Bulk Viscous Bianchi-III Models with Time Dependent G and?Λ

Bulk Viscous anisotropic Bianchi-III cosmological models are investigated with time dependent gravitational and cosmological constants in the framework of Einstein’s general relativity. In order to get some useful information about the time varying nature of G and Λ, we have assumed an exponentially decaying rest energy density of the universe. The extracted Newtonian gravitational constant G varies with time but its time varying nature depends on bulk viscosity and the anisotropic nature of the model. The cosmological constant Λ is found to decrease with time to a small but positive value for the models.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on Ġ may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.      

Higher Dimensional Unified Description of Early Universe with Variable <Emphasis Type="Italic">G</Emphasis> and Λ

A homogeneous and isotropic Friedmann-Robertson-Walker (FRW) model with varying gravitational and cosmological constant is studied in the context of higher dimensional space time. Exact solution of the field equations are obtained by using the “gamma law” equation of state p=(γ−1)ρ, where γ is adiabatic parameter varies continuously as the universe expands. The functional form γ which is assumed to be the function of scale factor R as proposed by Carvalho (1996) is used to analyse the behavior of scale factor R, cosmological constant Λ and the gravitational constant G for two different phases: inflation and radiation. The various physical aspects of the early cosmological models has also been discussed in the framework of higher dimensional space time.     

<Emphasis Type="Italic">C</Emphasis>-field Cosmological Models with Variable <Emphasis Type="Italic">G</Emphasis> in FRW Space–Time

C-field cosmological models based on Hoyle-Narlikar theory with variable gravitational constant G in the frame work of FRW (Friedmann-Robertson-Walker) space–time for positive and negative curvatures are investigated. To get the deterministic solutions in terms of cosmic time t, we have assumed G=R ⁿ and discussed for n=−1, −2, R being scalar factor. In both the cases, creation field C increases with time, the gravitational constant G and matter density (ρ) decrease with time in the model (21). In the model (41) G decreases with time and matter density (ρ) is constant. The other physical aspects of the models are also discussed.     

Determination of the gravitational constant G

A precise knowledge of the Newtonian gravitational constant G has an important role in physics and is of considerable meteorological interest. Although G was the first physical constant to be introduced and measured in the history of science, it is still the least precisely determined of all the fundamental constants of nature. The 2002 CODATA recommended value for G, G = (6.6742 ± 0.0010) × 10⁻¹¹m³ · kg⁻¹ · s⁻², has an uncertainty of 150 parts per million (ppm), much larger than that of all other fundamental constants. Reviewed here is the status of our knowledge of the absolute value of G, methods for determining G, and recent high precision experiments for determining G.     

Periodic Distribution of Galaxies in Generalized Scalar Tensor Theory

With the help of Nordtvedt's scalar tensor theory an exact analytic model of a non–minimally coupled scalar field cosmology in which the gravitational coupling G and the Hubble factor H oscillate during the radiation era is presented. A key feature is that the oscillations are confined to the early stages of the radiation dominated era with G approaching its present constant value while H becoming a monotonically decreasing function of time. The Brans Dicke parameter is chosen to be a function of Brans Dicke scalar field so that no conflict with observational constraints regarding its present value arises.     

Models of G time variations in diverse dimensions

A review of different cosmological models in diverse dimensions leading to a relatively small time variation in the effective gravitational constant G is presented. Among them: the 4-dimensional (4-D) general scalar-tensor model, the multidimensional vacuum model with two curved Einstein spaces, the multidimensional model with the multicomponent anisotropic “perfect fluid”, the S-brane model with scalar fields and two form fields, etc. It is shown that there exist different possible ways of explaining relatively small time variations of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on ? may be satisfied either in some restricted interval or for all allowed values of the synchronous time variable.     

Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G

We developed a gravity-gradiometer based on atom interferometry for the determination of the Newtonian gravitational constant G. The apparatus, combining a Rb fountain, Raman interferometry and a juggling scheme for fast launch of two atomic clouds, was specifically designed to reduce possible systematic effects. We present instrument performances and preliminary results for the measurement of G with a relative uncertainty of 1%. A discussion of projected accuracy for G measurement using this new scheme shows that the results of the experiment will be significant to discriminate between previous inconsistent values.     

Progress in Precise Measurements of the Gravitational Constant

The Newtonian gravitational constant G, which is one of the earliest fundamental constants introduced by human beings, plays an important role in cosmology, astrophysics, geophysics, metrology, and so on. In spite of the measurement of G having a relative longer history and more than 200 measurement results having been obtained during the past 200 years, G still remains the least precisely known among all fundamental physical constants up to now. Over the past three decades, many experimental physicists devoted themselves to the G measurement with various methods and resulted in a dozen precise values of G. However, the determined results are still in poor agreement with each other. A brief overview of the significance of the gravitational constant G is given herein, followed by an introduction into the history of G measurement. A summary of the five latest precise measurements performed during the past few years is presented. Finally, an outlook of the future development of G measurement is provided.     

On the Stability of a Class of Modified Gravitational Models

Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting is investigated. Specifically, after revisiting the f(R) case, R being the Ricci curvature, we present a stability condition around a de Sitter solution valid for modified gravitational models of generalized type F(R,G,Q), G and Q being the Gauss-Bonnet and quadratic Riemann invariants respectively. A generalization to higher order invariants is presented.     

The principle of reciprocity

It is shown that the validity of the principle of reciprocity for arbitrary motion impiies that the rate of a moving clock departs from the (instantaneous) special relativistic value by a term -xx/2c ² wherex is the distance of the clock. Through this effect the cosmological red shift can be understood as arising from the outward acceleration of radiating atoms in galactic gravitational fields. In this way the relation (GM/2cL ²) (1/H) between Newton's constant of gravitationG, the massM and linear dimensionL of a typical galaxy and Hubble's constantH is derived. This relation is verified by present-day observations. Implications of these considerations for quasars are briefly discussed.As a possible test of this theory it is suggested that the spectra of galaxies be searched for the presence of blue-shifted lines which are expected to be fainter by three to four magnitudes in comparison with the red-shifted lines.     

Interacting New Agegraphic Viscous Dark Energy with Varying <Emphasis Type="Italic">G</Emphasis>

We consider the new agegraphic model of dark energy with a varying gravitational constant, G, in a non-flat universe. We obtain the equation of state and the deceleration parameters for both interacting and noninteracting new agegraphic dark energy. We also present the equation of motion determining the evolution behavior of the dark energy density with a time variable gravitational constant. Finally, we generalize our study to the case of viscous new agegraphic dark energy in the presence of an interaction term between both dark components.     

Generalized self-similar scalar-tensor theories

In order to analyze how the gravitational constant, G, and the cosmological constant, Λ, may vary we study through symmetry principles the form of the functions in the generalized scalar-tensor theories under the self-similar hypothesis. The results obtained are absolutely general and valid for all the Bianchi models and the flat FRW one. We study the concrete example of the Kantowski–Sachs model finding some new exact self-similar solutions.     

Cosmologies with variable gravitational constant

In 1937 Dirac presented an argument, based on the socalled large dimensionless numbers, which led him to the conclusion that the Newtonian gravitational constantG changes with epoch. Towards the end of the last century Ernst Mach had given plausible arguments to link the property of inertia of matter to the large scale structure of the universe. Mach's principle also leads to cosmological models with a variable gravitational constant. Three cosmologies which predict a variableG are discussed in this paper both from theoretical and observational points of view.     

Einstein's First Steps Toward General Relativity: Gedanken Experiments and Axiomatics

Jahrbuch paper is an extraordinary document because it contains his first steps toward generalizing the 1905 relativity theory to include gravitation. Ignoring the apparent experimental disconfirmation of the 1905 relativity theory and his unsuccessful attempts to generalize the mass-energy equivalence, Einstein boldly raises the mass-energy equivalence to an axiom, invokes equality between gravitational and inertial masses, and then postulates the equivalence between a uniform gravitational field and an oppositely directed constant acceleration, the equivalence principle. How did this come about? What is at issue is scientific creativity. This necessitates broadening historical analysis to include aspects of cognitive science such as the role of visual imagery in Einstein's thinking, and the relation between conscious and unconscious modes of thought in problem solving. This method reveals the catalysts that sparked a Gedanken experiment that occurred to Einstein while working on the Jahrbuch paper. A mental model is presented to further explore Einstein's profound scientific discovery.     

On the Distribution of Radio Pulsars Above the Galaxy Plane

A mechanism of pulsar accumulation over the galaxy plane, caused by deceleration in the gravitational field and stopping at a certain distance of z from the plane is proposed. For pulsars with velocities close to the average observed velocity of about 300 km/s, the consideration of kinematics of such motion estimates the age of stopped pulsars of the order of ten millions years and the average distance from the galaxy plane of about 2 kpc. The consistency in the pulsar longitude distribution at |z| = 0.45–4.5 kpc and the distribution of the formation regions of massive stars in the galaxy disk was found.     

Methods for solving the system of nonlinear oscillation equations that determine the gravitational constant

Methods for solving a system of nonlinear oscillation equations are discussed. The perspective for functional enhancement of existing methods for determining the gravitational constant, G, at an aspheric configuration of interacting bodies was demonstrated. A paper that was presented in DAN SSSR, 245, N3 (1979) is analyzed. The dependence of the G value on the position of attracting masses may be explained by the paramagnetic effect. Its mass point imitation, which defines its value and position, resulted in the standard G value.     

Gravitational potential in fractional space

In this paper the gravitational potential with β-th order fractional mass distribution was obtained in α dimensionally fractional space. We show that the fractional gravitational universal constant G _α is given by , where G is the usual gravitational universal constant and the dimensionality of the space is α > 2.      

Variable <Emphasis Type="Italic">G</Emphasis> Corrections to Statefinder Parameters of Dark Energy

Motivated by several observational and theoretical developments concerning the variability of Newton’s gravitational constant with time G(t), we calculate the varying G correction to the statefinder parameters for four models of dark energy namely interacting dark energy holographic dark energy, new-agegraphic dark energy and generalized Chaplygin gas.