Search

It has been shown that AdS/CFT correspondence may be realized between some AdS-like cosmological space and CFT living on the boundary. By extending such works we studied the role of R2 term in the corrected action to the thermodynamic quantities, particularly by adding a boundary counterterms to the gravitational action and considering an AdS-like cosmological space. With such HD (higher derivative) terms and metric we calculated the free energy, as a function of N2T4 times 3/2(1 − 1/N2), that is comparable with perturbative result followed from boundary QFT. In fact the difference between the results obtained from AdS-like cosmological space and the results obtained from strong coupling limit of ℵ = 4 SCFT, by taking into account next to leading term in large N expansion, is just a 3/2 factor. Higher derivative term contributions also appear in entropy and energy via the redefinition of gravitation constant. We explicitly identify higher order counterterms effect in energy as a constant term namely E0. This value can be interpreted as the Casimir energy, so that, there is a full and perfect match between QFT and gravitational action when both R2 term and boundary counterterms are considered. So we can claim that our results have assured us that there is a good fit between AdS-like cosmological space and ℵ = 4 SU(N) super Yang-Mills quantum theory.

The Bouguer correction of the gravity data of a thin-layered material is a classic topic of research that has been extensively investigated in the field of geodesy. In the case of a flat Earth model, the Bouguer slab formula $$2\pi G h$$ is often utilized, where $$h$$ denotes the height, $$\rho$$ denotes the density of the thin layer, and $$G$$ denotes the gravitational constant. In the case of a spherical thin layer, the effect of gravity is usually expressed by $$4\pi G\rho h$$ . Another Bouguer correction formula also exists, expressed by the spherical harmonics for an arbitrary inhomogeneous layer on the Earth’s surface, i.e., $$2\pi G\rho \sum [1 + 1/\left( {2n + 1} \right)]h_{{nm}} Y_{{nm}}$$ , where the thickness is expressed by spherical harmonic series $$Y_{{nm}}$$ with coefficient $$h_{{nm}}$$ . This implies that the geometric character of the thin layer exerts a significant influence on the Bouguer correction. To investigate the relationship between the three cases, we review and re-derive the three Bouguer correction formulae in detail using Newton's formula and the “Love numbers” mathematical framework, and thoroughly discuss the differences and relations between them from a mathematical and geodetic point of view. After that, we use different formulae and discuss three applications case by case. Finally, we give some suggestions for the use of the Bouguer correction formula in general.

This paper proposes a fault diagnosis method for electrical machine drive system by using backpropagation neural network (BPNN) optimized by chaotic adaptive gravity search algorithm (GSA) and particle swarm optimization (PSO) algorithm. In this method, an adaptive gravitational constant factor based on iteration times and chaotic mapping is introduced to balance the global search ability and local development ability of GSA. Then, it is combined with PSO algorithm to solve the problem of prematurity and local optimum of PSO algorithm. Finally, combined with BPNN, a fault diagnosis model based on chaos adaptive GSA-PSO-BPNN is established. The experimental results show that the introduction of the attenuation factor of adaptive gravitational constant and the chaotic mapping can improve the classification performance of GSA-PSO-BPNN, and the feasibility and effectiveness of the chaotic adaptive GSA-PSO Algorithm are also proved.

Multilevel thresholding for image segmentation has always been a popular issue and has attracted much attention. Traditional exhaustive search methods take considerable time to solve multilevel thresholding problems. However, heuristic search algorithms have potential advantages in terms of solving such multilevel thresholding problems. Based on this idea, in this paper, a novel adaptive gravitational search algorithm (AGSA) is proposed to solve the optimal multilevel image thresholding problem; this algorithm is more efficient than the traditional exhaustive search method for grayscale image segmentation. In the AGSA, an adaptive parameter optimization strategy is used to tune the gravitational constant and the inertia weight. To verify the performance of the proposed algorithm, a series of classic test images are used to perform several experiments. In addition, the standard GSA and some optimization algorithms are compared with the proposed algorithm. The experimental results show that the proposed algorithm is obviously better than the other six algorithms. These promising results suggest that the AGSA is more suitable than existing methods for multilevel image thresholding.

Regression testing is an essential but expensive activity to re-execute all the test cases every time the software updates. Test case prioritization and minimization reduces the cost and efforts required for retesting by prioritizing the test cases based on their importance and minimizing the redundancy. Optimization approaches further enhance the effectiveness of these techniques. In this paper, a discrete and combinatorial gravitational search algorithm is proposed to solve the test case prioritization and minimization problems. Furthermore, an improved version is developed using the chaotic map to update the gravitational constant. The proposed algorithms are compared with the most commonly used algorithm, i.e., genetic algorithm. Three subject programs of varying sizes are used for evaluation. Simulation results prove that the proposed algorithms are more efficient and effective than the genetic algorithm for test case prioritization and minimization. Statistical representation via boxplots of APFD and interval plots of minimized suite size performance metrics, confirms that the improved gravitational search algorithm with chaotic gravitational constant has a more squeezed distribution than the standard gravitational search algorithm.

Due to its effective search mechanism, gravitational search algorithm (GSA) has become a very popular and robust tool for the global optimization in a very short span of time. The search mechanism of GSA is based on its two features, namely $$K_\mathrm{best}$$ archive and gravitational constant G. The $$K_\mathrm{best}$$ archive stores the best agents (solutions) at any evolutionary state and hence helps GSA for global search. Each agent interacts with exactly same agents of $$K_\mathrm{best}$$ archive without considering its current impact on the search process, which results a rapid loss of diversity, premature convergence and the high time complexity in GSA model. On the other hand, the exponentially decreasing behavior of G scales the step size of the agent. However, this scaling is same for all agents which may cause inappropriate step size for their next move, and therefore leads the swarm towards stagnation or sometimes skipping the true optima. To address these problems, an improved version of GSA called ‘A novel neighborhood archives embedded gravitational constant in GSA (NAGGSA)’ is proposed in this paper. In NAGGSA, we first propose two novel neighborhood archives for each agent which helps in increased diversified search with less time complexity. Secondly, a novel gravitational constant is proposed for each agent according to the distance-fitness based scaling mechanism. The performance of the proposed variant is tested over different suites of well-known benchmark test functions. Experimental results and statistical analyses reveal that NAGGSA remarkably outperforms the compared algorithms.

The performance of the Gravitational Search Algorithm (GSA) depends on the gravitational constant G, which controls the balance of exploration and exploitation abilities. Improving the setting of this parameter has attracted many researchers. In this paper, we analyzed the GSA stability using the von Neumann stability criterion. First, we modeled the iterative process by a second-order differential equation and derived the first and second-order stability conditions. Then, based on these criteria, we suggested a new law to adjust the initial value of the parameter G, depending on the distance between objects and then on the search space. Some supporting simulations were carried out using different update laws of the gravitational constant (e.g., exponential, log-sigmoid, linear, and chaotic) on CEC 2017 benchmark functions in different search space dimensions. The achieved results show that the new setting leads to significantly better outcomes in high-dimensional search spaces (greater than 20). A comparison with other metaheuristics (Particle Swarm Optimization, Artificial Bee Colony, and Grey Wolf Optimizer) reveals that the new setting proffers GSA competitiveness. Tests on 23 real-world problems (CEC 2011 benchmark problems and the iron ores sintering problem) further proved all the merits of the proposed parameter setting.

The major functions involved in power system security analysis are security assessment and security enhancement. The contingency analysis plays a vital role in the security assessment which has been carried out based on the performance index. Security enhancement incorporates security constrained optimal power flow (SCOPF) which ensures that system is operating at normal state by taking preventive and control actions. An improved artificial physics optimization (APO) evolutionary algorithm is presented in this paper for solving SCOPF problem. The trial and error approach is used for selection of gravitational constant (G) in standard APO method. In order to circumvent this problem, a fuzzy approach is used to tune the gravitational constant (G). Simulations are done on IEEE 30-bus system, Indian 75-bus system, and IEEE 118-bus test system. To evaluate the robustness, results obtained using the proposed method are compared with results obtained using standard conventional algorithms, namely APO, Bat algorithm, and genetic algorithm. The obtained results indicate that the proposed fuzzy adaptive artificial physics optimization (FAAPO) method is efficient as well as robust for solving SCOPF problem to get near global optimization solution compared to standard APO algorithm and other heuristic methods reported in the literature.

The precession of the perihelion of Mercury’s orbit is simulated numerically within the framework of the generalized law of universal gravitation in the field of the Sun and planets taking into account the ellipticity of the planet orbits and new data on the flattening, the mass of the Sun, and the gravitational constant. Calculations were carried out with increased accuracy (up to 19–20 decimal places) and iteration steps of 0.00005 s and 0.0001 s starting from the asteroid belt. It has been shown that the average precession of the perihelion of Mercury’s orbit in 100 years calculated within the framework of the generalized law of universal gravitation and averaged over long time periods from several hundred years to several thousand years taking into account the ellipticity of planet orbits is ~554.2”. This is less than the observed shift of the perihelion of Mercury’s orbit by ~19.9”. As is well known, the observed shift is ~574.1”. That is, the question on the adequacy of the generalized law of universal gravitation to the observances still remains open. However, it is possible that an object of small size (or several such objects) may be located inside Mercury’s orbit, and one more object, whose mass should not exceed at least ~0.2 of the Earth mass may be located at the diametrically opposite point of the Earth orbit behind the Sun. The results obtained are valid to within 1–2 decimal places.

We propose a new scheme for an improved determination of the Newtonian gravitational constant G and evaluate it by numerical simulations. Cold atoms in free fall are probed by atom interferometry measurements to characterize the gravitational field generated by external source masses. Two source mass configurations having different geometry and using different materials are compared to identify an optimized experimental setup for the G measurement. The effects of the magnetic fields used to manipulate the atoms and to control the interferometer phase are also characterized.

Ultra-cold atom experiment in space with microgravity allows for realization of dilute atomic-gas Bose-Einstein condensate (BEC) with macroscopically large occupation number and significantly long condensate lifetime, which allows for a precise measurement on the shape oscillation frequency by calibrating itself over numerous oscillation periods. In this paper, we propose to measure the Newtonian gravitational constant via ultra-cold atom BEC with shape oscillation, although it is experimentally challenging. We also make a preliminary perspective on constraining the modified Newtonian potential such as the power-law potential, Yukawa interaction, and fat graviton. A resolution of frequency measurement of $(1-100)\,\mathrm{nHz}$ at most for the occupation number $10^9$, just one order above experimentally achievable number $N\sim10^6-10^8$, is feasible to constrain the modified Newtonian potential with Yukawa interaction greatly beyond the current exclusion limits., Comment: v1, 10 pages, 3 figures; v2, references added, discussion extended for enlarged parameter space of Yukawa interaction, version accepted by EPJC

This paper presents an integrated feedforward-feedback control structure to control nonlinear dynamical systems. This intelligent control system exploits a modified recurrent wavelet neural network (MRWNN) in the feedforward (FF) and the feedback (FB) loops of the control structure. Specifically, the MRWNN is proposed to boost the approximation performance of a previously reported network by employing two amendments to the original structure. To optimize the parameters of both the FF and the FB controllers, an enhanced version of the gravitational search algorithm (GSA) is developed to improve the searching capability of the original algorithm. In particular, two modifications were adopted, including the removal of two control parameters related to the gravitational constant in the original algorithm and the utilization of the global best solution to constitute the next generation of agents. Hence, the proposed algorithm is called the simplified global gravitational search algorithm (SGGSA), which has demonstrated better optimization performance compared to those of other techniques, including the original GSA. By conducting several evaluation tests using different nonlinear time-variant dynamical systems, the effectiveness of the proposed control structure was confirmed in terms of control precision and robustness against external disturbances. In addition, the MRWNN has exhibited a superior control performance compared with other related controllers.

This study attempts to answer the question of what space is made of and explores in this objective the analogy between the Einstein’s gravitational geometrical theory in one- and two-dimensional linear deformations and a possible space material based on strain measures done on the Ligo or Virgo interferometers. It draws an analogy between the Einstein’s gravitational constant $$\kappa $$ and the Young’s modulus and Poisson’s ratio of an elastic material that can constitute the space fabric, in the context of propagation of weak gravitational waves. In this paper, the space is proposed to have an elastic microstructure of $$1.566\times 10^{-35}$$ m grain size as proposed in string theory, with an associated characteristic frequency f. The gravitational constant G is the macroscopic manifestation of the said frequency via the formula $$G = {\pi } {f}^{2} {/}\rho $$ , where $$\rho $$ is the density of the space material.

In this paper, we are concerned with an elliptic system arising from the Einstein–Maxwell–Higgs model which describes electromagnetic dynamics coupled with gravitational fields in spacetime. Reducing this system to a single equation and setting up the radial ansatz, we classify solutions into three cases: topological solutions, nontopological solutions of type I, and nontopological solutions of type II. There are two important constants: $$a>0$$ representing the gravitational constant and $$N\ge 0$$ representing the total string number. When $$0\le aN

The basic purpose of this communication, is to investigate the dynamical nature of Bianchi type-I universe with perfect fluid content in Saez-Ballester (SB) theory (Phys. Lett. A 113:467–470, 1986). We got the solution of modified Einstein’s field equations (EFEs) by considering the bilinearly varying deceleration parameter (BVDP) and the gravitational constant $(G)$ as a power function of average scale factor $a(t)$. We assumed that BVDP is function of cosmic time with $q(t)=\frac{\alpha (1-t)}{1+t}$, $\alpha \geq 0$. Our finding suggests that present universe has had transitional phase of expansion which was decelerating in the past and is accelerating phase at present time. We also observed that the DE parameter $(\Lambda )$ and energy density parameter $(\rho )$ are decreasing with respect to cosmic time and converge to a very small value at the late time. This result is in strong agreement with recent observations. Physical and geometric properties of the cosmological parameters are also presented in the communication.

Having 50 years of unique observations, lunar laser ranging (LLR) is used to test central elements of Einstein’s theory of relativity, like a possible temporal variation of the gravitational constant or metric parameters. Here, we focused on a possible violation of the equivalence principle (EP) due to assumed dark matter in the galactic center. According to the EP, Earth and Moon experience the same acceleration in the gravitational field of any matter including the galactic dark matter. In the latter case, a violation of the EP would cause an Earth–Moon range oscillation with a sidereal-month period. Recent LLR measurements with high accuracy give us the opportunity to carry out high-precision EP tests for dark matter. We estimated the amplitude of a possible sidereal range oscillation from LLR post-fit residuals. First, we analyzed the characteristics of the residuals for each station and selected a subset of best LLR data. Using this dataset, we obtained $$0.6\pm 1.0$$ mm (realistic error) as a final result for the sidereal amplitude in the direction of the galactic center. It strongly limits a possible violation of the EP for galaxy’s dark matter. Our investigations also show that, for the EP test, a good orbit coverage with good data is more relevant than the number of data or a long time span. As verification, a spectral analysis of the non-uniform LLR residuals has been performed. There again, no significant sidereal signal was found, confirming our previous result.

It is shown that in A. Einstein’s 1915 paper “Explanation of the perihelion motion of Mercury from the general theory of relativity” an error was actually incurred in the integration of the equation $$ \phi =\left[1+\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ , and in the result instead of $$ \phi \approx \uppi \left[1+\frac{5}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ (if we limit ourselves to first-order terms in the small quantity (α1 + α2)) the value $$ \phi \approx \uppi \left[1+\frac{3}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ was obtained, where α1 and α2 are the inverse values of the maximum and minimum distances of Mercury from the Sun, $$ \upalpha =\frac{2G{m}_0}{c^2} $$ is the gravitational radius, G is the gravitational constant, m0 is the mass of the Sun, c is the velocity of light (i.e., the Chinese mathematician Hua Di was actually right). And, as a result, for the precession of the orbit of Mercury in the gravitational field of a spherical Sun in the general theory of relativity (after 100 years) one obtains not ~43”, as A. Einstein obtained, but ~71.63”. Exactly this latter result is obtained by direct numerical modeling of the precession of the perihelion of Mercury’s orbit in the gravitational field of the Sun within the framework of the general theory of relativity if the fitting coefficient α in the equation of motion of Mercury (not to be confused with α in the above equations) is set equal to zero. The result $$ \phi \approx \uppi \left[1+\frac{3}{4}\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right] $$ , obtained by A. Einstein if it is obtained, happens only upon integration of either the equation $$ \phi =\left[1+\frac{\upalpha}{2}\left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ (if we also limit ourselves to first-order terms in the small quantity (α1 + α2)), i.e., in front of the integral in brackets the coefficient 1/2 should stand in front of the quantity α, or the equation $$ \phi =\left[1+\upalpha \left({\upalpha}_1+{\upalpha}_2\right)\right]\underset{\upalpha_1}{\overset{\upalpha_2}{\int }}\frac{dx}{\sqrt{-\left(x-{\upalpha}_1\right)\left(x-{\upalpha}_2\right)\left(1-\upalpha x\right)}} $$ (if we also limit ourselves to first-order terms in the small quantity (α1 + α2)), i.e., in the denominator under the differential in the integral, inside the square root\ a plus sign should stand in front of the quantity αx.

The Newtonian gravitational constant, G, is one of the most fundamental constants of nature, but we still do not have an accurate value for it. Despite two centuries of experimental effort, the value of G remains the least precisely known of the fundamental constants. A discrepancy of up to 0.05 per cent in recent determinations of G suggests that there may be undiscovered systematic errors in the various existing methods. One way to resolve this issue is to measure G using a number of methods that are unlikely to involve the same systematic effects. Here we report two independent determinations of G using torsion pendulum experiments with the time-of-swing method and the angular-acceleration-feedback method. We obtain G values of 6.674184 × 10−11 and 6.674484 × 10−11 cubic metres per kilogram per second squared, with relative standard uncertainties of 11.64 and 11.61 parts per million, respectively. These values have the smallest uncertainties reported until now, and both agree with the latest recommended value within two standard deviations.

On the basis of the special theory of relativity and a solution of the Schwarzschild equations of general relativity, a generalized equation of Friedmann–Einstein–de Sitter type has been obtained for the expanding Universe. As a result of our work on the boundary value problem for this equation, we have found the eigenvalue of the resulting eigenvalue problem, linking the density of the Universe in the comoving coordinates, the Hubble constant, and the gravitational constant. We have calculated a value for the density of matter in the Universe which is in agreement with the observational data. We have shown that the missing dark energy is the relativistic kinematic and potential energy of the expanding Universe.

Gravitational Search Algorithm (GSA) is a recent metaheuristic algorithm inspired by Newton’s law of gravity and law of motion. In this search process, position change is based on the calculation of step size which depends upon a constant namely, Gravitational Constant (G). G is an exponentially decreasing function throughout the search process. Further, in-spite of having different masses, the value of G remains same for each agent, which may cause inappropriate step size of agents for the next move, and thus leads the swarm toward stagnation or sometimes skipping the true optima. To overcome stagnation, we first propose a gravitational constant having different scaling characteristics for different phase of the search process. Secondly, a dynamic behavior is introduced in this proposed gravitational constant which varies according to the fitness of the agents. Due to this behavior, the gravitational constant will be different for every agent based on its fitness and thus will help in controlling the acceleration and step sizes of the agents which further improve exploration and exploitation of the solution search space. The proposed strategy is tested over 23 well-known classical benchmark functions and 11 shifted and biased benchmark functions. Various statistical analyzes and a comparative study with original GSA, Chaos-based GSA (CGSA), Bio-geography Based Optimization (BBO) and DBBO has been carried out.

The statement and solution of the problem of the expansion of the Universe in nonstationary spherically-symmetric coordinates in the Schwarzschild metric are considered without pressure taken into account. The observational data of astronomers investigating the rates of recession of distant stars are explained on the basis of the obtained solutions.

We discuss the notion of global scale invariance, as realized in the theory of induced gravity $\mathcal{L}=\sqrt{-g} [-\frac{1}{2} \epsilon \phi^{2} R+ \frac{1}{2} (\nabla\phi)^2 -V(\phi) + \mathcal{R}^2] + \mathcal{L}_{\rm m}$, whereby the Newton gravitational constant $ G_{\rm N}$ is generated from the expectation value of a scalar field $ \phi$ via the dimensional coupling parameter $ \epsilon$. Assuming the Friedmann space-time $ {\rm d}s^2={\rm d} t^2-a^2(t){\rm d} { x}^2$, where the radius function is of the form $ a= (t/t_0)^{2/3\gamma}$, and a power-law field $ \phi=\phi_0 t^n$ and matter energy-density source $ \rho_{{\rm m}} =\rho_{ot}^{m}$, which imply that $ m=-2 \gamma_{{\rm m}}/\gamma$ , $ \gamma_{{\rm m}}$ being the matter adiabatic index, conditions are derived for the positivity of $ \epsilon$. In the special case of the Milne universe, defined by $ \gamma = 2/3$, which is also the string equation of state, the line element is invariant under global coordinate transformations $ t\rightarrow t'=\zeta t$. There is then no creation of particle-anti-particle pairs, nor, analogously in the superstring theory, of string-anti-string pairs. These results follow from the correspondence principle, the respective classical wave states propagating without amplification or attenuation. Some aspects of scale and modular invariance of the superstring are also described.

We consider the gravitational collapse for neutron stars in the Hartree-Fock-Bogoliubov theory. We prove that when the number particle becomes large and the gravitational constant is small such that the attractive interaction strength approaches the Chandrasekhar limit mass slowly, the minimizers develop a universal blow-up profile. It is given by the Lane-Emden solution.

The idea of "asymptotically free" gravity is implemented using a constrained mimetic scalar field. The effective gravitational constant is assumed to vanish at some limiting curvature. As a result singularities in contracting spatially flat Friedmann and Kasner universes are avoided. The solutions in both cases approach de Sitter metric with a limiting curvature.We show that quantum metric fluctuations vanish when this limiting curvature is approached., Comment: 14 pages

In this paper, a new fuzzy adaptive artificial physics optimization (FAAPO) algorithm is used to solve security-constrained optimal power flow (SCOPF) problem with wind and thermal power generators. The stochastic nature of wind speed is modeled as a Weibull probability density function. The production cost is modeled with the overestimation and underestimation of available wind energy and included in the conventional SCOPF. Wind generation cost model comprises two components, viz. reserve capacity cost for wind power surplus and penalty cost for wind power shortage. The selection of optimal gravitational constant (G) is a tedious process in conventional artificial physics optimization (APO) method. To overcome this limitation, the gravitational constant (G) is fuzzified in this work. Therefore, based upon the requirement, the gravitational constant changes adaptively. Hence, production cost is reduced, settles at optimum point and takes less number of iterations. The proposed algorithm is tested on IEEE 30-bus system and Indian 75-bus practical system, including wind power in both the test systems. It is observed that FAAPO can outperform BAT algorithm and APO algorithm. Hence, the proposed algorithm can be used for integration of wind power with thermal power generators.

The precession of the perihelion of Mercury’s orbit for 100 years in the gravitational field of the Sun and the planets has been numerically modeled within the framework of a generalized law of universal gravitation with refined data on the parameters of the orbits of the planets (including the asteroid belt and Pluto), and also the gravitational constant and with a smaller iteration step (0.0002 s). The calculations were performed with enhanced computational accuracy. It has been shown that the average precession of Mercury’s orbit in 100 years within the framework of the generalized law of universal gravitation comprises ~565.3''. This is less than the observed shift of the perihelion by about 8.8''. The observed shift of the perihelion, as is well known, comprises ~574.1''. It is not ruled out that inside Mercury’s orbit some unknown undetected object (or several such objects) of small size remains to be found.

In this paper, we have studied the locally rotationally symmetric (LRS) Bianchi type-I cosmological model filled with a bulk viscous cosmological fluid in $$f(R)$$ gravity in the presence of time-varying gravitational and cosmological constant. We have used the power-law and intermediate scenario for scale factor to obtain the solution of the field equations. The evolution of temperature of a viscous Universe is also analysed.

The common nature of the dark sector - dark energy and dark matter - as shown in [1] follows readily from the consideration of generalized Newtonian potential as a weak-field General Relativity. That generalized potential satisfying the Newton's theorem on the equivalence of sphere's gravity and that of a point-mass located in its center, contains an additional constant which along with the gravitational constant is able to explain quantitatively both the dark energy (cosmological constant) and dark matter. So, gravity is defined not by one but two fundamental constants. We show that, the second constant is dimensional-independent and matter-uncoupled and hence is even more universal than the gravitational constant, thus affecting the strategy of observational studies of dark energy and of the search of dark matter., Comment: To appear in Eur Phys J C; 5 pages

We study a dynamic $\Lambda$ model with varying gravitational constant $G$ under the Kaluza-Klein cosmology. Physical features and the limitations of the present model have been explored and discussed. Solutions are found mostly in accordance with the observed features of the accelerating universe. Interestingly, signature flipping of the deceleration parameter is noticed and the present age of the Universe is also attainable under certain stringent conditions. We find that the time variation of gravitational constant is not permitted without vintage $\Lambda$., Comment: 9 pages, 5 figures, Accepted in International Journal of Theoretical Physics

In the 1950s, surprising links were proposed between cosmological theory and the geological and paleontological sciences. These links were mainly provided by Paul Dirac’s hypothesis of 1937 that the gravitational constant G decreases with cosmic time. Pascual Jordan, famous for his pioneering contributions to quantum theory, took up Dirac’s hypothesis; after the end of World War II, Jordan developed its geophysical consequences, concluding that the Earth is expanding. Much of Jordan’s later scientific work focused on the expanding Earth and other aspects of the earth sciences relating to the varying-G hypothesis. This chapter in the history of science has received almost no attention from either scientists or historians. The article analyzes Jordan’s cosmo-geological work in relation to the somewhat similar efforts of other “expansionists” in the period that led to the plate tectonic revolution in the earth sciences.

A class of multidimensional theories is identified in which the spatial and temporal variations in the gravitational constant and the fine structure constant have a common origin and are of the same magnitude. Arguments are presented in favor of the existence of these variations despite a lack of confirmed observational data on variations in the gravitational constant because of problems in constructing a unified theory of physical interactions and the well-known faint young Sun paradox. It is concluded that the gravitational constant probably depends nonlinearly on cosmological time.

We investigate the post-Newtonian parameter $\gamma$ and derive its formalism in generalized non-local (GNL) gravity,which is the modified theory of general relativity (GR) obtainedby adding a term $m^{2n-2}R\Box^{-n}R$ to the Einstein-Hilbert action.Concretely, based on parametrizing the generalized non-local action in which gravity is described by a series of dynamical scalar fields $\phi^i$in addition to the metric tensor $g_{\mu\nu}$,the post-Newtonian limit is computed, and the effective gravitational constant as well as the post-Newtonian parameters are directly obtained from the generalized non-local gravity. Moreover, by discussing the values of the parametrized post-Newtonian parameters $\gamma$, we can compare our expressions and results with thosein Hohmann and Jarv et al. (2016),as well as current observational constraints on the values of $\gamma$ in Will (2006).Hence, we draw restrictions on the nonminimal coupling terms $\bar{F}$ around their background values.

We have studied the time dependence of the gravitational constant $G$ and cosmological constant $\varLambda$ by taking into account an anisotropic and homogeneous Bianchi type-I space-time in the framework of the modified $f(R,T)$ theory of gravity proposed by Harko et al. (Phys. Rev. D 84:024020, 2011). For a specific choice of $f(R,T)=R+2f(T)$ where $f(T)=-\lambda T$ , two solutions of the modified gravity field equations have been generated with the help of a variation law between the expansion anisotropy ( ${\sigma}/{\theta}$ ) and the scale factor ( $S$ ), together with a general non-linear equation of state. The solution for $m\neq3$ corresponds to singular model of the universe whereas the solution for $m=3$ represents a non-singular model. We infer that the models entail a constant value of the deceleration parameter. A careful analysis of all the physical parameters of the models has also been carried out.

The derivation of the Vlasov–Maxwell and the Vlasov–Poisson–Poisson equations from Lagrangians of classical electrodynamics is described. The equations of electromagnetohydrodynamics (EMHD) type and electrostatics with gravitation are obtained. We obtain and compare the Lagrange equalities and their generalizations for different types of the Vlasov and EMHD equations. The conveniences of writing the EMHD equations in twice divergent form are discussed. We analyze exact solutions to the Vlasov–Poisson–Poisson equations with the presence of gravitation where we have different types of nonlinear elliptic equations for trajectories of particles with critical mass m2 = e2/G, which has an obvious physical sense, where G denotes the gravitation constant and e is the electron charge. As a consequence we have different behaviors of particles: divergence or collapse of their trajectories.

We study antigravity in F(R)-theory originating scalar-tensor theories and also in Brans-Dicke models without cosmological constant. For the F(R) theory case, we obtain the Jordan frame antigravity scalar-tensor theory by using a variant of the Lagrange multipliers method and we numerically study the time dependent effective gravitational constant. As we shall demonstrate in detail by using some viable F(R) models, although the initial F(R) models have no antigravity, their scalar-tensor counterpart theories might or not have antigravity, a fact mainly depending on the parameter that characterizes antigravity. Similar results hold true in the Brans-Dicke model, which we also studied numerically. In addition, regarding the Brans-Dicke model we also found some analytic cosmological solutions. Since antigravity is an unwanted feature in gravitational theories, our findings suggest that in the case of F(R) theories, antigravity does not occur in the real world described by the F(R) theory, but might occur in the Jordan frame scalar-tensor counterpart of the F(R) theory, and this happens under certain circumstances. The central goal of our study is to present all different cases in which antigravity might occur in modified gravity models.

About 300 experiments have tried to determine the value of the Newtonian gravitational constant, G, so far, but large discrepancies in the results have made it impossible to know its value precisely. The weakness of the gravitational interaction and the impossibility of shielding the effects of gravity make it very difficult to measure G while keeping systematic effects under control. Most previous experiments performed were based on the torsion pendulum or torsion balance scheme as in the experiment by Cavendish in 1798, and in all cases macroscopic masses were used. Here we report the precise determination of G using laser-cooled atoms and quantum interferometry. We obtain the value G=6.67191(99) x 10^(-11) m^3 kg^(-1) s^(-2) with a relative uncertainty of 150 parts per million (the combined standard uncertainty is given in parentheses). Our value differs by 1.5 combined standard deviations from the current recommended value of the Committee on Data for Science and Technology. A conceptually different experiment such as ours helps to identify the systematic errors that have proved elusive in previous experiments, thus improving the confidence in the value of G. There is no definitive relationship between G and the other fundamental constants, and there is no theoretical prediction for its value, against which to test experimental results. Improving the precision with which we know G has not only a pure metrological interest, but is also important because of the key role that G has in theories of gravitation, cosmology, particle physics and astrophysics and in geophysical models., 3 figures, 1 table

In this paper, by assuming the change of energy density $\dot {\rho }\neq 0$ we have considered cosmological scenarios of the generalized Chaplygin gas and modified generalized Chaplygin gas with variable Λ and G in the context of the flat Hořava-lifshitz gravity, respectively. The behavior of the trivial solutions obtained, are highly depended to free parameters of their equation of state α, β and also the running coupling constants of Hořava-Lifshitz gravity λ and μ. Contrary to our expectations, in the infrared limit λ=1 and μ=0 the gravitational constant G(t) divergence. We must report that, unlike standard cosmology, the values of free parameter β is restricted to negative values. In addition, we try to examine the evolution of the physical quantities relevant to the description of the early universe up now, namely the scale factor a, deceleration parameter q and the total entropy of the Hubble horizon S T H . We deduce that neither of these quantities not consistent with our current knowledge of cosmology, in IR limit. So, the most important conclusion of this paper is that, Chaplygin gas model with variable G, Λ within the Hořava-Lifshitz gravity, will not lead to physical valid results.

The gravitational constant, G, which governs the strength of gravitational interactions, is hard to measure accurately. Two independent determinations of G have been made that have the smallest uncertainties so far. Two independent determinations of the gravitational constant.

Two-fluid anisotropic Bianchi type-III cosmological model is investigated with variable gravitational constant G and cosmological constant Λ in the framework of Einstein’s general relativity. In the two-fluid model, one fluid represents the matter content of the universe and another fluid is chosen to model the cosmic microwave background radiation. The dynamics of the anisotropic universe with variable G and Λ are discussed. We also discussed in detail the behavior of associated fluid parameters and kinematical parameters.

In this paper, we have studied the cosmological models of Bianchi type-I universes in a different basic form filled with bulk viscous fluid, in the presence of time-dependent gravitational as well as cosmological constants. A set of new exact cosmological solutions have been obtained in both full and truncated causal theories. These solutions are suitable for describing the evolution of the universe in its early stages. The physical and dynamical consequences have been discussed in detail.

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.

A non-geometric relativistic theory of gravitation is developed by defining a semi-metric to replace the metric tensor as gravitational vector potential. The theory show that the energy-momentum tensor of the gravitational field belong to the gravitational source, gravitational radiation is contained in Einstein’s field equations that including the contribution of gravitational field, the real physical singularity in the gravitational field can be eliminated, and the dark matter in the universe is interpreted as the matter of pure gravitational field.

A brief review of theoretical models explaining the variation in the fine structure constant α in space and time is given. A method is described for constructing models in which variations in α and other fundamental physical constants, including the gravitational constant G, follow from the dynamics of extra space-time dimensions in the framework of a multidimensional theory of gravitation that is nonlinear with respect to curvature. An explicit example of such a model is constructed for explaining the observed spatial and temporal variations in α.

In the present work we revisit a model consisting of a scalar field with a quartic self-interaction potential non-minimally (conformally) coupled to gravity [1]. When the scalar field vacuum is in a broken symmetry state, an effective gravitational constant emerges which, in certain regimes, can lead to gravitational repulsive effects when only ordinary radiation is coupled to gravity. In this case, a bouncing universe is shown to be the only cosmological solution admissible by the field equations when the scalar field is in such a broken symmetry state., 10 pages, 1 figure

In order to study how the gravitational constant, G, varies within the Barber’s second self-creation theory of gravitation we find exact solutions for Bianchi type I, VII0, IX and Kantowski-Sach (KS) under the self-similar hypothesis. Some physical and geometrical properties of the models are also discussed and compare the obtained results with the current observations. We also compare our results with the obtained ones in the Brans-Dicke theory.

We study some features of entropic force approach in the presence of a noncommutative Schwarzschild-deSitter black hole. In this setup, there exists a similarity between the small and large scales. There are two finite cut-off in very short and long distances wherein the force and energy graph stop abruptly at those scales. We find that the existence of a deSitter core around the origin, induced by noncommutativity, in addition to a standard deSitter background at large scale may lead to a violation of the equivalence principle. Finally in order to directly observe the finite cut-off at short-scale gravity, caused by noncommutativity quantum fluctuations, we derive an effective gravitational constant., Comment: 14 pages, 4 figures, to appear in Astrophysics and Space Science

We investigate thermodynamics of viscous dark energy interacting with dark matter in a DGP braneworld. We show that the Friedmann equation in this setup can be rewritten as the first law of thermodynamics on the apparent horizon. We study the time evolution of the total entropy including the entropy of the matter fields inside the apparent horizon together with the entropy associated with the apparent horizon. Interestingly enough, we find that, in the presence of bulk viscosity, the generalized second law of thermodynamics is always preserved for both branches of the DGP braneworld. When the time varying gravitational constant is taken into account, the generalized second law of thermodynamics can be secured provided, where ? and u are, respectively, the bulk viscosity coefficient and the energy densities ratio of the two dark components on the brane. © 2013 Springer Science+Business Media New York., Shiraz Institute for Cancer Research, Shiraz University of Medical Sciences The Research Council

Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future., Comment: 23 pages, 9 figures. Invited review article, minor modifications to match published version

A gravitational gauge theory with a spin–affine connection (Lorentz connection) as a rotational gauge potential (fundamental dynamical variable) is suggested for reformulating the theory of Stephenson–Kilmister–Yang gravity, in which the Einstein field equation of gravity is a first-integral solution of a spin-connection gravitational gauge field equation. A heavy intermediate field $$\phi $$ that accompanies a matter field $$\varphi $$ is introduced in order to remove the conventional dimensionful gravitational coupling. Such a $$\varphi $$ – $$\phi $$ coupling can lead to dimensionless gravitational coupling (i.e., the gravitational constant is dimensionless) in the present gravitational gauge field theory. A low-energy effective Lagrangian density for the matter field can be obtained by integrating out the accompanying heavy field in generating functional of path integral formalism, and therefore, a dimensionful gravitational coupling coefficient (Einstein gravitational constant) emerges. Such a dimensionless coupling of gravity, where the dimensionful coupling is emergent at low energies, is considered for scalar and spinor fields, which serve as gravitating matter fields (gravitational source). Though there are higher derivatives (e.g., third- and fourth-order partial derivatives) of the scalar and spinor fields in the low-energy effective Lagrangian densities, the ordinary equations of motion of the scalar and spinor fields can also be emergent from the present gravitational gauge theory. Therefore, the Einstein gravity can be recovered from the present gravitational gauge theory. In addition to the gravitational Lagrangian of the spacetime-rotational gauge potential (i.e., spin–affine connection), the Lagrangian of a spacetime-translational gauge potential (i.e., vierbein) is also constructed. Thus, the present dimensionless gravitational gauge coupling preserves local rotational and translational gauge symmetries. Since the spin-connection gravitational gauge field equation is a third-order differential equation of metric (the Einstein field equation of gravity is a first-integral solution), it could provide a new route to the vacuum energy cosmological constant problem.

In this paper we consider higher dimensional FRW type cosmological models with time-varying gravitational constant G=G(t) and decaying vacuum energy Λ=Λ(t) in context of the open thermodynamical system of particle creation. The particle creation rate is determined by variable G and Λ. An Exact solution of the gravitational field equations is obtained by assuming the exact power-law solution of the scale factor of the universe. We evaluate the various cosmological parameters and discuss their physical significance in detail for radiation and matter-dominated phases of the universe. The solutions are also relevant for quintessence (accelerating) universe. We also discuss the relevance of the solutions for 5-dimensional Kaluza-Klein FRW type model with and without particle creation in radiation and matter-dominated phases as special case. We obtain the solution where the gravitational constant increases with time during no particle creation. The cosmological constant Λ, however, decreases with time in all the cases.