On Expanding MACH-EINSTEIN Universes

The “telescopic” gravodynamics of the MACH -EINSTEIN -Doctrine gives expanding “MACH ian clouds” as world models. The universe becomes a closed system (according to the classical statistical mechanics) if and only if the total energy H of this cloud, i.e. its HAMILTON ian, vanishes. This cloud is the MACH ian equivalent to the EINSTEIN-de SITTER universe of general relativity (or of “NEWTON ian cosmology”). However, the MACH ian cloud with H = o describes a linearly expanding universe.     

Bianchi I型宇宙中矢量暴涨理论相关问题的研究

通过矢量暴涨理论,研究了与之相关的问题,特别是粒子生成对慢滚过程、相图以及各向异性的影响.计算结果表明,粒子生成对标量场的影响使得相图上出现一个峰,峰的方向不受初始条件和质量改变的影响.而对于矢量场,情况则不同,粒子生成对应的峰其方向会改变,这与质量的变化有关.相应地,体系的各向异性也会随之增强或减弱.各向异性的程度不仅决定于慢滚过程,还决定于慢滚后的粒子生成过程.粒子生成可以成为宇宙各向同性化的原因.     

Time evolution of the unstable two-fluid density fluctuations in Robertson-Walker Universes

We consider density fluctuations of a two-fluid model consisting of hydrogen plasma and radiation prior to the cosmic hydrogen recombination. As investigation method that of the dispersion relations is applied, which have been derived from the general-relativistic sound-wave equations taking into account the coupling between plasma and radiation carefully. We obtain growing unstable acoustic modes within the mass range 2 · 10⁶ M _⊙ < M < 6 · 10 ¹² M _⊙. In a second step the coupled differential equations for the amplitudes of the unstable modes are integrated numerically with respect to time where the integration extends from the initial time prior to the hydrogen recombination up to the present time. We find a significant increase of the amplitudes up to 4 orders of magnitude, if the Universe is described by a cosmological model with a positive cosmological constant (Λ ? 2,2 · 10^-56 cm^-2) and a positive curvature (Lemaître-Universe) without an essential amount of cold dark matter. We conclude that the existence of galaxies confirm these statements.     

Generation of Bianchi Type V Universes Filled with A Perfect Fluid

Assuming a perfect fluid distribution of matter Bianchi type Vspace-time is considered and using a new generation techniqueit is shown that the field equations are solvable for anyarbitrary cosmic scale function. Solutions for particularforms of cosmic scale functions are obtained, and thegeometrical and physical properties of these solutions discussed.     

On the REYNOLDS Stresses in Mean‒Field Hydrodynamics I. Incompressible Homogeneous Isotropic Turbulence

We consider an incompressible fluid undergoing turbulent motions. Using the methods of mean-field electrodynamics the relations between the REYNOLDS stresses and the mean velocity field are deduced in linear approximation. The homogeneous isotropic case is treated in more detail and we show that the effects can be described by a turbulent viscosity which proved to be positive in any case.     

Inflation in Bianchi type-IX Einstein-Cartan Cosmological Model

Within the framework of Einstein-Cartan theory with Weyssenhoff fluid, we investigate an inflation model for an anisotropic Bianchi type-IX cosmological model. The system of field equations is solved numerically and an inflation epoch is achieved. The general condition for the inflation to occur is also discussed. This anisotropic model evolves quickly towards to an isotropic one.     

Classical Matter Fields in Homogeneous Cosmological Models

The behaviour of classical massive scalar and vector fields as sources of homogeneous world models is examined. The consequence of the violation of the strong energy condition by the massive scalar field for the evolution of an cosmological model is discussed.     

Inflation and the Cosmic Microwave Background

I give a status report and outlook concerning the use of the cosmic microwave background anisotropies to constrain the inflationary cosmology, and stress its crucial role as an underlying paradigm for the estimation of cosmological parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mutual Potential of Homogeneous Polyhedra

The mutual gravitational potential between a pair of homogeneous polyhedra is expressed using an infinite series. The nested volume integrals are evaluated analytically and result in simple tensor expressions containing no special functions. However, complexity increases as O(6 ⁿ ), where n is the term degree. An alternate formulation due to Liebenthal is also presented.     

Extended Schubart Averaging

The purpose of this paper is the presentation of an integrator for the average motion of an asteroid in mean motion commensurability with Jupiter. The program is valid for any (p+q)/p mean motion commensurability (except whenq=0) and uses a double precision version of DE (Shampine and Gordon 1975) as propagator. The averaged equations of motion of the asteroid are evaluated in a non-singular way for any value of the eccentricities and the inclinations and the orbit of Jupiter is described by the most important terms in Longstop 1B (Nobiliet al. 1989). This integrator can be considered as an extension of the well known Schubart Averaging (Schubart 1978) in which Jupiter is moving on a fixed ellipse.     

Extended dust emission in NGC 7465

We present SCUBA 850-μm, JCMT  CO( J =2→1)  , B -band imaging and VLA H  i observations of the NGC 7465/4/3 group of galaxies. The 850-μm emission associated with NGC 7465 extends to at least ∼2 R ₂₅ and is well correlated with the H  i . We investigate a range of possible mechanisms by which dust beyond R ₂₅ may be heated to give the observed extended submillimetre emission. By modelling the dust heating by stars in two extreme geometries, we fail to find any reasonable star formation scenario that is consistent with both the 850-μm and optical data. Furthermore, we do not detect any  CO( J =2→1)  emission coincident with the extended dust and atomic gas as would be expected if significant star formation were occurring. We show that shock-heating of dust via cloud–cloud collisions in the stripped interstellar medium of NGC 7465 could be sufficient to explain the extended 850-μm emission and lack of optical emission in the stripped gas, and suggest that cloud–cloud collisions may be an important dust heating mechanism in gas-rich systems.     

Inflation and compactification from Galaxy redshifts?

The distribution of galaxies in the pencil-beam surveys of Broadhurstet al. which proved periodical across 8–10 consecutive steps in a flat dust model withq ₀=0.5 is found to reveal extended periodicity up to 16–17 phase-coherent steps, covering the total sample, in a flat, moderately inflationary model withq ₀=–0.5 (vacuum/dust ratio 2/1). In the latter model the vacuum component helps to reach the critical density and lengthens the expansion time-scale. It is shown that the explanation of the found periodicity as a consequence of space compactification as suggested by G. Paál twenty years ago in connection with apparent quasar periodicities is still possible.     

Homogeneous spheres with constant adriatic index

Compressible homogeneous spheres with constant adiabatic index γ were studied for their dynamical stability by Chandrasekhar and he found that for each value of u (≡ mass to size ratio), there is a value of γ = γ_c, such that for γ < γ_c, the configuration is dynamically unstable. On examining the properties of the Chandrasekhar's spheres (homogeneous spheres with constant γ) it is found that these spheres are non-isentropic, and the speed of sound within these spheres is finite. The authors find that (i) for the causality condition to be fulfilled throughout the configuration, the value of γ ≤ [2/(surface redshift)], (ii) for a given value of u, the binding coefficient, α_r = (M_r -M)/M, vanishes for some value of γ = γ_b and for all the values of γ < γ_b the configurations are unbound, and (iii) for u≤ (1/3), one can find configurations which are bound, dynamically stable, and the speed of sound is less than that of light throughout the configuration, whereas, for u >(1/3), the physically viable models of homogeneous density distribution are not possible. If the configuration is considered to be isentropic, then both γ and the speed of sound become infinite throughout the configuration. This revised version was published online in July 2006 with corrections to the Cover Date.     

Homogeneous metagalactic origin of cosmic rays

Starting with the hypothesis that cosmic rays are evenly distributed in the metagalaxy, it is shown that the flux of the electron-positron component, which is produced through --e decays, following the nuclear collisions of the cosmic ray beam with the intergalactic medium, takes <-4×10¹⁶ sec to reach steady state. The corresponding value of the flux of thepositron component and its implications regarding the homogeneous model of the metagalactic origin of cosmic rays are discussed.On leave from Tata Institute of Fundamental Research, Bombay, India.     

Scale Factor of Isotropic Homogeneous Universe

Four fundamental expressions of isotropic homogeneous universe lead to the scale factor equations. Their solution is achieved by developing the factor as a power series of time, establishing the recursion relations among its coefficients, performing the summation of this power series and obtaining the scale factor as a function of time in a closed form. This one should be used in comparison to observational data with different cosmological models, generally present within this formalism.