Magnetized Bianchi Type III String Universe with Time Decaying Vacuum Energy Density Λ

Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using the technique given by Letelier (Phys. Rev. D 28:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations the expansion θ in the model is considered as proportional to the eigen value s² ₂\sigma^{2}_{~2} of the shear tensor s^j _i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. It is observed that the particle density and the tension density of the string are comparable at the two ends and they fall off asymptotically at similar rate. But in early stage as well as at the late time of the evolution of the universe we have two types of scenario (i) universe is dominated by massive strings and (ii) universe is dominated by strings depending on the nature of the two constants L and ℓ. The value of cosmological constant Λ for the model is found to be small and positive which is supported by the results from recent supernovae Ia observations. Some physical and geometric properties of the model are also discussed.     

Klein-Gordon thermal equation for a planck gas

In this paper the quantum hyperbolic equation formulated in our earlier paper [Found. Phys. Lett. 10, 599 (1997)] is applied to the study of the propagation of the initial thermal state of the universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced,V _P = ħ/8t_P = 1.125 10¹⁸ GeV, wheret _P is a Planck time. For the barrier heightV <V _P , the master thermal equation isthe modified telegrapher’sequation, and for barrier heightV >V _P the master equation is theKlein- Gordon equation. The solutions of both type equations for Cauchy boundary conditions are discussed.     

Bianchi type III models with anisotropic dark energy

The general form of the anisotropy parameter of the expansion for Bianchi type-III metric is obtained in the presence of a single diagonal imperfect fluid with a dynamically anisotropic equation of state parameter and a dynamical energy density in general relativity. A special law is assumed for the anisotropy of the fluid which reduces the anisotropy parameter of the expansion to a simple form (D μ H^-2V^-2{\Delta\propto H^{-2}V^{-2}}, where Δ is the anisotropy parameter, H is the mean Hubble parameter and V is the volume of the universe). The exact solutions of the Einstein field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power-law volumetric expansions. The isotropy of the fluid, space and expansion are examined. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models and evolves into the well-known cosmological constant in the model for exponential volumetric expansion.     

Inflationary Scenario in Bianchi Type I Space-Time

Inflationary scenario in Bianchi Type I space-time is discussed. To get the deterministic model of the universe, it has been considered that the energy-momentum tensor of particles ∼T ⁴, almost vanishes in the course of expansion of universe and total energy-momentum tensor reduces to vacuum stress tensor. This leads to a∼e ^Ht where a is scale factor and H the Hubble constant and effective potential V(φ)=constant where φ is Higg’s field and n is a constant. The physical and geometrical aspects of the model in the context of inflationary scenario are also discussed.     

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.     

Axially Symmetric Bianchi Type-IX Inflationary Universe in General Relativity

Axially symmetric Bianchi type-IX space-time in the presence of mass less scalar field with a flat potential V is investigated. To get an inflationary universe, we have considered a flat region in which potential V is constant. Some physical and kinematical properties of the model are discussed.     

Bimetric general relativity and cosmology

A modification of the general relativity theory is proposed (bimetric general relativity) in which, in addition to the usual metric tensorg _v describing the space-time geometry and gravitation, there exists also a background metric tensor _v The latter describes the space-time of the universe if no matter were present and is taken to correspond to a space-time of constant curvature with positive spatial curvature (k=1). Field equations are obtained, and these agree with the Einstein equations for systems that are small compared to the size of the universe, such as the solar system. Energy considerations lead to a generalized form of the De Donder condition. One can set up simple isotropic closed models of the universe which first contract and then expand without going through a singular state. It is suggested that the maximum density of the universe was of the order ofc ^{5 –1} G ^–210⁹³ g/cm³. The expansion from such a high-density state is similar to that from the singular state (big bang) of the general relativity models. In the case of the dust-filled model one can fit the parameters to present cosmological data. Using the radiation-filled model to describe the early history of the universe, one can account for the cosmic abundance of helium and other light elements in the same way as in ordinary general relativity.     

The gravitational field in the wave zone I. The radiating terms of the metric tensor

We consider an asymptotically flat space-time generated by a perfect fluid source of compact spatial support. Using the de Donder gauge conditions, the Einstein equations are reduced to a new form of Poisson-type equations. A formal iterative scheme is set up to solve these equations by expanding the components of the metric tensor in powers ofc ^–1. The coefficient of each power ofc ^–1 depends on the asymptotically retarded timeu andx, y, z and satisfies a Poisson-type equation. Assuming asymptotic flatness the solution is carried out in the first orders. The results are explicit expressions of the metric up to orderc ^–4 in terms of the source functions. These expressions hold over all space-time. A further expansion in powers ofr ^–1 gives the first terms of the metric that contribute to gravitational radiation.     

Probability diffusion in non-Markhovian,non-Gaussian molecular ensembles: A theoretical analysis and computer simulation

A theoretical generalisation of the Fokker/Planck equation for atomic and molecular diffusion is compared with the results of a molecular dynamics simulation of a triatomic molecule ofC _2v symmetry. The molecular dynamics results are non-Markhovian and non-Gaussian in nature, markedly so in the case of the centre of mass linear velocityV. This may be ascertained by simulating the long-time limit of the three dimensional kinetic energy autocorrelation function <V ²(t)V ²(0)>/<V ²(0)V ²(0)>, which falls well below the theoretical Gaussian value of 3/5. By expressing the Mori continued fraction as a multidimensional Markhovian chain of differential equations and expressing this in turn as a non-Gaussian probability-diffusion equation of the Kramers/Moyal type it is possible to account for the simulation results in a qualitative fashion.     

Multi-component KdV hierarchy,V-algebra and non-Abelian toda theory

We prove the recently conjectured relation between the 2 × 2-matrix differential operatorL = ² –U and a certain nonlinear and nonlocal Poisson bracket algebra (V-algebra), containing a Virasoro subalgebra, which appeared in the study of a non-Abelian Toda field theory. In particular, we show that thisV-algebra is precisely given by the second Gelfand-Dikii bracket associated withL. The Miura transformation that relates the second to the first Gelfand-Dikii bracket is given. The two Gelfand-Dikii brackets are also obtained from the associated (integro-) differential equation satisfied by fermion bilinears. The asymptotic expansion of the resolvent of (L -) = 0 is studied and its coefficientsR _l yield an infinite sequence of Hamiltonians with mutually vanishing Poisson brackets. We recall how this leads to a matrix KdV hierarchy, which here are flow equations for the three component fieldsT,V ⁺,V ^– ofU. ForV ^± = 0, they reduce to the ordinary KdV hierarchy. The corresponding matrix mKdV equations are also given, as well as the relation to the pseudo-differential operator approach. Most of the results continue to hold ifU is a Hermitiann ×n matrix. Conjectures are made aboutn ×n-matrix,mth-order differential operatorsL and associatedV _(n,m)-algebras.     

Photoproduction of Boson Pairs in a Radiation-Dominated Universe. II

The average number of pairs of scalar massive particles produced by a decaying photon in a radiation-dominated universe is calculated. The dependence of the expression obtained on the energy of the initial photon is investigated. Numerical estimates are found for the formative time t ₀ of the processes of decay of photons in an early universe and for the total number N ^(±) _{out pair} of photoproduced scalar pairs. The estimates are: t ₀ 3 min and N ^(±) _{out pair} 10³¹·N ^(±) ₀(0), where N ^(±) ₀(0) is the total number of pairs produced from the vacuum of a free quantized field.     

General relativity in a (2+1)-dimensional space-time: An electrically charged solution

We have found a static electrically charged solution to the Einstein-Maxwell equations in a (2+1)-dimensional space-time. Studies of general relativity in lower dimensional space-times provide many new insights and a simplified arena for doing quantum mechanics. In (2+1)-dimensional space-time, solutions to the vacuum field equations are locally flat (point masses are conical sigularities), but when electromagnetic fields are presentT ^ab O and the solutions are curved. For a static chargeQ we find andds ²= –(kQ ² /2)In(r _c /r)dt ² + (2/kQ ²[ln(r _c /r)]^–1 dr ² +r ² d ² wherer _c is a constant. There is a horizon atr =r _c like the inner horizon of the Reisner-Nordström solution. We have produced a Kruskal extension of this metric which shows two static regions (I and III) withr <r _c and two dynamical regions (II and IV) withr>r _c . A spacelike slice across regions I and III shows a football-shaped universe with chargeQ at one end and –Q at the other. Slices in the dynamical regions (II and IV) show a cylindrical universe that is expanding in region II and contracting in region IV. Electromagnetic solutions to the Einstein-Maxwell field equations in lower dimensional space-times can be used to provide new insights into Kaluza-Klein theories. In terms of the Kaluza-Klein theory, for example, electromagnetic radiation in a (2+1)-dimensional space-time is really gravitational radiation in the associated (3+1)-dimensional Kaluza-Klein space-time. According to Kaluza Klein theory the absence of gravitational radiation in (2+1)-dimensional space-time implies (correctly) the absence of electromagnetic radiation in (1+1)-dimensional space-time.     

Fermions and expanding universe

The coupledDirac-Einstein equations for a homogeneous isotropic space-time forbid aclosed universe but lead to the standard cosmological model for aflat universe. Therefore only theopen universe is left as a nontrivial situation. There some of the desired cosmological effects emerge in a natural way:inflation, creation ex nihilo, etc.     

Higher dimensional cosmologies

Einstein equations are derived for D-dimensional space-time that spontaneously compactify to the product M⁴ × Π_{i = 1}^α M^d_i in which the metric is taken to be of the generalized Robertson-Walker form. Cosmological solutions for these equations are studied with power law, oscillatory and exponential behaviour for the D-dimensional Einstein-Maxwell, N = 2, D = 10 and N = 1, D = 11 supergravity models. In the Einstein-Maxwell case the presence of a cosmological constant forces the extra dimensions to be static. Nevertheless, it is possible to find solutions with vanishing effective 4 dimensional cosmological constant with an expanding 4-dimensional space-time. In the supergravity models the requirement of having compact extra dimensions restricts the solutions to have expansion only in the 4-dimensional space-time. Matter contribution is added to the energy-momentum tensor in an attempt to find new solutions.     

On the origin of cosmic rays and the value of fundamental length

It is suggested that the physical mechanism responsible for the acceleration of cosmic rays is due to the stochastic (or fluctuational) structure of space-time at small distances. A method of introducing fluctuations in a conformally flat Riemannian space-time metric due to ultrahigh energy particles is presented, from which a nonlinear dynamics of particles and equations for the electromagnetic field are obtained. The former admits the acceleration mechanism for cosmic-ray particles and the extreme energy increases during the evolution of the Universe. In our model the energy of the cosmic-ray particle and its radius (the effective Schwarzschild), the age of the universe, and the value of the fundamental length are connected with one another and are determined by a unified formula, Einstein's relation for the relativistic particle energy. It allows one to define experimentally the value of the fundamental length, which is l=1.56×10 ^–33 cm for the maximum proton energy observed in cosmic rays. The problem of the energy spectrum of the cosmic rays and the ratio of intensities of the electron component to the proton component at the same energy level are also discussed.On leave of absence from the Academy of Sciences, Mongolian People's Republic, Ulan-Bator, Mongolia.     

Five Dimensional Cosmological Models in General Relativity

A five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and Λ. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as G∼t ^−(1−ω) whereas the variation for the cosmological constant follows as Λ∼t ⁻², L ~ ([(R)\dot]/R)²\Lambda \sim (\dot{R}/R)^{2} and L ~ [(R)\ddot]/R\Lambda \sim \ddot{R}/R where ω is the equation of state parameter and R is the scale factor.     

Hestenes' Tetrad and Spin Connections

Defining a spin connection is necessary for formulating Dirac's bispinor equation in a curved space-time. Hestenes has shown that a bispinor field is equivalent to an orthonormal tetrad of vector fields together with a complex scalar field. In this paper, we show that using Hestenes' tetrad for the spin connection in a Riemannian space-time leads to a Yang-Mills formulation of the Dirac Lagrangian in which the bispinor field Ψ is mapped to a set of SL(2,R)× U(1) gauge potentials F_α^K and a complex scalar field ρ. This result was previously proved for a Minkowski space-time using Fierz identities. As an application we derive several different non-Riemannian spin connections found in the literature directly from an arbitrary linear connection acting on the tensor fields (F_α^K, ρ). We also derive spin connections for which Dirac's bispinor equation is form invariant. Previous work has not considered form invariance of the Dirac equation as a criterion for defining a general spin connection.