Bianchi Type I Universe Models with Irreversible Matter Creation

The effects of matter creation on the evolution and dynamics of an anisotropic Bianchi type I space–time is investigated in the framework of open thermodynamic systems theory. For a cosmological fluid obeying a Zel'dovich type equation of state =p and with particle creation rate proportional to the square of the mean Hubble function and to the energy density of matter, respectively, the general solution of the gravitational field equations can be expressed in an exact parametric form. Generically all models start from a non-singular state. In the large time limit anisotropic cosmological models with particle creation rate proportional to the square of the Hubble function end in an isotropic flat (inflationary or non–inflationary) phase while models with particle source function proportional to the energy density of matter do not isotropize, ending in a Kasner–type geometry.     

Cosmological models with constant deceleration parameter in Brans-Dicke theory

A detailed study of cosmological models with constant deceleration parameterq is undertaken in the framework of Brans-Dicke theory. These models are divided into two categories: (i) singular models with expansion driven by big-bang impulse, (ii) non-singlar models with expansion driven by creation of matter particles. Prigogine's hypothesis of creation of matter out of gravitational energy is analysed and extended to BD cosmology. To accommodate the creation of new particles, the universe is regarded as an open thermodynamical system and the energy conservation equation is modified with the incorporation of a creation pressure termp _c in the energy-momentum tensor . The exact solutions of the field equations of BD theory with are obtained using the power law relation=KR , which leads to models with constantq. The behaviour of the solutions is investigated for different range of values ofa. The role played by the BD scalar field and creation of matter particles in the expansion of the universe is investigated. It is found that one particular model with constantq has exponential expansion.     

Cosmological Models with Matter Creation in Open Thermodynamic Systems

Regarding the universe as an open thermodynamicsystem, the creation of matter/radiation particles outof gravitational energy is investigated. A new class ofFRW models with creation of matter is obtained and their properties are examined. A suitablechoice of the particle number density function n(t) =(A/t)^3/2 leads toinflationary solutions during the particle creationphase; subsequently the universe enters the Friedmann era. It is found that fora physically acceptable solution > 1. Acomparative study is made for = 4/3, 2, 8/3, and10/3 in order to find a viable model of theuniverse.     

A Class of Planar Discrete Velocity Models for Gas Mixtures

We present a method for the construction of a simple class of physically acceptable planar discrete velocity models (DVMs) for binary gas mixtures. We want five conservation laws (no more, no less) with binary collisions. We first consider a collision with a particle at rest and different possibilities for the three other particles. We associate other particles and find semisymmetric qv _i models with q=7, 9, 11, 13 and 15, symmetric with respect to the two coordinate axes, but not to an exchange between the two axes. In order to avoid spurious mass conservation relations for the species without particle at rest, we find, for the two coordinate axes, that the tips of the momenta of the particles must be on two intervals parallel to one axis with opposite values on the other. There remain some physically acceptable q=9 (the smallest) and 11, 13, 15 models (adding multiple collisions for some others). Second, we construct the associated symmetric models qv _i^qv _i, which are superpositions of the qv _i model and another ^qv _i, rotated by /2. The possible previous defect of the spurious mass invariant for qv _i is transmitted to the symmetric one. We explain another defect coming from qv _i and ^qv _i having only one common particle, then spurious invariants exist for the momentum conservations along the two axes. We get four physically acceptable symmetric 17v _i (and three intermediate semisymmetric 13v _i models) and one 25v _i model superposition of two 11v _i and two 15v _i models (other acceptable symmetric 11v _i, 13v _i, and 25v _i models exist with multiple collisions).     

Walks in Rigid Environments: Continuous Limits

We derive the continuous limits of kinetic equations for spatially discrete systems generated by the motion of a particle in a random array of scatterers. The type of scatterer at a vertex changes after the r-th visit of the particle to this vertex, where 1r. Such deterministic cellular automata belong to the class of walks in rigid environments. It has been recently shown that they form the simplest dynamical models with sub-diffusive, diffusive and super-diffusive behaviour. Due to the deterministic character of the dynamics, the continuous limit equations obtained for these models are of the Euler type rather than the diffusive type. The reason for that is that the fluctuations in these models are relatively small and there is no scaling of probabilities similar, for example, to those in the case of biased random walk, that can account for them.     

Particle masses in the early universe: Matter and entropy productions

This article deals with the particle and entropy productions in the early universe, which is regarded as a thermodynamically open system in the sense of Prigogine, by incorporating the epoch dependence of elementary particle masses. The epoch dependence of particle masses for some of the Robertson-Walker (RW) universes appears as a consequence of previous considerations of the hadronic matter extension in the inner space-time regarded as anisotropic and Finslerian in character. The nature of the evolution of the early universe has been discussed in the framework of the modified thermodynamic energy conservation law and the new mass formula apart from the other Einstein equation. The trivial solution of these equations is the usual inflationary stage of the early universe, whereas the matter-dominated RW universe appears as the nontrivial solution. It is shown that at the transition epocht=10^–23 sec the creation phenomenon stops and the usual cosmology of the radiation era follows with Pascal's equation of state. This model can also account for the observed specific entropy per baryon of the present universe and the generation of the large value ofK ^–1, whereK=Gm _p ² /c,m _p being the mass of the proton.     

Particle creation by a black hole as a consequence of the Casimir effect

Particle creation by a black hole is investigated in terms of temperature corrections to the Casimir effect. The reduction of the Hawking effect to more familiar effects observed in the laboratory enables us to reveal the mechanism of particle creation. The blackbody nature of the Hawking radiation is due to the interaction of virtual particles with the surface of a cavity formed by the Schwarzschild gravitational field potential barrier. These particles are squeezed out by the contraction of the potential barrier and appear to an observer atJ ⁺ as the real blackbody ones.     

A physical characterization of the adiabatic vacuum in Robertson-Walker universe

As the red shift shows no sign of oscillatory behavior in an expanding universe we postulate that the energy _k of a scalar field does not oscillate in such a universe. In the massive case, expanding the differential equation for _k in mass powers, we find that the nonoscillatory solution coincides with the adiabatic solution up to them ⁶ order. We also demonstrate that this solution is unique for all the evolution of the universe with cosmological interest. Using the nonoscillatory solution as the one that defines the good vacuum state, we compute the particle and energy creation for a simple model of expanding universe. Both quantities turn out to be finite.     

Friedmann Cosmology with Matter Creation in Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f(R, T) (R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f(R, T)=R+2f(T) with “gamma-law” equation of state p = (γ?1)ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.     

Über die Amputierung der Vertexfunktionen instabiler Teilchen

The normalized form of the amputated vertex functions of an unstable particle is derived from the requirement that the general Ansatz (1) for the scattering amplitude of two stable particles with a resonance in the energy-variable is unitary in the energy interval below the threshold for three particle production. A Klein-Gordon equation for the unstable particle associated with the resonance is derived. The results a re applied to the creation of ⁺ and ⁰ mesons in inelastic scattering processes.     

SUSY and GUT threshold effects in SUSYSU(5) models

We study consequences of the threshold effects of supersymmetric (SUSY) and superheavy (GUT) particles to the gauge coupling unification condition in two specific supersymmetricSU(5) models, the minimal model and the missing doublet model with natural doublet-triplet splitting. We present a consistent treatment of theSU(2)×U(1) breaking mass terms in the SUSY particle threshold effects, as well as that of the top quark threshold effect, which have been ignored in previous works. The GUT threshold effects are constrained by the proton decay experiments and by some theoretical consistency conditions, but they are strongly model dependent. For example, under a certain assumption for the SUSY particle masses, the minimal model favors a large (>1 TeV) SUSY breaking scale or a high _s(m _z )(<0.12), whereas=" the=" missing=" doublet=" model=" allows=" a=" low="><1 tev)=" susy=" breaking=" scale=" for=" 0.11=">_s(m _z )>0.13. The consequences of these two models in the proton decay experiments are also briefly discussed.     

Cosmology with time-varyingG

It is shown that a Universe with a time-varying gravitational constantG necessarily implies creation if the rest mass of matter particlesm _p is constant. In this case, from Einstein's field equations, the conditions for energy-momentum propagation are ·(GT ^v ) from which matter and photon propagation equations are derived. Free matter particle propagation is not affected by creation that is given byGN _pm_p=const, whereN _p is the number of matter particles within a proper volume. This relation introduces explicitly the rest mass of the Universe into the field equations. Free photon propagation is affected by creation that is given byGT v R=const, whereN is the number of photons within a proper volume, which is the cosmic red shift law. Conservation of the cosmic background photon distribution determines photon creation asG ³ N ⁴ . The results are applied to the caseG t ^–1 equivalent toN _p ÷ t.It is found that at an aget=1, 0^–40 t _o, of the order light takes to travel a proton size, Planck's units become of the order of the proton's massm _p, sizer _p, and timer _p/c. Hence, matter particles at this age are quantum black holes. Evaporation of these quantum black holes at this age gives a background blackbody radiation that, red shifted to present timet ₀, gives the present cosmic microwave background.A cosmological model of the Friedmann type is constructed. The red shift versus distance relation is derived taking into account creation. Using a Hubble's constantH _obs=50 km sec^–1 Mpc^–1 and a deceleration parameterq _obs=1.0 the model is of the typek=1 and gives a present aget ₀=6.81×10⁹ yr, consistent with Uranium model ages. Thus, the three results for the age of the Universe, i.e., radioactive decay, Hubble's constant, and stellar evolution are brought together in this creation model. The matter-dominated era occurs fort>7.6×10^–3 t ₀, while the radiation-dominated era occurs for 7.6×10^–3 t _o>t>10^–40 t _o. The origin of the Universe is placed at this last limit, which is Planck's time at the corresponding G, consisting of quantum black holes at a temperature T_i=3×10¹¹K.     

Cosmological Models with Bulk Viscosity in the Presence of Adiabatic Matter Creation and with Variable G, c, and Λ

Some properties of cosmological models with a time variable bulk viscous coefficient in the presence of adiabatic matter creation and variable G, c, are investigated in the framework of a specifically flat FRW line element. We trivially find a set of solutions through Dimensional Analysis. In all the studied cases it is found that the behaviour of these "constants" is inversely proportional to the cosmic time. It is found that with the solution obtained our model verifies the principles of general covariance and Lorentz invariance. Finally we emphasize that the envisaged models are free of the horizon and entropy problem.     

Gravitational vacuum hypothesis and cosmology with variable particle number

We discuss a heurisitic model of gravitational vacuum as a set of virtual, radiating planckeons, particles with Planck size (L) and mass (/cL). Combined with Dirac's large number hypothesis, this gives the minimum universe scale factor valuea _min10^–13 cm, the strong interaction length (a = L just whena=a _min ). Taking this state as an initial one using standard quantum techniques, we consider particle creation by planckeons. Under some reasonable assumptions we obtain the present number of particles with nucleon mass close to observations,N 10⁸⁰. A criterion for gravitational stability of particles is formulated and some applications of the corresponding mass formula are considered. In particular, Fermi's weak interaction constant is expressed in terms ofa andL and a finite value for the neutrino mass is obtained.     

Quantum system in contact with a thermal environment: Rigorous treatment of a simple model

We study the quantum dynamics of a particle of massM in an external potentialV(Q), interacting with a simple model environment—a harmonic chain of 2N particles with massm and spring constantk. The classical version of this model was studied by Rubin and is equivalent to standard models of a particle interacting with a phonon bath. Settingm=m*/L andk=k*L, we prove that for a suitable class of potentialsV and initial states ₀, the time evolution of the massM particle converges, whenN andL , to the time evolution governed by the Quantum Langevin Equation (QLE) which has been found by Ford, Kac and Mazur. Furthermore we show that, for this class of potentials, the QLE has a unique solution for all positive times, such solution can be expressed as a convergent expansion in the deviation ofV(Q) from a harmonic potential. The equilibrium properties of the particle with massM can be expressed in terms of an integral, over path space, with a Gaussian measure which has mean zero and covariance proportional to ; where is the friction constant, andh is the Plancks' constant (divided by 2).Supported in part by AFOSR Grant No. 86-0010     

Semiclassical elementary particle models

Some simple models of elementary particles are discussed; they may be described as semiclassical, quark, shell models. Particles are assumed to be composed of spherical concentric charged shells. Three basic types of shell are allowed, quantum numbers are associated with each type such as to establish a quantum number correspondence between the shell types and the (p, n, ) quarks. Particles are identified through the quantum numbers of their constituent shells (quarks).The basic assumptions underlying the models considered are relationships between the electromagnetic energy associated with elementary particles (quark systems) and particle masses. The electromagnetic energy is represented classically; the models are semiclassical in that the shell radii are related to particle Compton wavelengths.Particle mass and magnetic moment formulas are derived, possible values for quark masses are suggested, and possible connections of the models considered with particle symmetry schemes are discussed.     

Cosmological Models in Barber's Second Self-Creation Theory

An attempt has been taken to solve the field equations of Barber's second self creation theory with a perfect fluid in an inhomogeneous anisotropic Locally rotationally symmetric Bianchi type I space-time where the metric potentials are arbitrary functions of x and t. Because of the mathematical complexities, for particular forms of metric potentials vacuum, Zeldovich and radiation models are determined. It is shown that -vacuum model does not exist with the above choice of metric potentials. Even though the geometrical structure of Zeldovich and radiation models are the same and reveal same physical behaviour but they are governed by different Barber's scalar.     

Creation of vector bosons by an electric field in curved spacetime

We investigate the creation rate of massive spin-1 bosons in the de Sitter universe by a time-dependent electric field via the Duffin–Kemmer–Petiau (DKP) equation. Complete solutions are given by the Whittaker functions and particle creation rate is computed by using the Bogoliubov transformation technique. We analyze the influence of the electric field on the particle creation rate for the strong and vanishing electric fields. We show that the electric field amplifies the creation rate of charged, massive spin-1 particles. This effect is analyzed by considering similar calculations performed for scalar and spin-1/2$1/2$ particles.     

Scalar particle with polarizability in a uniform external magnetic field

The model of a scalar structured particle is considered, which possesses polarizability in an external electromagnetic field. The expression for the 4-dimensional current density is found. The exact solution of the equations describing a scalar particle with polarizability in a uniform external magnetic field is obtained. Up to the terms of order O(H²), the energy spectrum can be formally obtained by the substitution of the particle mass in the expression for a pointlike scalar particle: mm–H²/2, where is the magnetic polarizability of the particle. It is shown that the rms radius of a trajectory can be obtained by the substitution of the charge in the well-known formula for a structureless scalar particle: ee(1{-H²/m)^1/2 (where is the electric polarizability).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 91–94, January, 1991.I thank A. I. L'vov for discussions.     

Spectral stochastic processes arising in quantum mechanical models with a non-L 2 ground state

A functional integral representation is given for a large class of quantum mechanical models with a non-L ² ground state. As a prototype, the particle in a periodic potential is discussed: a unique ground state is shown to exist as a state on the Weyl algebra, and a functional measure (spectral stochastic process) is constructed on trajectories taking values in the spectrum of the maximal Abelian subalgebra of the Weyl algebra isomorphic to the algebra of almost periodic functions. The thermodynamical limit of the finite-volume functional integrals for such models is discussed, and the superselection sectors associated to an observable subalgebra of the Weyl algebra are described in terms of boundary conditions and/or topological terms in the finite-volume measures.Supported by DFG, Nr. Al 374/1-2