as to be formed by particlestill CMB Also the gravitational field it is not affectedby this plasma And the second respectively the gen-eration of top quarks pairs which can explain the pres-ervation of the external Higgs field and thus is wasprevented this field decay The generation of pairs ofmagnetic monopoles which couple in strings can ex-plains the decoration of CMB and the presence ofFigure 3 The Faraday rotation

FP 12

Full Paper

the dark matter This because the Inflation field di-minish very fast the field of individual monopolesbecomes very low today or to explain the dark mat-ter it needs to be conserved in some neutral particleslike these magnetic monopoles strings when the con-served value is B

PFM = 1015 [T] in case of dark matter

already found in[8]We also point out that the observed power spec-

trum of temperature fluctuations in the CMB is likelyto depend on frequency Such dependence is theoreti-cally expected to originate from foreground effectssuch as the Sunyaev-Zeldovich effect at highermultipoles In contrast the effects of a PMF are fre-quency-independent because the PMF affects the pri-mary CMB as a background Therefore the correla-tion between the PMF and other foreground effectsshould be weak Because of this one should be able toeventually distinguish the PMF from foreground ef-fects by using more than two observational data sets atdifferent frequencies

The present model presents a unitary theory ofUniverse evolution as from Universe Inflation to mat-ter creation CMB imprints origin dark matter fieldvalue and the number of primordial blackholes

CONCLUSIONS

The values of the field for different epochs (quarkshadrons leptons) resulted to be correlated with Infla-tion evolution especially in the reheating period Theapplication of Schwinger effect has ours permitted tocalculate the numbers and masses for all kinds of pairs(gluons quarks magnetic monopoles) The presenceof magnetic monopoles (being of spin-1) at quarks cre-ation is mandatory since its furnishe the necessarymagnetic field B

Thus in the work is found that the monopoles pairssuppression is by bounding its in strings The genera-tion of top quarks pairs can explain the preservationof the external Higgs field also by bounding its insome ways like the scalar Higgs particles (H) and thusit is was prevented the decay of thesis fields The gen-eration of pairs of magnetic monopoles which couplein strings can explains the decoration of CMB andthe presence of dark matter Since the Inflation fielddiminishes very fast the field of individual monopolesdiminish also or to explain

CMB B-imprints and the presence of the darkmatter it needs that this field to be conserved in someparticles like theses magnetic monopoles strings wherethe conserved value today is B

PFM = 1020 [T] already

found in[8] and that of the Higgs field is 125GeV

REFERENCES

[1] BICEP2 I Detection of B-mode Polarization at DegreeAngular Scales arxiv14033985v2[astr-phCO] 18 Mar(2014)

[2] David HLyth Antonio Riotto Particle Physics Mod-els of Inflation and the Cosmological Density Pertur-bation arxivhep-ph9807278v4 (1999)

[3] (a) Andrei Linde Particle Physics and InflationaryCosmology arxivhep-th0503203v1 26 Mar (2005) (b)Lev AKofman The Origin of Matter in the UniverseReheating after Inflation arxivastro-ph9605155v1(1966)

[4] (a) Stefan Mehedinteanu The Numerical Analysis ofBeta Decay Stimulation by the High Thermal Spike ofPhoton Incidence to Valence nucleons httpviXraorgabs14040100 April (2014) (b) StefanMehedinteanu On the photonuclear rates calculationfor nuclear transmutation of beta decay nuclides byapplication of the Ginzburg-Landau theory Journal ofNuclear and Particle Physics 2(3) 57-70 (2012) (c)Akihiro Shibata et al Non-Abelian dual Meissner ef-fect in SU(3) Yang-Mills theory and confinementdeconfinement phase transition at finite temperaturearxiv14033888v1[hep-lat] (2014)

[5] Andrew RLiddle David HLyth The Cold Dark Mat-ter Density Perturbation arxivastro-ph9303019v1(1993)

[6] Stefan Mehedinteanu Numerical Analysis of PairsCreation by Schwinger Effect in Nucleons and the Beta-Decay Process Acceleration MEHTAPress Jof Phys-ics amp Astronomy 2(3) (2013)

[7] (a) AHGuth SYPi PhysRevLett 49 1110 (1982) (b)SWHawking IGMoss NuclPhysB 224 180 (1983)(c) AAStarobinsky PhysLettB 117 175 (1982) (d)JMBardeen PJSteinhardt MSTurner PhysRevD28 679 (1983) (e) Alan HGuth Inflation arxivastro-ph0404546v1 27 Apr (2004)

[8] Stefan Mehedinteanu The connection between quan-tum mechanics amp gravity Prespacetime Journal 5(1)44-59 January (2014)

[9] Masahiro Kawasaki Motohiko Kusakabe Updatedconstraint on a primordial magnetic field during bigbang nucleosynthesis and a formulation of field effectsarxiv12046164v2[astro-phCO] (2012)

[10] Dai GYamazaki Kiyotomo Ichiki Toshitaka KajinoGrant JMathews New Constraints on the PrimordialMagnetic Field arxiv10012012v1[astro-phCO] (2010)

[11] Levon Pogosian Amit PSYadav Yi-Fung Ng TanmayVachaspati Primordial Magnetism in the CMB ExactTreatment of Faraday Rotation and WMAP7 Boundsarxiv11061438v3[astro-phCO] Sep (2011)

[12] Jin Young Kim Taekoon Lee Light bending in radia-tion background arXiv13106800v1[hep-ph] Oct (2013)

[13] Dai GYamazaki Kiyotomo Ichiki Toshitaka KajinoGrant JMathews Effects of a Primordial MagneticField on Low and High Multipoles of the CMBarxiv08012572v3 [astro-ph] (2008)

FP 13

Full Paper

[14] Matias Zaldarriaga The Polarization of the CosmicMicrowave Background arxivastro-ph0305272v2(2003)

[15] Diego DHarari Justin DHayward Matias ZaldarriagaDepolarization of the Cosmic Microwave Backgroundby a Primordial Magnetic Field and its Effect uponTemperature Anisotropy arxivastro-ph9608098v1(1996)

[16] Bruce ABassett Shinji Tsujikawa David Wands Infla-tion Dynamics and Reheating arxivastro-ph0507632v22 Feb (2006)

[17] Stefan Mehedinteanu Numerical analysis of pairs cre-ation by Schwinger effect in nucleons and the beta-de-cay process acceleration MEHTAPress Jof Physicsamp Astronomy 2(3) (2013)

[18] Jon Urrestilla Ana Achacuteucarro Julian Borrill AndrewRLiddle The evolution and persistence of dumbbellsarxivhep-ph0106282v3 Sep (2002)

[19] (a) Tanmay Vachaspati Estimate of the primordialmagnetic field helicity arxivastro-ph0101261v3 (2001)(b) Dario Grasso Hector RRubinstein Magnetic Fieldsin the Early Universe arxivastro-ph0009061v2 (2001)

[20] Isabella Masina The Gravitational Wave Backgroundand Higgs False Vacuum Inflationarxiv14035244v1[astro-phCO] 20 Mars (2014)

[21] Hao Sun Chong-Xing Yue Precise photoproductionof the charged top-pions at the LHC with forward de-tector acceptances arxiv14010250v1[hep-ph] (2014)


Stefan Mehedinteanu

CITON Center of Technology andEngineering for Nuclear Projects StrAtomistilor No 409 BOP-5204-MG-4 Oras Magurele Ilfov (ROMANIA)E-mail mehedintzyahoocom

In present work is established a correlation with Inflation Dynamics especially at the reheat-ing era when the Inflaton field is sufficiently strong and the energy of the vacuum can belowered in order to create by Schwinger effect pairs of quarks (u d t) gluons bosons (W)gluons (monopoles) the magnetic monopoles themselves (of spin 1) Also in the work iscalculated the Inflation Dynamics putting in evidence all the epochs (quarks hadrons leptons)That ours permitting to observe that the potential nears the end of reheating (at quarks epoch) isvery much reduced thus at smH end 0030][10 61

the potential becomes V

end = 100GeV at

confinement smH end 33][1091 V = 100MeV and the quarks pairs created by Schwinger effectget 26MeV Therefore apparently is not any trace of an external residual field like of Higgsfield In others words the Inflation can not explains the Higgs field only if we consider that the

top (t) and antitop ( t ) quarks pairs also produced by Schwinger effect they form a bound statethat is a composite Higgs boson field as in the frame of Topcolor model This is a model ofdynamical electroweak symmetry breaking in which the top quark and anti-top quark form atop quark condensate and act effectively like the Higgs boson This is analogous to the phe-nomenon of superconductivity These theories will ultimately be tested at the LHC in its Run-II commencing in 2015 In our present model the things are similarly an equivalence of mymodel with that of the Standard Model is given in previously author works Thus in mymodel the Inflaton potential by Schwinger effect during the reheating period generates allkinds of particles gluons magnetic monopoles themselves and fermions (quarks top quarks)In the model theses gluon-gluon interactions constrain color fields to string-like objects calledflux tubes which exert constant force when stretched The difference with Standard Modelis that it results a probability 1 (or a continuously production rates) for gluons and a numberof 1090 quarks Finally at all the gluons are being captured by all 3 flux_tubes generated by eequarks ( 1090) pairs together forming nucleons of an incredibly exactly number 1090 which is theknown number of particles in Universe Since the reheating potential continues to diminish atapproximately V 01[GeV]-that corresponding to confinement the production of gluons(monopoles) quarks stops But a near e field it was created inside nucleons as was found inpreviously authors works This field makes possible the beta decay of free neutrons and later ofisotopes Also this field creates a Lorenz force between quarks flux tube and gluons (in structuresof gauge monopoles type current) that is found to explain the gravity of nucleons (mass) Thereare found the number and mass of top quarks pairs locked in Higgs field and its decay Also isdiscovered the exact origin of primordial magnetic field (PMF) which can B-imprints CMBnamely the magnetic flux of magnetic (anti)monopole coupled in strings and generated by a thesame Schwinger effect Thus at the end of CMB time all (1090) of magnetic monopoles pairsproduced are already bounded in strings and the light of B curl type imprinted is due of theirsmagnetic field resulted to be B

PMF = B

CMB 15 1012[T] either as itself or by Faraday rotation

of 0051rad 295 that gives l = 68 for a frequency of 41GHz Therefore the monopoles pairssuppression by bounding its in strings that explains the magnetic monopoles absence mentionedin Iflation works Also in order to pass the plasma period as to be formed by particles it needsto preserve the magnetic field in some way like in theses strings till CMB That it is not the casewith gravitational field which it is not affected by this plasma

Abstract

Full Paper

Corresponding authorsName amp Address

Stefan MehedinteanuCITON Center of Technology andEngineering for Nuclear Projects StrAtomistilor No 409 BOP-5204-MG-4 Oras Magurele Ilfov (ROMANIA)E-mail mehedintzyahoocom

Key WordsInflation Reheating Wave number BICEP2-B-curl pattern Quarks Gluons MonopolesHiggs field Epochs

Manuscript Num JOPA_325Journal Name Journal of Physics amp AstronomyManuscript Title The Quarks and Magnetic Monopoles Themselves Pairs Production by theSchwinger Effect at the End of Inflation at the Origin of Pattern Matter Creation and of the HiggsFieldArticle Type Full PaperCorresponding Author stefan

FP 3

Full Paper

INTRODUCTION









endk) = N() or k

end = keN[m] where

kend


end


endeN [m1]


GH3

8(1)











r









FP 4

Full Paper










050160

r [5] cor-


and to HI = (08 12) 1014 GeV






43

42

)(3

8

3

8

cc

GVGVH



22

6a

ac or

432

4

2

2

2 )(3

6

ccM

cV

a

a

c Plank

(2)

][61 2

2

2

2

m

c

H




2

PlanckM

cG

(3)



2

c


length Mc

lCompton


GlPlanck

when M = MPlanck



L =

ecBWhere

22

3

4242

1

4

8

4

82

ec

cec

G

c

c

G

l

F

c

G

R P

L

(4)

Now we have

eB

G

ecBc

c

G

R

2

4

82 3

42

(5)


GM

ecB

GM

ecBc

c

G

Reraction

2

int

22

4

42 8

82

(6)


eraction

= Bpair

N

particles




Or ][6 2

22 m

eBcH

(61)


That with GeVVTBGeV

1137

111010][1071 re-

sults ][10721 252

2

m

R or H = 5 1035 [s] or H1 =


FP 5

Full Paper

If B22GeV


If we use ][102 42

1510TB

GeV H1 = 15 1029 [m]











leave = k

endeN results

kend_M1

= kleave_M1

eN (7)

or )(10][101052 211

1_

51



Hend

kend

= 1 and aleave

= 1

for ][10871 271

1_ mrH monopole

ComptonMleave

with N = 51 re-

sults kleave_M1

= 7 102 [m] and 21

4

_ 10

1093

end

endCMBend H

ka



as[910]

2

_

2

0_

2

0

1)(

)(

)()()(

CMBend

leave

CMBend

leaveleave

PMF

endCMB atB

ta

tatBBtB (8)


4 1012 GeV is

][1066)(

)( 47

2

0

22 CNE

c

VE

e

C

leave

(9)

Bleave


=B



CMBend Hkl




with N



the end of aend



monopol =


= lp =


THE MATTER CREATION


FP 6

Full Paper







Nkk entryreCMB N

entryreCMB ekk 11

kCMB

= kre-entry

eN N() = 51Or k

re-entryk

CMB = eN




=V

lockeda

end = 274208 = 119GeV with N = 39






TABLE 1


100E-02 250E-05 390 180E-27 100E+10 110E-15 250E-03 256E-05 142E+34

100E+05 250E-05 390E+09 180E-27 100E+03 700E-18 250E-10 256E-05 142E+20

100E+06 260E-05 380E+10 180E-27 100E+02 700E-17 260E-11 153E+18

100E+09 260E-05 370E+13 180E-27 100E-01 700E-14 260E-14 153E+12

100E+15 250E-05 390E+19 180E-27 100E-07 700E-08 250E-20 256E-05 142E+00

100E+21 250E-05 390E+25 180E-27 100E-13 700E-02 250E-26 142E-12

180E+25 250E-05 700E+29 180E-27 560E-18 120E+03 140E-30 430E-21

FP 7

Full Paper

due of BPMF

at CMB time is

0

2

0

3

02952][0510

8

3

rad

Bc

eF CMB

(10)



lC



LC








)()2(

3

1323

)(

1 1ln)(4

1)(

tjgTp

jj

T

gg

T etgpxddtd

dWCpf (11)

)(cos12

)(12

1 ttC

)(

3cos1

2

)(12

32 ttC


end 104 the


T = 3 C





R = (EEcr)2 (c4)(83)1 exp(E

crE) (12)



ecmEcr32 (13)

TABLE 2


100E+09 860E+08 115E+00 100E-08 214E+02 115E-08 860E-01 399E+18

180E+14 860E+14 280E-01 100E-02 510E+01 200E-03 481E+00 129E+17

180E+21 130E+21 139E+00 180E+04 178E+02 200E+04 720E-01 156E+18

180E+25 860E+24 208E+00 100E+08 119E+02 200E+08 480E-01 692E+17




end see TABLE 1 V a

end = 4


monopol a

end = 1011 26 109 = 262GeV


FP 8

Full Paper


= 85 1082 [m3

s] where C = 71 1019 [m]


end = 4 1012 [GeV] 169 106 [J] gener-



B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38




Compton 047 1 pair



pairsVRN matter

ew

MMpairs




aend








end0030][1061 the










FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 3

Full Paper

INTRODUCTION









endk) = N() or k

end = keN[m] where

kend


end


endeN [m1]


GH3

8(1)











r









FP 4

Full Paper










050160

r [5] cor-


and to HI = (08 12) 1014 GeV






43

42

)(3

8

3

8

cc

GVGVH



22

6a

ac or

432

4

2

2

2 )(3

6

ccM

cV

a

a

c Plank

(2)

][61 2

2

2

2

m

c

H




2

PlanckM

cG

(3)



2

c


length Mc

lCompton


GlPlanck

when M = MPlanck



L =

ecBWhere

22

3

4242

1

4

8

4

82

ec

cec

G

c

c

G

l

F

c

G

R P

L

(4)

Now we have

eB

G

ecBc

c

G

R

2

4

82 3

42

(5)


GM

ecB

GM

ecBc

c

G

Reraction

2

int

22

4

42 8

82

(6)


eraction

= Bpair

N

particles




Or ][6 2

22 m

eBcH

(61)


That with GeVVTBGeV

1137

111010][1071 re-

sults ][10721 252

2

m

R or H = 5 1035 [s] or H1 =


FP 5

Full Paper

If B22GeV


If we use ][102 42

1510TB

GeV H1 = 15 1029 [m]











leave = k

endeN results

kend_M1

= kleave_M1

eN (7)

or )(10][101052 211

1_

51



Hend

kend

= 1 and aleave

= 1

for ][10871 271

1_ mrH monopole

ComptonMleave

with N = 51 re-

sults kleave_M1

= 7 102 [m] and 21

4

_ 10

1093

end

endCMBend H

ka



as[910]

2

_

2

0_

2

0

1)(

)(

)()()(

CMBend

leave

CMBend

leaveleave

PMF

endCMB atB

ta

tatBBtB (8)


4 1012 GeV is

][1066)(

)( 47

2

0

22 CNE

c

VE

e

C

leave

(9)

Bleave


=B



CMBend Hkl




with N



the end of aend



monopol =


= lp =


THE MATTER CREATION


FP 6

Full Paper







Nkk entryreCMB N

entryreCMB ekk 11

kCMB

= kre-entry

eN N() = 51Or k

re-entryk

CMB = eN




=V

lockeda

end = 274208 = 119GeV with N = 39






TABLE 1


100E-02 250E-05 390 180E-27 100E+10 110E-15 250E-03 256E-05 142E+34

100E+05 250E-05 390E+09 180E-27 100E+03 700E-18 250E-10 256E-05 142E+20

100E+06 260E-05 380E+10 180E-27 100E+02 700E-17 260E-11 153E+18

100E+09 260E-05 370E+13 180E-27 100E-01 700E-14 260E-14 153E+12

100E+15 250E-05 390E+19 180E-27 100E-07 700E-08 250E-20 256E-05 142E+00

100E+21 250E-05 390E+25 180E-27 100E-13 700E-02 250E-26 142E-12

180E+25 250E-05 700E+29 180E-27 560E-18 120E+03 140E-30 430E-21

FP 7

Full Paper

due of BPMF

at CMB time is

0

2

0

3

02952][0510

8

3

rad

Bc

eF CMB

(10)



lC



LC








)()2(

3

1323

)(

1 1ln)(4

1)(

tjgTp

jj

T

gg

T etgpxddtd

dWCpf (11)

)(cos12

)(12

1 ttC

)(

3cos1

2

)(12

32 ttC


end 104 the


T = 3 C





R = (EEcr)2 (c4)(83)1 exp(E

crE) (12)



ecmEcr32 (13)

TABLE 2


100E+09 860E+08 115E+00 100E-08 214E+02 115E-08 860E-01 399E+18

180E+14 860E+14 280E-01 100E-02 510E+01 200E-03 481E+00 129E+17

180E+21 130E+21 139E+00 180E+04 178E+02 200E+04 720E-01 156E+18

180E+25 860E+24 208E+00 100E+08 119E+02 200E+08 480E-01 692E+17




end see TABLE 1 V a

end = 4


monopol a

end = 1011 26 109 = 262GeV


FP 8

Full Paper


= 85 1082 [m3

s] where C = 71 1019 [m]


end = 4 1012 [GeV] 169 106 [J] gener-



B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38




Compton 047 1 pair



pairsVRN matter

ew

MMpairs




aend








end0030][1061 the










FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 4

Full Paper










050160

r [5] cor-


and to HI = (08 12) 1014 GeV






43

42

)(3

8

3

8

cc

GVGVH



22

6a

ac or

432

4

2

2

2 )(3

6

ccM

cV

a

a

c Plank

(2)

][61 2

2

2

2

m

c

H




2

PlanckM

cG

(3)



2

c


length Mc

lCompton


GlPlanck

when M = MPlanck



L =

ecBWhere

22

3

4242

1

4

8

4

82

ec

cec

G

c

c

G

l

F

c

G

R P

L

(4)

Now we have

eB

G

ecBc

c

G

R

2

4

82 3

42

(5)


GM

ecB

GM

ecBc

c

G

Reraction

2

int

22

4

42 8

82

(6)


eraction

= Bpair

N

particles




Or ][6 2

22 m

eBcH

(61)


That with GeVVTBGeV

1137

111010][1071 re-

sults ][10721 252

2

m

R or H = 5 1035 [s] or H1 =


FP 5

Full Paper

If B22GeV


If we use ][102 42

1510TB

GeV H1 = 15 1029 [m]











leave = k

endeN results

kend_M1

= kleave_M1

eN (7)

or )(10][101052 211

1_

51



Hend

kend

= 1 and aleave

= 1

for ][10871 271

1_ mrH monopole

ComptonMleave

with N = 51 re-

sults kleave_M1

= 7 102 [m] and 21

4

_ 10

1093

end

endCMBend H

ka



as[910]

2

_

2

0_

2

0

1)(

)(

)()()(

CMBend

leave

CMBend

leaveleave

PMF

endCMB atB

ta

tatBBtB (8)


4 1012 GeV is

][1066)(

)( 47

2

0

22 CNE

c

VE

e

C

leave

(9)

Bleave


=B



CMBend Hkl




with N



the end of aend



monopol =


= lp =


THE MATTER CREATION


FP 6

Full Paper







Nkk entryreCMB N

entryreCMB ekk 11

kCMB

= kre-entry

eN N() = 51Or k

re-entryk

CMB = eN




=V

lockeda

end = 274208 = 119GeV with N = 39






TABLE 1


100E-02 250E-05 390 180E-27 100E+10 110E-15 250E-03 256E-05 142E+34

100E+05 250E-05 390E+09 180E-27 100E+03 700E-18 250E-10 256E-05 142E+20

100E+06 260E-05 380E+10 180E-27 100E+02 700E-17 260E-11 153E+18

100E+09 260E-05 370E+13 180E-27 100E-01 700E-14 260E-14 153E+12

100E+15 250E-05 390E+19 180E-27 100E-07 700E-08 250E-20 256E-05 142E+00

100E+21 250E-05 390E+25 180E-27 100E-13 700E-02 250E-26 142E-12

180E+25 250E-05 700E+29 180E-27 560E-18 120E+03 140E-30 430E-21

FP 7

Full Paper

due of BPMF

at CMB time is

0

2

0

3

02952][0510

8

3

rad

Bc

eF CMB

(10)



lC



LC








)()2(

3

1323

)(

1 1ln)(4

1)(

tjgTp

jj

T

gg

T etgpxddtd

dWCpf (11)

)(cos12

)(12

1 ttC

)(

3cos1

2

)(12

32 ttC


end 104 the


T = 3 C





R = (EEcr)2 (c4)(83)1 exp(E

crE) (12)



ecmEcr32 (13)

TABLE 2


100E+09 860E+08 115E+00 100E-08 214E+02 115E-08 860E-01 399E+18

180E+14 860E+14 280E-01 100E-02 510E+01 200E-03 481E+00 129E+17

180E+21 130E+21 139E+00 180E+04 178E+02 200E+04 720E-01 156E+18

180E+25 860E+24 208E+00 100E+08 119E+02 200E+08 480E-01 692E+17




end see TABLE 1 V a

end = 4


monopol a

end = 1011 26 109 = 262GeV


FP 8

Full Paper


= 85 1082 [m3

s] where C = 71 1019 [m]


end = 4 1012 [GeV] 169 106 [J] gener-



B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38




Compton 047 1 pair



pairsVRN matter

ew

MMpairs




aend








end0030][1061 the










FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 5

Full Paper

If B22GeV


If we use ][102 42

1510TB

GeV H1 = 15 1029 [m]











leave = k

endeN results

kend_M1

= kleave_M1

eN (7)

or )(10][101052 211

1_

51



Hend

kend

= 1 and aleave

= 1

for ][10871 271

1_ mrH monopole

ComptonMleave

with N = 51 re-

sults kleave_M1

= 7 102 [m] and 21

4

_ 10

1093

end

endCMBend H

ka



as[910]

2

_

2

0_

2

0

1)(

)(

)()()(

CMBend

leave

CMBend

leaveleave

PMF

endCMB atB

ta

tatBBtB (8)


4 1012 GeV is

][1066)(

)( 47

2

0

22 CNE

c

VE

e

C

leave

(9)

Bleave


=B



CMBend Hkl




with N



the end of aend



monopol =


= lp =


THE MATTER CREATION


FP 6

Full Paper







Nkk entryreCMB N

entryreCMB ekk 11

kCMB

= kre-entry

eN N() = 51Or k

re-entryk

CMB = eN




=V

lockeda

end = 274208 = 119GeV with N = 39






TABLE 1


100E-02 250E-05 390 180E-27 100E+10 110E-15 250E-03 256E-05 142E+34

100E+05 250E-05 390E+09 180E-27 100E+03 700E-18 250E-10 256E-05 142E+20

100E+06 260E-05 380E+10 180E-27 100E+02 700E-17 260E-11 153E+18

100E+09 260E-05 370E+13 180E-27 100E-01 700E-14 260E-14 153E+12

100E+15 250E-05 390E+19 180E-27 100E-07 700E-08 250E-20 256E-05 142E+00

100E+21 250E-05 390E+25 180E-27 100E-13 700E-02 250E-26 142E-12

180E+25 250E-05 700E+29 180E-27 560E-18 120E+03 140E-30 430E-21

FP 7

Full Paper

due of BPMF

at CMB time is

0

2

0

3

02952][0510

8

3

rad

Bc

eF CMB

(10)



lC



LC








)()2(

3

1323

)(

1 1ln)(4

1)(

tjgTp

jj

T

gg

T etgpxddtd

dWCpf (11)

)(cos12

)(12

1 ttC

)(

3cos1

2

)(12

32 ttC


end 104 the


T = 3 C





R = (EEcr)2 (c4)(83)1 exp(E

crE) (12)



ecmEcr32 (13)

TABLE 2


100E+09 860E+08 115E+00 100E-08 214E+02 115E-08 860E-01 399E+18

180E+14 860E+14 280E-01 100E-02 510E+01 200E-03 481E+00 129E+17

180E+21 130E+21 139E+00 180E+04 178E+02 200E+04 720E-01 156E+18

180E+25 860E+24 208E+00 100E+08 119E+02 200E+08 480E-01 692E+17




end see TABLE 1 V a

end = 4


monopol a

end = 1011 26 109 = 262GeV


FP 8

Full Paper


= 85 1082 [m3

s] where C = 71 1019 [m]


end = 4 1012 [GeV] 169 106 [J] gener-



B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38




Compton 047 1 pair



pairsVRN matter

ew

MMpairs




aend








end0030][1061 the










FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 6

Full Paper







Nkk entryreCMB N

entryreCMB ekk 11

kCMB

= kre-entry

eN N() = 51Or k

re-entryk

CMB = eN




=V

lockeda

end = 274208 = 119GeV with N = 39






TABLE 1


100E-02 250E-05 390 180E-27 100E+10 110E-15 250E-03 256E-05 142E+34

100E+05 250E-05 390E+09 180E-27 100E+03 700E-18 250E-10 256E-05 142E+20

100E+06 260E-05 380E+10 180E-27 100E+02 700E-17 260E-11 153E+18

100E+09 260E-05 370E+13 180E-27 100E-01 700E-14 260E-14 153E+12

100E+15 250E-05 390E+19 180E-27 100E-07 700E-08 250E-20 256E-05 142E+00

100E+21 250E-05 390E+25 180E-27 100E-13 700E-02 250E-26 142E-12

180E+25 250E-05 700E+29 180E-27 560E-18 120E+03 140E-30 430E-21

FP 7

Full Paper

due of BPMF

at CMB time is

0

2

0

3

02952][0510

8

3

rad

Bc

eF CMB

(10)



lC



LC








)()2(

3

1323

)(

1 1ln)(4

1)(

tjgTp

jj

T

gg

T etgpxddtd

dWCpf (11)

)(cos12

)(12

1 ttC

)(

3cos1

2

)(12

32 ttC


end 104 the


T = 3 C





R = (EEcr)2 (c4)(83)1 exp(E

crE) (12)



ecmEcr32 (13)

TABLE 2


100E+09 860E+08 115E+00 100E-08 214E+02 115E-08 860E-01 399E+18

180E+14 860E+14 280E-01 100E-02 510E+01 200E-03 481E+00 129E+17

180E+21 130E+21 139E+00 180E+04 178E+02 200E+04 720E-01 156E+18

180E+25 860E+24 208E+00 100E+08 119E+02 200E+08 480E-01 692E+17




end see TABLE 1 V a

end = 4


monopol a

end = 1011 26 109 = 262GeV


FP 8

Full Paper


= 85 1082 [m3

s] where C = 71 1019 [m]


end = 4 1012 [GeV] 169 106 [J] gener-



B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38




Compton 047 1 pair



pairsVRN matter

ew

MMpairs




aend








end0030][1061 the










FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 7

Full Paper

due of BPMF

at CMB time is

0

2

0

3

02952][0510

8

3

rad

Bc

eF CMB

(10)



lC



LC








)()2(

3

1323

)(

1 1ln)(4

1)(

tjgTp

jj

T

gg

T etgpxddtd

dWCpf (11)

)(cos12

)(12

1 ttC

)(

3cos1

2

)(12

32 ttC


end 104 the


T = 3 C





R = (EEcr)2 (c4)(83)1 exp(E

crE) (12)



ecmEcr32 (13)

TABLE 2


100E+09 860E+08 115E+00 100E-08 214E+02 115E-08 860E-01 399E+18

180E+14 860E+14 280E-01 100E-02 510E+01 200E-03 481E+00 129E+17

180E+21 130E+21 139E+00 180E+04 178E+02 200E+04 720E-01 156E+18

180E+25 860E+24 208E+00 100E+08 119E+02 200E+08 480E-01 692E+17




end see TABLE 1 V a

end = 4


monopol a

end = 1011 26 109 = 262GeV


FP 8

Full Paper


= 85 1082 [m3

s] where C = 71 1019 [m]


end = 4 1012 [GeV] 169 106 [J] gener-



B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38




Compton 047 1 pair



pairsVRN matter

ew

MMpairs




aend








end0030][1061 the










FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 8

Full Paper


= 85 1082 [m3

s] where C = 71 1019 [m]


end = 4 1012 [GeV] 169 106 [J] gener-



B = A (14)

Vt

AE

(15)

Thus

][1064)(

)( 30

2

0

22 CNE

c

VE

e

C

and E

cr = 38




Compton 047 1 pair



pairsVRN matter

ew

MMpairs




aend








end0030][1061 the










FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 9

Full Paper







= (Ez0 Bx0)



E

E

E

BcEBc

VcJWKB expcoth)(4

2

0

(17)









(18)


(19)


CNEe

cmEc

as from




][1064)(

)(30

2

0

2

2 CNc

Emonopol

Compton

monopol

monopol

(20)


monop E



3

0

22

2

0

22

)(

)(

cmV

c

VE

e

C

(21)





endendmatter aHV

][10 310 sm JWKB




Cpairsnecessary NV



that it is a very



JWKB

VCompton



day) becomes V Vcr


monopole




max and the n p





FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 10

Full Paper



THE SPECTRUM AT CMB



netic field

8

2

0

effB(22)


LC




[J] BPMF



0

)()()(l

l

lm

ml

ml YrCrV (23)




6

200

][ 8 a

BT EM

(24)



)()()(where n






a




c)1 1016 cm where T

c 100GeV is





lt 10nGs

and nB lt 24)


FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 11

Full Paper



PMF








0



2

0

0

28

3

B

eF (25)



= B(t

) is




0 109


0) a2 (t

0)




PMF = B

CMB 15 1012 [T]




FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 12

Full Paper






CONCLUSIONS






REFERENCES














FP 13

Full Paper









FP 13

Full Paper









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