A dynamical model for gravitation

A gravitational model is proposed that relates the terrestrially measured value of the gravitational constantG directly to the density and angular velocity of the galaxy. The model indicates a constant scalar value forG within most regions of our galaxy, but predicts thatG will be different in other galaxies and zero in intergalactic space. The model offers explanations for galactic cluster stability, discrepancies in terrestrial measurements ofG, and atomic particle stability. The model also provides a causal relationship between strong, electromagnetic, weak, and gravitational interactions. The two postulates required for the proposed model reduce to two assumptions made in GRT in regions whereG is constant; these postulates are consistent with the existence of a 2.7 K blackbody background radiation.     

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.     

Projective and volume-preserving bundle structures involved in the formulation ofA(4) gauge theories

The bundle structures required by volume-preserving and related projective properties are developed and discussed in the context ofA(4) gauge theories which may be taken as the proper framework for Poincaré gauge theories. The results of this paper include methods for extending both tensors and connections to a principal fiber bundle havingG1(4,R)xG1(4,R) as its structure group. This bundle structure is shown to be a natural arena for the generalized (±) covariant differentiation utilized by Einstein for his extended gravitational theories involving nonsymmetric connections. In particular, it is shown that this generalized (±) covariant differentiation is actually a special case of ordinary covariant differentiation with respect to a connection on theG1(4,R) xG1(4,R) bundle. These results are discussed in relation to certain properties of generalized gravitational theories based on a nonsymmetric connection which include the metric affine theories of Hehl et al. and the general requirement that it should be possible to formulate well-defined local conservation laws. In terms of the extended bundle structure considered in this paper, it is found that physically distinct particle number type conservation expressions could exist for certain given types of matter currents.     

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.     

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.     

<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.     

Non-minimal Maxwell-modified Gauss–Bonnet cosmologies: inflation and dark energy

In this paper we show that power-law inflation can be realized in non-minimal gravitational coupling of electromagnetic field with a general function of the Gauss–Bonnet invariant. Such a non-minimal coupling may appear due to quantum corrections. We also consider modified Maxwell-F(G) gravity in which non-minimal coupling between electromagnetic field and f(G) occurs in the framework of modified Gauss–Bonnet gravity. It is shown that inflationary cosmology and late-time accelerated expansion of the universe are possible in such a theory.     

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.     

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.     

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.      

A look at the abandoned contributions to cosmology of Dirac,Sciama, and Dicke

The separate contributions to cosmology of the above researchers are revisited and a cosmology encompassing their basic ideas is proposed. We study Dirac's article (1938) on the large number hypothesis, Sciama's proposal (1953) of realizing Mach's principle, and Dicke's considerations (1957) on a flat‐space representation of general relativity with a variable speed of light (VSL). Dicke's tentative theory can be formulated in a way which is compatible with Sciama's hypothesis on the gravitational constant G. Additionally, such a cosmological model is shown to satisfy Dirac's second ‘large number’ hypothesis on the total number of particles in the universe being proportional to the square of the epoch. In the same context, Dirac's first hypothesis on an epoch‐dependent G – contrary to his prediction – does not necessarily produce a visible time dependence of G. While Dicke's proposal reproduces the classical tests of GR in first approximation, the cosmological redshift is described by a shortening of measuring rods rather than an expansion of space. Since the temporal evolution of the horizon R is governed by , the flatness and horizon problems do not arise in the common form.     

Event horizons in static electrovac space-times

The following theorem is established. Among all static, asymptotically flat electrovac fields with closed, simply-connected equipotential surfacesg _{0 0}=const.. the only ones which have regular event horizonsg _{0 0}=0 are the Reissner-Nordström family of spherisymmetric solutions withmG ^1/2|e|/c. In the special case where the gravitational coupling of the electromagnetic energy density is neglected (G=0) all solutions are computed explicitly, thus extending an earlier result ofGinzburg for a magnetic dipole inSchwarzschild's space-time. Possible implications for gravitational collapse are briefly discussed.On leave of absence from the Mathematics Department, University of Alberta, Edmonton, Canada.     

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.      

Cosmology withG and Λ coupling scalars

Cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einstein's theory is considered. A general method of solving the field equations is given. Fifteen exact solutions for zero pressure models satisfyingG=G ₀(R/R ₀) ⁿ are given in the Appendix; they are briefly discussed.     

Electrostatic potential in a gravitational field

The electrostatic potential in a gravitational field is estimated up to the order ofe ² G ² in the framework of the conventional quantum field theory. It is shown that the electrostatic potential is different from the classical one. We find that this discrepancy is attributable to the process in which a particle emits three massless ones which are absorbed by three other particles.     

Note on the natural system of units

We propose to substitute Newton’s constant G _N for another constant G ₂, as if the gravitational force would fall off with the 1/r law, instead of the 1/r ²; so we describe a system of natural units with G ₂, c and ℏ. We adjust the value of G ₂ so that the fundamental length L = L _Pl is still the Planck’s length and so G _N = L × G ₂. We argue for this system as (1) it would express longitude, time and mass without square roots; (2) G ₂ is in principle disentangled from gravitation, as in (2 + 1) dimensions there is no field outside the sources. So G ₂ would be truly universal; (3) modern physics is not necessarily tied up to (3 + 1)-dim. scenarios and (4) extended objects with p = 2 (membranes) play an important role both in M-theory and in F-theory, which distinguishes three (2, 1) dimensions. As an alternative we consider also the clash between gravitation and quantum theory; the suggestion is that non-commutative geometry [x _i , x _j ] = Λ² θ _ij would cure some infinities and improve black hole evaporation. Then the new length Λ shall determine, among other things, the gravitational constant G _N.     

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.     

Solutions of the Einstein-Maxwell equations with many black holes

In Newtonian gravitational theory a system of point charged particles can be arranged in static equilibrium under their mutual gravitational and electrostatic forces provided that for each particle the charge,e, is related to the mass,m, bye=G ^1/2 m. Corresponding static solutions of the coupled source free Einstein-Maxwell equations have been given by Majumdar and Papapetrou. We show that these solutions can be analytically extended and interpreted as a system of charged black holes in equilibrium under their gravitational and electrical forces.We also analyse some of stationary solutions of the Einstein-Maxwell equations discovered by Israel and Wilson. If space is asymptotically Euclidean we find that all of these solutions have naked singularities.Alfred P. Sloan Research Fellow, supported in part by the National Science Foundation.     

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.     

Holographic Dark Energy in Higher Derivative Gravity with Varying Gravitational Constant

In this paper we investigate the holographic dark energy scenario in higher derivative gravity with a varying gravitational constant. We introduce a kind of energy density from higher derivative gravity which has role of the same as holographic dark energy. We obtain the exact differential equation , which determine the evolution of the dark energy density based on varying gravitational constant G. We also find out a cosmological application of our work by evaluating a relation for the equation of state of dark energy for low redshifts containing varying G correction.