Cosmic Time Variation of the Gravitational Constant

A pre-relativistic cosmological approach to electromagnetism and gravitation is explored that leads to a cosmic time variation of the fundamental constants. Space itself is supposed to have physical substance, which manifests by its permeability. The scale factors of the permeability tensor induce a time variation of the fundamental constants. Atomic radii, periods, and energy levels scale in cosmic time, which results in dispersionless redshifts without invoking a space expansion. Hubble constant and deceleration parameter are reviewed in this context. The time variation of the gravitational constant at the present epoch can be expressed in terms of these quantities. This provides a completely new way to restrain the deceleration parameter from laboratory bounds on the time variation of the gravitational constant. This variation also affects the redshift dependence of angular diameters and the surface brightness, and we study in some detail the redshift scaling of the linear sizes of radio sources. The effect of the varying constants on source counts is discussed, and an estimate on the curvature radius of the hyperbolic3-space is inferred from the peak in the quasar distribution. The background radiation in this dispersionless, permeable space-time stays perfectly Planckian. Cosmic time is discussed in terms of atomic and gravitational clocks, as well as cosmological age dating, in particular how the age of the Universe relates to the age of the Galaxy in a permeable space-time. This revised version was published online in July 2006 with corrections to the Cover Date.     

Distributions of Constant Directional Derivatives and a Model of Spiral Galaxy Arms

Image analysis of over one hundred nearby galaxies (He, 2003) indicates that for any spiral galaxy image of small inclination there is evidence of two orthogonalsets of iso-ratio curves in different scales which, like curvilinear coordinate lines, expand over different galaxy components. This result sets a constraint on galaxy patterns and a general model equation which carries this constraint is given in its geometric form in He (2003). In the current paper the author reformulates the geometric equation into one quasilinearsystem of 3 partial differential equations with 3 dependents (the tangent direction of one set of iso-ratio curves and the two ratio profiles along the two sets of iso-ratio curves respectively). With one profile assumed to be a nonzero constant, there are two dependents and the system of two partial differential equations is a hyperbolic one. The author uses the standard method of characteristics and the boundary condition of ideal arms which are found by setting the above constant to be zero, to solve the hyperbolic system. This provides one analytic method to model galaxy patterns. Its varying parameters will be useful for galacticarm classification and for investigation of galaxy structure.     

Some Bianchi Type I Viscous Fluid Cosmological Models with a Variable Cosmological Constant

Some Bianchi type I viscous fluid cosmological models with a variable cosmological constant are investigated in which the expansion is considered only in two direction i.e. one of the Hubble parameter is zero. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density whereas the coefficient of shear viscosity is considered as constant in first case whereas in other case it is taken as proportional to scale of expansion in the model. The cosmological constant Λ is found to be positive and is a decreasing function of time which is supported by results from recent supernovae Ia observations. Some physical and geometric properties of the models are also discussed.     

Brans-Dicke Cosmology with non-vanishing Cosmological Constant and Non-Zero Curvature

A model of the universe based on Brans-Dicke theory with non-vanishing cosmological constant and non-zero curvature is studied. Equations (13) and (16) have been obtained by the assumption f(t) = φ(t)a ³ (t),which give the values of the scale factor, a(t) and scalar field, φ(t) in terms of the observable parameters. Also, for a particular case of matter dominated universe, Equation (20) is obtained which gives the relation between various parameters. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Ionization Rate During the Decoupling Period in a Universe with Nonzero Cosmological Constant

Nonzero cosmological constant favours cosmological models with larger Hubble constant. The evolution of ionization during decoupling period in a universe with nonzero cosmological constant is computed by using a corrected recombination coefficient. Also presented in this paper is the redshift distribution of the last scattering surfaces of the cosmic background photons while the cosmological constant is nonvanishing. Finally, we give a brief estimation about the influence of H_e on the last scattering surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modulation of Solar Constant by Active Regions during 1980

Irradiance records of the Nimbus-7 and SMM satellites indicate a systematic downward trend of the solar constant of the order of a few hundredths of a percent and a slow variation of the solar constant on a time scale from days to weeks. The reason for the downward trend is not known as yet; it seems that the slow variation of the solar constant is linked with the solar rotation period via the effect of solar active regions. This paper deals with the connection between the solar constant variation and the age of the solar active regions. It seems that decreases in the solar constant took place when sunspot groups developing quickly in time and space with complex structure occurred on the solar disk. On the other hand, when the “older” groups with simple structure were dominant the value of the solar constant increased slightly or these groups could reduce the effects of “younger” groups.     

Fractional crystallization of iron meteorites: Constant versus changing partition coefficients

Abstract— Analyses of magmatic iron meteorites, plotted on LogC_i vs. LogC_Ni diagrams, often form linear arrays. Traditionally, this linearity has been ascribed to fractional crystallization under the assumption of constant partition coefficients (i.e., Rayleigh fractionation). Paradoxically, however, partition coefficients in the Fe-Ni-S-P system are decidedly not constant. This contribution provides a rationale for understanding how trends on LogC_i vs. LogC_Ni diagrams can be linear, even when partition coefficients are changing rapidly.     

An ultraviolet-selected galaxy redshift survey – II. The physical nature of star formation in an enlarged sample

We present further spectroscopic observations for a sample of galaxies selected in the vacuum ultraviolet (UV) at 2000 Å from the FOCA balloon-borne imaging camera of Milliard et al. This work represents an extension of the initial study by Treyer et al. Our enlarged catalogue contains 433 sources (≃3 times as many as in our earlier study) across two FOCA fields. 273 of these are galaxies, nearly all with redshifts z ≃0–0.4. Nebular emission-line measurements are available for 216 galaxies, allowing us to address issues of excitation, reddening and metallicity. The UV and H α luminosity functions strengthen our earlier assertions that the local volume-averaged star formation rate is higher than indicated from earlier surveys. Moreover, internally within our sample, we do not find a steep rise in the UV luminosity density with redshift over 0< z <0.4. Our data are more consistent with a modest evolutionary trend, as suggested by recent redshift survey results. Investigating the emission-line properties, we find no evidence for a significant number of AGN in our sample; most UV-selected sources to z ≃0.4 are intense star-forming galaxies. We find that the UV flux indicates a consistently higher mean star formation rate than that implied by the H α luminosity for typical constant or declining star formation histories. Following Glazebrook et al., we interpret this discrepancy in terms of a starburst model for our UV-luminous sources. We develop a simple algorithm which explores the scatter in the UV flux–H α relation in the context of various burst scenarios. Whilst we can explain most of our observations in this way, there remains a small population with extreme UV–optical colours which cannot be understood.     

On the Hubble Law in a Nonexpanding Nonstationary Universe with Cosmological Constant

A nonsingular, homogeneous, isotropic cosmological model with cosmological constant in flat space-time theory of gravitation is studied. The second law of thermodynamics yields a nonexpanding (nonstationary) universe without entropy production. At the beginning of the universe radiation, matter and vacuum energy given by the cosmological constant are zero and then emerge from gravitational energy. In the course of time the energy of radiation and matter decrease whereas the vacuum energy increases forever. Light emitted from a distant galaxy loses energy on his way to the observer producing the observed redshift. The velocity of light in the past is greater than the present one. This may explain superluminal velocities but only for large redshifts. The sum of the density parameters of matter, radiation and vacuum energy is a little greater than one. All the matter can be baryonic. There is no age problem of the universe. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of Constant Torque on Equilibria of Satellite in Circular Orbit

We consider the equilibria of a satellite in a circular orbit under the action of gravitational and constant torques. The number of equilibria depending on the parameters of the problem is found by the analysis of an algebraic equation of order 6. The domains with different numbers of equilibria are specified, and the equations of boundary curves are determined in function of values of the components of constant torque. Classification of different distributions of number of equilibria is made for arbitrary values of the parameters.     

Solitary waves of vortices

We study the propagation of solitary waves of vortices within a spherical shell which constitutes the uppermost layer of a solid planet. This solid-liquid configuration rotates with constant angular velocity about an axis which is fixed with respect to the solid surface. The fluid within the shell is inviscid, incompressible, and of constant density. The motion imparted by the planetary rotation upon this fluid mass is governed by the Laplace tidal equation from which the potential of the extraplanetary forces has been deleted. Consistent with this ocean model, we establish that the stream function of a solitary wave of vortices must satisfy a third-order partial differential equation. We obtain solutions to this wave equation by imposing the condition that the vertical component of vorticity be functionally related to the stream function. We find that this dependence must necessarily be of the exponential type and that the solution to the wave equation then reduces to a quadrature depending on some arbitrary parameters. We prove that we can always choose the values of these parameters in order to approximate the integral in question by means of an analytic function: we reach a representation of the stream function of a solitary wave of vortices in terms of hyperbolic functions of time and position.This paper is dedicated to the memory of Professor Zdenek Kopal.     

Why Newtonian gravity is reliable in large-scale cosmological simulations

Until now, it has been common to use Newtonian gravity to study the non-linear clustering properties of large-scale structures. Without confirmation from Einstein's theory, however, it has been unclear whether we can rely on the analysis (e.g. near the horizon scale). In this work we will provide confirmation of the use of Newtonian gravity in cosmology, based on the relativistic analysis of weakly non-linear situations to third order in perturbations. We will show that, except for the gravitational-wave contribution, the relativistic zero-pressure fluid equations perturbed to second order in a flat Friedmann background coincide exactly with the Newtonian results. We will also present the pure relativistic correction terms appearing in the third order. The third-order correction terms show that these terms are the linear-order curvature perturbation times the second-order relativistic/Newtonian terms. Thus, the pure general relativistic corrections in the third order are independent of the horizon scale and are small when considering the large-scale structure of the Universe because of the low-level temperature anisotropy of the cosmic microwave background radiation. Since we include the cosmological constant, our results are relevant to currently favoured cosmology. As we prove that the Newtonian hydrodynamic equations are valid in all cosmological scales to second order, and that the third-order correction terms are small, our result has the important practical implication that one can now use the large-scale Newtonian numerical simulation more reliably as the simulation scale approaches and even goes beyond the horizon. In a complementary situation, where the system is weakly relativistic (i.e. far inside the horizon) but fully non-linear, we can employ the post-Newtonian approximation. We also show that in large-scale structures, the post-Newtonian effects are quite small.     

1300 micron continuum and C18O line mapping of giant molecular cloud cores. II. W3, NGC 2264, NGC 6334I, RHO Ophiuchi and S140

In this paper we present nearly simultaneous 1300 microns continuum and J = 2-1 C18O maps of the cores of five molecular clouds, W3, NGC 2264, NGC 6334I, rho Oph, and S140. The purpose of this experiment was to compare these two column density tracers. We find that dust continuum and C18O emission are equally effective tracers of column density in molecular cloud cores and give a good indication of cloud structure. When the maps are analyzed in terms of the quantity q = Q/[a rho RX(C18O)], we find that q does not vary by much more than an order of magnitude either within objects or from object to object, implying that nominal dust parameters of absorption efficiency, radius, and gas-to-dust ratio and CO abundance are on average correct in a variety of sources. We did detect source-to-source variations in q. This variation could be either in the dust-to-CO number density ratio or in grain parameters. These variations are not well correlated with total source luminosity, average or typical temperature, or total column density. The best example of this variation appears to be rho Oph where q is about a factor of 7 lower than is typically found. Our approach is analogous to the study of the A nu to CO ratio and is probably equivalent to extending this study to large A nu if the same grains are responsible for both optical opacity and far-infrared to millimeter-wave emission. There is no fundamental reason to expect A nu/NCO or q to be constant and, in fact, we have found that it is not constant in even a small source sample.     

Entanglement entropy of acoustic black hole in Bose–Einstein condensate

We study the entanglement entropy associated to the phonons generated via the Hawking mechanism of acoustic black holes in a Bose–Einsten condensate. The lowest energy allowed for the radiated phonons is found to be a function of space coordinate. Based this, we calculate the entanglement entropy, which contains three parts: a leading term, which is a constant of value 1/6, a logarithmic correction term and some series terms. We discuss the convergence of the series terms.     

Secular Effects on Orbits of Binary Stars Induced by Temporal Variation of Gravitational Constant (Case for Elliptical Orbit)

In this paper we investigate the influence of a varying gravitation constant on the orbits of celestial bodies. Regarding the eccentric anomaly as an independent variable, we find the solutions to the perturbed equations of motion. In the first order solutions, we find the secular and periodic variations in semi-major axis. For the other orbital elements only periodic variations exhibit. However in the second order solutions, the longitude of periastron and the mean longitude have secular terms. Applying the calculations to six selected binaries, we give the numerical estimations of the variations of orbits. These results are then carefully compared and discussed.     

Warm anisotropic inflation with bulk viscous pressure in intermediate era

The aim of this paper is to study the warm inflation during intermediate era in the framework of locally rotationally symmetric Bianchi type I universe model. We assume that the universe is composed of inflaton and imperfect fluid having radiation and bulk viscous pressure. To this end, dynamical equations (first model field equation and energy conservation equations) under slow-roll approximation and in high dissipative regime are constructed. A necessary condition is developed for the realization of this anisotropic model. We assume both dissipation and bulk viscous coefficients variable as well as constant. We evaluate entropy density, scalar (tensor) power spectra, their corresponding spectral indices, tensor–scalar ratio and running of spectral index in terms of inflaton. These cosmological parameters are constrained using recent Planck and WMAP7 probe.     

Cosmological Models With Negative Constant Deceleration Parameter In Lyra Geometry

Bermann [Nuovo Cimento B (1983), 74, 182] presented a law of variation of Hubble’s parameter that yields constant deceleration parameter models of the Universe. In this paper, we study some cosmological models with negative constant deceleration parameter within the framework of Lyra geometry. PACS Nos: 98.80 cq, 04.20 jb, 04.50     

The strength of regolith and rubble pile asteroids

We explore the hypothesis that, due to small van der Waals forces between constituent grains, small rubble pile asteroids have a small but nonzero cohesive strength. The nature of this model predicts that the cohesive strength should be constant independent of asteroid size, which creates a scale dependence with relative strength increasing as size decreases. This model counters classical theory that rubble pile asteroids should behave as scale‐independent cohesionless collections of rocks. We explore a simple model for asteroid strength that is based on these weak forces, validate it through granular mechanics simulations and comparisons with properties of lunar regolith, and then explore its implications and ability to explain and predict observed properties of small asteroids in the NEA and Main Belt populations, and in particular of asteroid 2008 TC₃. One conclusion is that the population of rapidly rotating asteroids could consist of both distributions of smaller grains (i.e., rubble piles) and of monolithic boulders.     

Exact solution of a triaxial gyrostat with one rotor

The problem of the attitude dynamics of a triaxial gyrostat under no external torques and one constant internal rotor, is a three degrees-of-freedom system, although thanks to the existence of integrals of motion it can be reduced to only one degree-of-freedom problem. We introduce coordinates to represent the orbits of constant angular momentum as a flow on a sphere. This representation shows that the problem is equivalent to a quadratic Hamiltonian depending on two parameters. We find the exact solution of the orbits in terms of elliptic functions. By making use of properties of elliptic functions we find the solution at each region of the parametric partition from the solution of one region. We also prove that heteroclinic orbits are planar curves.