According to Our theory of Bhattacharya's Model of Universe- [Theory of Rupak Bhattacharya and Professor Pranab Bhattacharya], "......The Universe consists of now large masses of matter and antimatter organized into galaxies, stars, and planets. According to this view about construction of the universe, the matter and antimatter should co-exist at some early stage in the Big Bang. For it only if the temperature was high enough it should be possible for nucleons and anti nucleons to rub their shoulders with each other’s. Simple theory suggests that they should after ward annihilate each other’s with production of photons and neutrinos. To account a universe in which matter and anti matter were separated in separate galaxies it is therefore necessary to explain how such a separation could have taken place at very early stage in the development of primeval fire ball?
It is one of the most fundamental questions in cosmology. The question of existence of antimatter in significant quantities in the present universe. in our galaxy! The question of whether antimatter had an equal role with matter in making up galaxies? In a contemporary Para diagram of Grand Unified theories & Gauge Theories (String Theories) these questions are related to the questions of nature of charge, parity variations at high energy. The questions of separating matter and antimatter, proton and antiproton, helium and anti helium. The symmetry between matter and antimatter [ i.e baryon symmetry in the cosmology ] that was once observed at accelerator had forced many scientists and astrophysicist to think that there existed also a similar balance in the universe of matter and antimatter at most early phase of the universe. But we don’t see or don’t find antimatter in our observable universe. Our observable universe is made of matter only. Why? Antimatter annihilate with matter. If that was so, then there would not be any matter to make up galaxies, our observable universe. Was the matter and antimatter mixed together? Or was the matter and antimatter were in two separate compartments? If the later was true, then we must have another Universe. That universe was made of antimatter.(Authors Theory). However universe consisted of large mass of matter and antimatter- standard BigBang model says so. On this view, in authors opinion, is that matter and antimatter must co-existed all together at some early stage of Big Bang.? For it ,only when the temperature was high enough, it was possible for nucleons and anti nucleons, quarks and anti quarks to rub their shoulders with each others, and simple theory suggest that these rubbing resulted annihilation with production of photons and neutrinos. H. Alfeven etal ( Alfeven .H – Rev. Mod. Physics Vol37; P652; 1965) did bring out a mechanism which permitted region of matter and antimatter to co-exist together in our galaxy, even without appreciable mixing. Otherwise in early state of universe [when a homogeneous universe] there would have to be also a mechanism for separating matter and antimatter so that galaxies were formed in clusters. Then the big questions are 1) what was the mechanism for separation of matter and antimatter? 2) Where went the bulk of antimatter? 3) Does the antimatter stars or antimatter galaxies were capable of nuecleosynthesis? Does the antimatter stars or antimatter galaxies at all exists that Mr. Rupak Bhattacharjee suggested in his concept of anti Universe? 5) If at all exists what is the way of communication from our universe made of matter to a Universe made of antimatter?Pranab Kumar- Does the universe contain also anti galaxies- a myth or a reality? Space Light Vol 4 P7-13; 1998). Defining a region of mass MR as a typical unit of matter and antimatter According to the conventional Big Bang model of the universe, there were small excess of baryon particles (~1 in 109) over the anti particles in the early stage of evolution of universe. At that time the thermal energy “KT” exceeded the rest energy mpc2 of baryon particles. It was to the excess amount of KT, for that we see the present existence of matter in the universe. So as the thermal energy dropped bellow mc2, the baryons and anti baryons started annihilated and there leaving just excess of baryons intact. Let us consider a model of universe that was initially filled up with the thermal radiations. Its expansion was described by the scale factor R (t) which behaved approximately like t -1/2 while the temperature varied likeR-1. For the early stage of the universe, the effect of space curvature was negligible. It was known in the history of such a model, the model can be divided in to several periods according to content of thermal radiation. The Hadronic (KT≥100mev), Leptonic (KT≥ 1mev) and Radiative (KT≥300K). Super imposed on division, on evolution of baryons, we have to consider also other periods. The separation period (KT≥350Mev), annihilation period (KT≥25Kev) and coalescence period (T>300K). There was some interest in 1970s regarding the existence of the antimatter in the universe. Stiegman. G in 1969 ( Stiegman. G. – Nature Vol224; P447; 1969) showed that if the space time were filled with equal mixture of matter and antimatter then gamma ray flux that resulted from nucleon and anti nucleon annihilation would be far above the observed limit. But there were much possibilities that matter and antimatter existed quite separately in large regions consisting solely of one charecteristic type, perhaps in the form of galaxies and anti galaxies (Bhattacharjee Rupak and Bhattacharya separation, one can assume that a process probably existed in the early Big Bang model. This process could however separated matter and antimatter into contiguous regions at some early epoch of Big Bang. We can also assume that the regions remain separated until and after decoupling would prevent collision between them, owing to the effect of radiation. After decoupling, the material contained in several such regions started to collapse and coalesce. The collapse and coalescence led to an annihilation of particles from regions to anti regions. The rate at which coalescence occurred, depended on the scale of density fluctuation. Defining a blob of mass MB, as the largest commonly occurring density fluctuation, existing at decompleing, we know from galaxy forming theory that the minimum mass of the blob was ~107MO jeans mass. It is also well known that any gravitational bound group of blob will eventually undergo collapse. But due to the expansion of the universe, the collapse would not proceed rapidly until the density contracted. The collision cross section for blob contained in such group became very high once collapse set in. So if both matter and antimatter were present in early universe, one must expect a considerable amount of annihilation to occur at the time of collapse. SO There must be a separation period for matter and antimatter. In the separation period the particles and antiparticles [Quarks and antiquarks/ R particles and Anti R particles/ Neutrinos and anti neutrinos/ Gluons and antigluons] separated spatially as a consequence of their statistical repulsion. This was initially induced by fluctuation (Bhattacharjee Rupak and Bhattacharya Pranab Kumar- Does universe contain antigalaxies – a myth or a reality? – Space Light Vol4; P7-13; 1998). One can compute the size as “δ,” as the individual condensation containing an excess of nucleon and anti- nucleon reached during 10-5 S of the period. The total baryonic number in that period was 1028. Near the end of separation period the universe was filled up with emulsion of nucleons and anti nucleons with a topical size δ=3x10-4c.m. The next came annihilation period. When temperature fell bellow the critical temperature (T) the particles and antiparticles [quarks and anti quarks] started to annihilate. The annihilate process was then controlled by diffusion so that densities D and N (Nucleons) and N-(anti nucleons) satisfy the equation as given below
δΝ/δΤ=DV-2N-αN N-, δN-/δΤ=δV-N-αNN- (Bhattacharjee Rupak). At the end of this period a typical fraction of 10-8 or more nucleon survived. They were still in the form of emulsion with a typical size of 105cm and with a typical mass of 1010 gram( 100,000,000, kilogram) within a sphere of radius. This was however very far from a galactic mass. During annihilation the process first gave birth chiefly to pions and through their decay to high-energy photons, electrons, positrons, and neutrinos successively. The transfer of momentum by photons and electrons produces an annihilation pressure at boundary between matter and antimatter. To find the behavior of matter and antimatter, which were probably in contact through a common boundary, the effect of high-energy photons and leptons was a dominant feature, because these particles exerted a very strong pressure and kept the heating system on. Radiative pressure was very dominant, so that pressure due to heating tended to balance annihilation. With the possible exception of cosmic gumma rays, observation yielded essentially no information on the relative amount of matter and antimatter beyond our solar system. What the observation told us was that matter and antimatter are rarely ,if ever found together. What was the mechanism that matter and antimatter were then separated?. Consider a gas of proton, antiproton, electron and positron, which is sufficiently diluted and then annihilation can not be neglected there. In general, such a gas will be situated in a magnetic field say “B” , in a Gravitational field say “G” and in a electromagnetic field of flux “F”. Each of the fields will then be assumed static and homogenious. In particular length scale for variation in “B” must be large enough that particle drifts arising from magnetic in homogenetics are also negligible. The protons and antiprotons will be much more strongly influnced by Gravitational field than by Radiation field. As well as spiraling around the magnetic line of forces the heavy particles will therefore have a drift velocity Vh= mPxgxB/qB2 ,where mP is the proton mass, q is the particle charge,.[Bhattacharjee Rupak & Bhattacharya Pranab Kumar – Does the Universe contain also anti galaxies- a myth or a reality- Space Light; Vol4 P7-13;1998] .Because of their small mass, and larger scattering cross section, the electrons and positrons will feel much weaker Gravitational force due to radiation pressure. It is however to be noted that just electric current through gas does not heavily result in seperation of charges, and the opposed drift of matter need not produce an actual matter- antimatter seperation. On the other hand , matter and antimatter in an isolated cloud or in extended medium, with an appropriate field configeration should achieve some degree of seperation. Because , proton and antiproton ,electron and positron fluxes will not be equal in general. There will be some seperation of charge leading to an electrical field “ E “ and ExB drift. As ExB drift increases, the heavy particles acquire an inertia which tends to remove the original difference between proton and antiproton and electron and positron fluxes. So the big question appeared before us What happened to these antimatter?. After the Plank epoch, when the age of the universe was t ≤10-43S and the temperature of the universe was T≥109Gev , we can be sure enough , that the interactions between the matter and the antimatter at their first quark level or Between R+/ R_[R particle level] became unimportant. This was because of that rate for gravitational interaction was much less then the expansion rate of the universe. Although the interactions between matter and antimatter particles kept each of them separately in a thermal equlibrium and thus probably Two world were created. These Two world did not feel each others existence at very microscopic level. During the primordial nucleosynthesis of the early universe, which started 1S after the initial Big Bang moment, the yield of the Big Bang depended on the expansion rate of the Universe. The expansion density PT= P+Ps by R0/R= [(δπGN/3)(P+Ps)]1/2 where P and Ps= density of matter and Antimatter, R= Cosmic scale factors. During this early epoch the universe was radiation dominated with P=g (π2/30)T4 where g counts the effective number of degrees of freedom particles (Rupak Bhattacharjee). The temperature of the particle world and that of anti particle world were not the same. The inflation occurred in the two worlds in both the sector but not necessarily simultaneously. The inflation involved was a random event in the nucleation of a bubble or in the formation of a fluctuation region. At the beginning of the inflation the universe was in false vacuum state for both the world. The bubble nucleated for one world, first say for antimatter world. As the bubble grew exponentially in physical size, both the temperature of matter and antimatter decreased exponentially. At this time the ratio of entropy remained constant. When the antiparticle vacuum energy was converted into radiation, the antiparticle temperature raised and entropy decreased. Eventually a bubble of fluctuation region formed for the matter world within the antimatter bubble. During the second phase of inflation, new bubble grew exponentially. When the vacuum energy of ordinary matter world converted into radiation, the temperature of particle world raised to a temperature, which was exponentially larger than the temperature of the antiparticle world. Thus the entropy was reduced further. To an exponentially small value and the matter dominated the visible universe. According to Big Bang model of Universe, there was small excess of matter then antimatter (~1 in 109) in the early stage of evolution, when the thermal energy KT exceeded the rest of energy mpc2. The baryons and anti baryons annihilated and then leaving just excess of baryon intact. From a fit of nucleon-nucleon scattering theory, the evidence of π, η7, ω, ρ, and mesons can divide the nucleon and anti nucleon scattering amplitude. There are bound states of nucleon and anti nucleon pairs, which can be identified with mesons π, ρ, ω, and η7. Such a situation in which some particles appear as bound states and act as agent for Special Forces. Dashen .R (Dashen. R Physics Review-Vol187; P345; 1969) summarized a basic formula relating to Gibb’s potential Ω to it’s value Ω0 for free particles and to collision matrix –
S Ω =Ω0 -KT/2π∫δEc-E/KT trace [clogs (E) ee-∑u1n1]. Analysis of this result drives a phase transition at a temperature of KT of the order of 350 Mev. Above this temperature, nucleon and anti nucleon tended to remain separately from each other’s.
Professor Pranab Kumar Bhattacharya
See E. Book "our Universe started in a Big Bang Gospel or Just Be?"
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