A Magnetic-Monopole-Based Mechanism to the formation of the Hot Big Bang Modeled Universe
aa r X i v : . [ phy s i c s . g e n - ph ] M a r March 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906
Modern Physics Letters Ac (cid:13)
World Scientific Publishing Company
A Magnetic-Monopole-Based Mechanism to the formation of the HotBig Bang Modeled Universe ∗ Qiu-He Peng and Jing-Jing Liu † Department of Astronomy, Nanjing University, Nanjing, Jiangshu 210000, China College of Marine Science and Technology, Hainan Tropical Ocean University, Sanya, Hainan572022, [email protected]
Chi-Kang Chou National Astronomical Observatory, Chinese Academy of Sciences, Beijing, 100000, China
Received (Day Month Year)Revised (Day Month Year)There are some particle physics theories that go beyond the so-called ”standard cosmo-logical model” to predict the existence of magnetic monopoles (MMs). The discovery ofmagnetic monopoles would be an incredible breakthrough in high-energy physics. Theexistence of MMs in the early Universe has been speculated and anticipated from GrandUnified Theory. If MMs exist, the inverse powers of the unification mass will not sup-pressed the baryon number violating effects of grand unified gauge theories. Therefore,MM catalyzing nucleon decay is a typical strong interaction. This phenomenon is dueto the boundary conditions that must be imposed on the core of MM fermion fields. Wepresent a possible mechanism to explain the formation of the Hot Big Bang Cosmology.The main ingredient in our model is nucleon decay catalyzed by magnetic monopoles (i.e.,the Rubakov-Callan effect). It is shown that Hot Big Bang developed naturally, becausethe luminosity due to the Rubakov-Callan effect is much greater than the Eddingtonluminosity (i.e., L m > L Edd ). Keywords : Cosmology; Rubakov-Callan effect; Magnetic Monopole.PACS Nos.: 97.60.Bw, 26.30.Jk, 23.40.-s.
1. Introduction
On the standard model of the Hot Big Bang Cosmology, the early Universe is de-picted by extrapolating back to a hot and dense initial state of Planck length and ∗ This work was supported in part by the National Natural Science Foundation of China undergrants 11565020, 11965010, and the Counterpart Foundation of Sanya under grant 2016PT43,2019PT76 the Special Foundation of Science and Technology Cooperation for Advanced Academyand Regional of Sanya under grant 2016YD28, the Scientific Research Starting Foundation for515 Talented Project of Hainan Tropical Ocean University under grant RHDRC201701, and theNatural Science Foundation of Hainan Province of China under grant 118MS071, 2019RC239. † Corresponding author. 1 arch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906 Peng et al.,
Planck time derived according to the uncertainty principle. In 1992, the origin of theBig Bang was discussed by Thakur(1992). They developed a singularity-free modelof the universe within the framework of the Friedmann-Lemaitre-Robertson-Walkercosmology. Then the Big Bang model on its origin and development have been in-vestigated by Alpher(1999). The standard cosmological model and some relatedissues have been discussed by some astronomers and scholars(e.g., ). Recently, amacroscopic view of the standard cosmological model was given by Ignat’ev et al.,(2018). Khlopov (2018) also discussed the standard models of particle physics andcosmology. Their results showed that the modern Standard cosmological model ofinflationary Universe and baryosynthesis is deeply involved particle theory beyondthe Standard model. Brian.(2018), also redefined the standard model of cosmol-ogy. However, the formation of the Hot Big Bang itself has not been investigated.In this paper, we will present a possible mechanism to explain the formation ofthe Hot Big Bang Cosmology. The main ingredient in our model is nucleon decaycatalyzed by magnetic monopoles (MMs).The experiment tells us that the magnetic north and south poles cannot be di-vided into magnetic monopoles (MMs), i.e., isolated magnetic charges. Petrus (1269)discussed this issue in the 13-th century. There are strong theoretical reasons to be-lieve that MMs should exist. Hooft and Polyakov (1974) showed that MMs arean inevitable prediction of Grand Unified Theory of elementary particle interac-tions,
12, 13 and the same is generally true for more modern theories of everything,such as superstring theory. Therefore, it would be an incredible breakthrough ifpeople could find a MM particle in high-energy physics.Although magnetic monopole has not been discovered, it plays an important rolein the theoretical research of high energy physics.For example, magnetic monopolesprovide powerful theoretical tools for studying properties of strongly coupled non-abelian canonical field theory, such as quantum chromodynamics, and in particularits supersymmetric variantsAlthough MMs have not been found, they play an important role in theoreticalresearch of high-energy physics. For example, the MMs give powerful theoreticaltools for exploring properties of strongly coupled non-Abelian gauge field theory,such as quantum chromodynamics, and in particular its supersymmetric variants. Therefore, the study MMs and its related problems (e.g., search for MMs) is a hottopic in the field of high-energy physics and astrophysics.
The existence of MMs in the early Universe has been speculated and anticipatedfrom grand unification. The goal of such theories is to unity the strong, weak, andelectromagnetic interaction in terms of quarks and leptons within the framework ofa gauge field theory based on non-Abelian symmetry group. These theories maketwo startling predictions: namely, the instability of the proton, and the existence ofstable and heavy MMs.Most of physicists believe that the existence of MMs had been ruled out by ex-periments. However, experiments only indicated that the flux of MMs on the Earthis too low to be observed. We summarize some predictions from the model of super-arch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906
A Magnetic-Monopole-Based Mechanism to the formation of the Hot Big Bang Modeled Universe massive object with MMs, which match up with recent astronomical observationsquantitatively. They may signal the presence of MMs in supermassive objects, suchas one at the Galactic Center. In 2001, we discussed ultra-high-energy cosmic raysfrom supermassive objects with MMs, as well as high-energy radiation from quasars,active galactic nuclei, and the Galaic Center with MMs.
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Very recently, someissue on MMs were illustrated by our group (e.g.,
22, 27, 28
We discussed a series ofimportant but puzzling physical mechanisms concerning the energy source, variouskinds of core-collapse supernovae explosion mechanisms during central gravitationalcollapse in astrophysics. The puzzles of possible association of γ -ray burst with grav-itational wave perturbation, the heat source for the molten interior of the core ofthe Earth and the cooling of white dwarfs were also investigated. We have madeuse of the estimations for the space flux of MMs and nucleon decay induced byMMs, called the Rubakov-Callen (RC) effect , to obtain the luminosity due tothe RC effect and also investigated other problems related to supernova explosion(e.g., ).Rubakov (1981, 1988) and Callan(1983) have shown that the fermion wavefunction is literally sucked into the core because of the potential between the s -waveof a fermion and that of a MM. Due to sucking of the s -wave, the catalysis crosssection saturates the uncertainty bound: h σv i ≈ E − F , where E F is the Fermi energy.The actual catalysis section depends on the Grand Unified Theory. In SU(5), weknow M + m → M + π − + e + or M + p → M + π + e + . It is then expected that MMcatalysis has great potential to produce astrophysical fireworks, and applications ofthe R − C effect to quasars and active galactic nuclei have also made remarkableachievements.
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In this paper, we will use the R-C effect to explain the formation of the HotBig Bang. We want to propose a possible mechanism to describe how the Big Bangdeveloped. The main ingredient in our model is the MMs catalyzing nucleon decaywith strong cross section of interaction.
2. The Astronomical evidence for both the absence of black holesand the existence of MMs at our Galactic Center
Eatough et al.(2003) reported a measurement of a strong magnetic field aroundthe supermassive black hole at the centre of the Galaxy. We know that at r =0 .
12 pc near the Galactic center (hereafter GC), the minimum value of outwardradial magnetic field is
B > B Alphen ∼ .
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Considering the RC effect,the MMs may catalyze nucleon decay, which can beused as an energy source. However, this dilemma in the GC may be naturallyarch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906 Peng et al., solved by our super-massive star model with
MMs . At r = 0 .
12 pc near the GC,the observed outward radial magnetic field strength (i.e.,
B > is in goodagreement with our theoretical predictions. In our model, at least three predictions were quantitatively confirmed by sbuse-quennt observations. Firstly, the GC emits large numbers of positrons at a rateabout 10 e + / sec or so. This is consistent with the high-energy astrophysical ob-servations. Secondly, at r = 0 .
12 pc of the super-massive object core, the radialmagnetic field strength produced by the
MMs condensed is about B ≈ (10 ∼ Finally, for the super-massive stellar object at the GC, we predicted theirsurface temperatures to be about 123 K, corresponding to a frequency of 10 Hz(at the sub-millimeter range). This frequncy predicted is quite close to the observedvalue (i.e., 10 Hz). The implications of the facts that these predictions were quantitatively con-firmed by astronomical observations are: 1) There is no supermassive black hole atthe center of our galaxy; 2) These are the evidences for the existence of MMs.
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We would like to declare that the astronomical observations are really the phys-ical experiments in cosmic space, although MMs have not been detected by thephysicists up to now.
3. An united model of supernova explosion driven by MMs
Regarding the RC effect as a source of energy, MMs can catalyze the decay ofnucleons. Therefore we propose a unified model supernova explosions caused byMMs. The main idea is as follows. Taking the nucleon decay induced by MMs inparticle physics and making estimation for the space flux of MMs, we can obtain aformula to estimate the luminosity due to the RC effect.According to the RC luminosity formula, we discuss the issue that the supernovaexplosion would develop just when its luminosity is much greater than the Edding-ton’s luminosity due to RC effect in the star. We present a unified treatment for allkinds of core-collapse supernovae (e.g., SNII, SNIb, SNIc, Ultra-luminous supernova(ULSN)). We will also discuss the gamma-ray burst generation mechanism in detailin our paper. Those weak or/and dark explosions of supernova will be also naturallyexpressed by our idea due to the fact that its RC luminosity is just greater thanthe Eddington’s luminosity of the star.The very important result is that no matter how massive the supernova is, aneutron star (NS) will be formed after supernova explosion due to the R − C effectby a small amount MMs remained in the new born NS. However, this theory doesnot apply to black holes.Besides, both the heat source for the core of the Earth and the energy sourceneeded for the white dwarf interior are also solved by the same treatment using theRC effect. The possible association of the short gamma-ray burst detected by theFermi gamma-ray Burst Monitoring Satellite (GBM) and the LIGO gravitationalarch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906 A Magnetic-Monopole-Based Mechanism to the formation of the Hot Big Bang Modeled Universe wave event (GW150914) may be reasonably explained by our unified model. In thepresent paper, based on the same idea, we propose further a model of hot big bangcosmology driven by MMs without initial singularity of the Universe .
4. The standard cosmology
A most fundamental feature of the standard cosmology is the expansion of the Uni-verse. The expansion, discovered in the 1920’s. led to Hubble’s law and played afundamental role in observational cosmology. Almost all the galaxy spectra mea-sured by observers in the world are redshifted, illustrating the universality of theexpansion with redshift z . For a smaller distance, we can also interpret it as asimple Doppler effect by the redshift z . Thus, we have z = λ − λ λ = vc , (1)where the speed of light is much larger than the secession velocity of galaxies. λ and λ are the original radiation wavelength and the observed wavelength, respectively.However, for a larger distance, Eq.(1) must be replaced by1 + z = p v/c p − v/c . (2)For large recession velocities of the distant galaxies, the Hubble’s law may bewritten as v = Hd. (3)In a homogeneous isotropic Universe, the expansion rate is constant in time andthe recession time of the distant galaxies may be obtained as t = dv = 1 H ≈
138 ( billion year ) , (4)where 0 . ≤ h ≤ H ≈ − Mpc − , and H − is the age of the Universe. Theredshift of galaxies varies linearly with the distance for z <<
1. In addition, thehomogeneous cosmology predicts the existence of the black-body cosmic microwavebackground radiation and the abundances of helium and the primordial nucleosyn-thesis of other elements. These are the great achievements of the Lemaˆıtre model and the pioneering theories of the Hot Big Bang. Now we describe briefly some of the relevant physics for Universe expansion.The radius of the expanding Universe R satisfies dR ( t ) /dt >
0. For homogeneousuniverse expansion, we have ρR =constant, and T R =constant, where ρ denotesthe matter density, T is the background temperature. The radiation energy densityis denoted by aT , where a is the Stephen Boltzmann constant, and the rest massenergy density is denoted by ρc , then the ratio is written asΓ = aT ρc . (5)arch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906 Peng et al.,
We note that the early Universe could be dominated by matter or radiation.The matter in the Universe consists of both ordinary visible matter that can bedetected and dark matter that is invisible. The radiation is mainly comes from thecosmic background microwave radiation. For convenience, we present the followingrelevant data at the present time ρ M = (0 . − . ρ c = (03 . − . × − g cm − , (6) E M = ρ M c = (0 . − . × − erg cm − , (7) E r = aT R , T R = 2 . K, a = 7 . × − erg cm − K − , (8) E r = 4 . × − erg cm − , E << E . (9)where the superscript (0) represents the present moment, ρ M is the average densityof matter in the Universe at the present moment, ρ c is the critical density of thecorresponding material at the boundary between the closed Universe model and theopen Universe model, E M represents the average energy density of matter in theUniverse at the present moment, E r represents the energy density of the radiationfield in the Universe, T R represents the temperature of the cosmic radiation field(the cosmic background), and a is the radiation constant.We note that both the radiation energy density and the matter density decreasewith the time during the universe expansion. At the same time, radiation fromgalaxy spectra are all redshifted during the expansion. The density of radiant en-ergy decays much faster with time than the density of matter, and then radiationis dominated in the early Universe. About several thousand years after the cre-ation of the Universe, it was the dividing line between the radiation-dominated andmaterial-dominated ages. At the dividing line, we have Γ = 1 , aT r = ρ m c .Our whole universe was once in a very small volume, higher material density andtemperature. When the temperature is higher than 10 K or more, the universe wasproduced by Hot Big Bang. This is from astronomical observations (now the universeis expanding), we obtain that the early universe must be in the hot and dense state.However, people don’t know realistically the physical reason of early universe byhot big bang (i.e., the outbreak mechanism of early universe). The physical reasonof the Hot Big Bang theory of the Universe has never been discussed up to nowreally.There are many speculations about the Hot Big Bang. For example, when thetime extrapolates from the present moment back to the initial singularity ( t = 0),we have R → , ρ → ∞ , T → ∞ , so the Universe will arise singularity. Theseare very interesting theoretical speculations such as the baby Universe, and theUniverse wave function proposed by Hawking based on the uncertainty principle,but the physical reason for the formation of the Hot Big Bang itself has never beeninvestigated. Using the R − C effect we will propose a possible mechanism for theHot Big Bang in the next section.arch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906 A Magnetic-Monopole-Based Mechanism to the formation of the Hot Big Bang Modeled Universe
5. An oscillating model of the Universe
In history, some oscillating Universe models had been proposed, but the physicalreason of the Universe expansion during the oscillation has not been discussed. Thecontinuum and continuum-particle models for both oscillating and ever-expandingmodel universes are considered, with the consequences of various interactions be-tween the components being traced and the connection with the irreversibility ofoscillating models noted by Landsberg & Reeves. Similar to the models above, ourmodel of the Universe is also the oscillating model between the expansion phase dueto the Hot Big Bang and the contracting phase due to the gravitational attraction,but we propose the physical mechanism for the Hot Big Bang of the Universe inthis paper.At the present time t , the radius of the Universe is R , baryon density ρ , andthe cosmic background temperature T , then at a later time t during the contractingphase, the corresponding radius of the Universe R , the baryon density ρ , and thecosmic background temperature T are given by RR = ( ρρ ) − / , (10) TT = ( RR ) − = ( ρρ ) / , . (11)It is generally estimated and believed that there are 2 × galaxies. Everygalaxy is roughly the size of over Milky galaxy with 10 stars, then the totalnumber of stars in the Universe is about 2 × − × . The mass of the sunis 2 × g, then the total mass of the Universe of the baryons is 2 . × g andthe total number of the baryons is 10 . If the content of the magnetic monopolesof the same polarity contained in the Universe is ζ ≡ N m /N B = 10 − ( ζ/ζ up ), here N m and N B are the number of magnetic monopole and baryons, respectively. Here ζ up is the Parker upper limit ζ up ≈ − . So the total number of the magneticmonopoles of the same polarity contained in the Universe may be estimated to be N m = 10 ( ζ/ζ up ). The magnetic monopoles in the high temperature baryon plasmaare strongly compressed and moving very fast toward the center via electromagneticinteraction.The R − C luminosity produced due to catalyzing nucleon decay by the MMs isgiven
27, 46 as L M = π r c n m n B h σv T i m B c = N m n B h σv T i m B c , = 10 ( n B n nuc )( ζζ up )( σ (RC)10 − cm ) ergs / s . (12)When the total mass of the Universe is compressed into supermassive body, thecorresponding Eddington luminosity is given by L Edd = 10 ( MM J ) ≈ ergs / s (13)arch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906 Peng et al.,
If the whole Universe is compressed such that( n B n nuc )( ζζ up )( σ (RC)10 − cm ) > − , (14)i.e., ( n B n nuc ) > − [( ζζ up )( σ (RC)10 − cm )] − , (15)Then L m > L Edd and the whole Universe must violently explode outward leadingnaturally to the Hot Big Bang. From Eq.(10), we my estimate the radius of theUniverse at the Hot Big Bang to be R ≈ × − R [( ζζ up )( σ (RC)10 − cm )] / , (16)i.e., R ≈ × − [( ζζ up )( σ (RC)10 − cm )] / pc , (17)where we have used the present radius of the Universe R ≈ pc and the presentaverage baryon density given from Eq.(6). The temperature at the Hot Big Bangalso can be estimated to be TT ≈ × [( ζζ up )( σ (RC)10 − cm )] − / , (18)where T = 2 .
6. Summary and Discussions
In this paper, we have used the R − C effect to explain the formation of the Hot BigBang and presented a possible mechanism that can delineate the details of how theBig Bang developed. The main ingredient in our description of the Hot Big Bangis MMs catalyzing nucleon decay with strong interaction cross section. Our resultsshowed that whether the Universe is in an accelerating expansion phase needs fur-ther discussion. On the other hand, the direct observational evidence on the darkenergy is also lost by the observational error analyses of SNIa. Our model of the HotBig Bang is obtained in terms of the Rubakov-Callan luminosity and no other the-oretical arguments or anticipation are required. In our model, the expansion phasemay finally end followed by the contraction phase due to gravitational attraction.The popular view of indirect observational evidence for the accelerating expan-sion of the universe comes from the comparison of theoretical simulations of thearch 23, 2020 0:25 WSPC/INSTRUCTION FILE mpla201906 A Magnetic-Monopole-Based Mechanism to the formation of the Hot Big Bang Modeled Universe accelerating expansion of the universe and the deviation observation of the isotropyof the cosmic microwave background temperature using WMAP satellite observa-tion data. The popular idea of indirect observational evidence for the acceleratingexpansion of the Universe comes from the comparison of theoretical simulations ofthe Universe accelerating expansion and the Universe with the observational dataof WMAP satellite for the deviation observation of the isotropy of the cosmic mi-crowave background temperature using WMAP satellite observation data. In recentyears, the results of some research groups are in line with our ideas. For instance,Nielsen et al. (2016) analyzed recent observations of a group SNIa . Their con-clusions did not support the accelerating expansion of the Universe. More recently,David et al. (2017) also did not support the idea of the accelerating expansion ofthe Universe. As is well known, the 2011 Nobel prize awarded to three astronomers (i.e.,Riess, Schmist and Perlmutter), because they proposed the accelerating expansionof the Universe, which was confirmed by astronomical observations. The methodof this paper is based on Guy et al. (2007). All these researches are based on theSNIa standard candle assumption. In fact, although the average error provided bythe UNION2 was only 0.16 m because 685 SNIa completed big samples. We usedthe observational data of the 685 SNIa from UNION2 to reexamine and analyzethe average error and found that the average total observational error of SNIais obviously greater than 0 . m , so we can not decide whether the Universe isaccelerating expansion or not .
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In our oscillating model of the Universe, theexpanding matter is gradually decelerating due to the Newtonian attraction duringthe Universe expansion process. When the kinetic energy of the expanding matteris lower than the potential energy of the whole Universe relative to the expandingmatter, the Universe expansion contracts.
Acknowledgments
We would like to thank Prof. Daniel Wang, Prof. Y.F. Huang, Prof. P.F. Chenand Prof. J. L. Han for their help to inform us some new information of observa-tions. This work was supported in part by the National Natural Science Foundationof China under grants 11565020, 11965010, and the Counterpart Foundation ofSanya under grant 2016PT43, and 2019PT76, the Special Foundation of Scienceand Technology Cooperation for Advanced Academy and Regional of Sanya un-der grant 2016YD28, the Scientific Research Starting Foundation for 515 TalentedProject of Hainan Tropical Ocean University under grant RHDRC201701, and theNatural Science Foundation of Hainan Province of China under grant 118MS071.
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