Gravitational Constant Research Articles

Classical and quantum gravity from the axioms of relativistic quantum mechanics

It is common practice to describe elementary particles by irreducible unitary representations of the Poincaré group. In the same way, multi-particle systems can be described by irreducible unitary representations of the Poincaré group. Representations of the Poincaré group are characterised by fixed eigenvalues of two Casimir operators corresponding to a fixed mass and a fixed angular momentum. In multi-particle systems (of massive spinless particles), fixing these eigenvalues leads to correlations between the particles. In the quasi-classical approximation of large quantum numbers, these correlations take on the structure of a gravitational interaction described by the field equations of conformal gravity. A theoretical value of the corresponding gravitational constant is calculated. It agrees with the empirical value used in the field equations of general relativity.

Deriving the cosmological constant from the Euler–Lagrange equation of second-order differentiable gravitational field Lagrangian

The principles underlying the variational approach prove to be invaluable tools in articulating physical phenomena, particularly when dealing with conserved quantities. The derivation of gravitational field equations from the Euler–Lagrange equation, a result of the first-order derivative of Lagrange field density, is a well-established concept. However, within the context of this paper, the field equations stem from the second-order differentiable field Lagrangian in the Euler–Lagrange equation. The Euler–Lagrange equation of the first-order differentiable field Lagrangian yields the gravitational field equations incorporating matter fields and the cosmological constant. On the other hand, the Euler–Lagrange equation of the second-order differentiable field Lagrangian gives rise to the equation governing the cosmological constant. The procedure of determining the cosmological constant through the Euler–Lagrange equation adheres to fundamental mathematical theory encompassing higher-order Euler–Lagrange equations. This theory implies that utilizing higher-order Euler–Lagrange equations may result in instability due to negative energy. The cosmological constant is postulated to be intertwined with negative vacuum energy density. The value assigned to the gravitational constant, as ascertained through the employment of the general relativistic equation, is not only significantly small and nonzero but also demonstrates remarkable compatibility with the value inferred from observational deductions.

Constrain the time variation of the gravitational constant via the propagation of gravitational waves

The gravitational constant variation means the breakdown of the strong equivalence principle. As the cornerstone of general relativity, the validity of general relativity can be examined by studying the gravitational constant variation. Such variations have the potential to affect both the generation and propagation of gravitational waves. Here, our focus lies on the effect of gravitational constant variation specifically on the propagation of gravitational waves. In a previous paper (An et al., 2023 [13]) we have studied such effect based on a Maxwell-like equation. That work admits two drawbacks. The assumption that describing gravitational waves with Maxwell-like equation is not solid. And more such treatment can only deal with space dependent gravitational constant. In the current paper we will remedy these two issues. We employ two analytical methods, namely based on the Fierz-Pauli action and the perturbation of Einstein-Hilbert action around Minkowski spacetime, both leading to the same gravitational wave equation. By solving this equation, we find the effects of gravitational constant variation on gravitational wave propagation. The result is consistent with previous investigations based on Maxwell-like equations for gravitational waves for space dependent gravitational constant cases. In addition we can constrain the time variation of the gravitational constant via the propagation of gravitational waves based on GW170817 data. And more, we find that small variations in the gravitational constant result in an amplitude correction at the leading order and a phase correction at the sub-leading order for gravitational waves. These results provide valuable insights for probing gravitational constant variation and can be directly applied to gravitational wave data analysis.

The conformal sector of Quantum Einstein Gravity beyond the local potential approximation

The anomalous scaling of Newton's constant around the Reuter fixed point is dynamically computed using the functional flow equation approach. Specifically, we thoroughly analyze the flow of the most general conformally reduced Einstein-Hilbert action. Our findings reveal that, due to the distinctive nature of gravity, the anomalous dimension η of the Newton's constant cannot be constrained to have one single value: the ultraviolet critical manifold is characterized by a line of fixed points (g⁎(η),λ⁎(η)), with a discrete (infinite) set of eigenoperators associated to each fixed point. More specifically, we find three ranges of η corresponding to different properties of both fixed points and eigenoperators and, in particular, for the range η<ηc≈0.96 the ultraviolet critical manifolds has finite dimensionality.

From Newton to universal Planck natural units – disentangling the constants of nature

This study exploits a historical gap in the evolution of metric systems that resulted from the incomplete implementation of the ‘rationalization’ concept published by Heaviside in 1893 and by ignoring the suggestion of Maxwell in 1873 to use the simplest form of Newton’s gravitational law expression with no proportionality constant. Bridging this gap required deriving an experimental Rationalized Metric System (RMS) and a corresponding Universal Planck Natural Unit System (UPNUS) in [ LT ] units. The described solution combines Heaviside’s rationalization of Newton’s law and makes the unit of mass dimensions [ L3T−2 ], as suggested by Maxwell. Consequently, the modified Coulomb’s law, changes the unit of electric charge to the same dimensions as those of mass. The elimination of the kilogram and ampere has a disentangling effect on the dependencies among the constants of nature and opens new horizons. New systems have the potential to become powerful exploratory tools in fundamental research and education because of the simplification of the relationships among physical quantities. Some highlights from the analyzed examples are worth mentioning. The well-known expression for the Stoney mass (m S ) when converted to RMS units is reduced to the electron charge quantity, whereas traditional metric systems entangle the charge, speed of light, and gravitational constant, forming an entity in the dimension of mass, as first presented by Stoney in 1874. Furthermore, a well-substantiated conjecture is proposed, wherein the Stoney energy E S = m S c 2 is likely the long-sought, finite electric field energy of the electron, and the gravitational constant appears to be the limiting factor. In UPNUS, the most disentangled fundamental expression, apart from the Stoney mass, is the elementary charge as the function of the fine structure constant α and the Planck mass namely with and of the same [ L3T−2 ] dimensions in Planck units, where

Experimental Data-Analysis Methods Analyze Multiphase-Flow Data Sets

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper OTC 32170, “Performance Mapping of Multiphase-Flow Model—Connecting the Dots From Experimental Data,” by Auzan A. Soedarmo, SPE, Eduardo Pereyra, SPE, and Cem Sarica, SPE, The University of Tulsa. The paper has not been peer reviewed. Copyright 2023 Offshore Technology Conference. Reproduced by permission. _ In the complete paper, the authors present exploratory data analyses to evaluate comprehensively the performance of a steady-state multiphase-flow point model in predicting high-pressure, near-horizontal data from independent experiments. This effort provides wide-ranging insight that can reflect the current state of the art of multiphase-flow modeling and pinpoint areas where improvements are needed. Much of the complete paper is devoted to the literature relating to the authors’ work; these specific citations are not included in this synopsis. Introduction The emergence of “big data” has encouraged the use of data from various sources to enhance the decision-making process. The authors write that, unfortunately, multiphase-flow studies often are performed in theoretical silos, within which specific experiments were performed and upon which certain model improvements were proposed. Therefore, it is easy to lose sight of the larger context in terms of current understanding and modeling capability. This disconnected approach also has produced an ever-growing, potentially unmanageable list of closure relationships, which can be counterproductive for model development. Experimental Data-Analysis Methodology For their study, the authors collected near-horizontal (–5° to +5°) gas/liquid data from literature with a gas density of 5 kg/m3 or greater. Atmospheric data were excluded because gas and air at such conditions are typically very compressible, meaning that superficial gas velocity can vary considerably along the pipe. One also can argue that high-gas-density cases are more relevant to typical high-pressure field applications. The authors collected more than 2,000 data points for pressure drop, holdup, and flow patterns. This accumulated data set by no means can be categorized as “big data” in a traditional sense; however, the authors write that it is sufficient for demonstrating how exploratory data analysis may extract actionable insights from data sets from various independent sources. This data set is henceforth called the “HP data set.” No high-viscosity liquid (10 cP or higher) is included in the HP data set. When comparing experimental data collected under different conditions, it is helpful to reduce the problem’s dimensionality (down from 10 dimensions in two-phase gas/liquid flow, excluding the gravitational acceleration constant). A traditional approach would be to use dimensionless numbers such as Reynolds and Froude numbers. A single dimensionless number, however, can only account for limited parameters. For example, the Reynolds number only considers the inertia and viscous effects, while the Froude number only considers the inertia and gravity effects. Therefore, a mechanistic multiphase-flow model is used in this study that accounts for all dimensions of the multiphase-flow problems and reduces them into one dimension, namely the discrepancy between the predicted value and experimental data.

Gravito-electromagnetic perturbations of MOG black holes with a cosmological constant: quasinormal modes and ringdown waveforms

In this paper, we present a black hole solution with a cosmological constant in the Scalar-Tensor-Vector Modified Gravity (MOG) theory, where the strength of the gravitational constant is determined by G = G N(1 + α).We derive the master equations for gravito-electromagnetic perturbations and numerically solve for the Quasinormal Mode (QNM) spectrum and the ringdown waveforms.Our research results show that increasing the MOG parameter α leads to a decrease in both the real and imaginary parts of the QNM frequencies for electromagnetic and gravitational modes.Similarly, increasing the cosmological constant Λ also results in a decrease in both the real and imaginary parts of the QNM frequencies for these modes.These trends are observed when compared to standard Schwarzschild-de Sitter (S-dS) or MOG black holes, respectively.Meanwhile, the result indicates that in the MOG-de Sitter spacetime, the frequencies for electromagnetic and gravitational modes display isospectrality, and exhibit the same ringdown waveforms.Our findings have implications for the ringdown phase of mergers involving massive compact objects, which is of particular relevance given the recent detections of gravitational waves by LIGO.

Searching for a secular variation of the gravitational constant using strong gravitational fields

Searching for a secular variation of the gravitational constant using strong gravitational fields

The Upgraded Planck System of Units That Reaches from the Known Planck Scale All the Way down to Subatomic Scales

Natural systems of units {Ui} need to be overhauled to include the dimensionless coupling constants {αUi} of the natural forces. Otherwise, they cannot quantify all the forces of nature in a unified manner. Thus, each force must furnish a system of units with at least one dimensional and one dimensionless constant. We revisit three natural systems of units (atomic, cosmological, and Planck). The Planck system is easier to rectify, and we do so in this work. The atomic system discounts {G,αG}, thus it cannot account for gravitation. The cosmological system discounts {h,αh}, thus it cannot account for quantum physics. Here, the symbols have their usual meanings; in particular, αG is the gravitational coupling constant and αh is Dirac’s fine-structure constant. The speed of light c and the impedance of free space Z0 are resistive properties imposed by the vacuum itself; thus, they must be present in all systems of units. The upgraded Planck system with fundamental units UPS:={c,Z0,G,αG,h,αh,…} describes all physical scales in the universe—it is nature’s system of units. As such, it reveals a number of properties, most of which have been encountered previously in seemingly disjoint parts of physics and some of which have been designated as mere coincidences. Based on the UPS results, which relate (sub)atomic scales to the Planck scale and the fine-structure constant to the Higgs field, we can state with confidence that no observed or measured physical properties are coincidental in this universe. Furthermore, we derive from first principles Koide’s K=2/3 enigmatic constant and additional analogous quark and vector boson constants. These are formal mathematical proofs that justify a posteriori the use of geometric means in deriving the quark/boson mass ladder. This ladder allows us to also calculate the Higgs couplings to the vector bosons and the Weinberg angle in terms of K only, and many of the “free” parameters of the Standard Model of particle physics were previously expected to be determined only from experiments.

Bayesian analysis of systematic errors in the determination of the constant of gravitation

Measurements of the gravitational constant G are notoriously difficult. Individual state-of-the-art experiments have managed to determine the value of G with high precision: although, when considered collectively, the range in the measured values of G far exceeds individual uncertainties, suggesting the presence of unaccounted for systematic effects. Here, we propose a Bayesian framework to account for the presence of systematic errors in the various measurement of G while proposing a consensus value, following two paths: a parametric approach, based on the maximum entropy principle, and a non-parametric one, the latter being a very flexible approach not committed to any specific functional form. With both our methods, we find that the uncertainty on this fundamental constant, once systematics are included, is significantly larger than what quoted in CODATA 2018. Moreover, the morphology of the non-parametric distribution hints towards the presence of several sources of unaccounted for systematics. In light of this, we recommend a consensus value for the gravitational constant G = 6.6740^{+0.0015}_{-0.0015} times 10^{-11} textrm{m}^3 textrm{kg}^{-1} textrm{s}^{-2}.

Cosmogenesis as symmetry transformation

We consider the quantized bi-scalar gravity, which may serve as a locally Lorentz invariant cosmological model with varying speed of light and varying gravitational constant. The equation governing the quantum regime for the case of homogeneous and isotropic cosmological setup is a Dirac-like equation which replaces the standard Wheeler–DeWitt equation. We show that particular cosmogenesis may occur as a result of the action of the symmetry transformation which due to Wigner’s theorem can either be unitary or antiunitary. We demonstrate that the transition from the pre-big-bang contraction to the post-big-bang expansion – a scenario that also occurs in string quantum cosmologies – can be attributed to the action of charge conjugation, which belongs to the class of antiunitary transformations. We also demonstrate that the emergence of the two classical expanding post-big-bang universe–antiuniverse pairs, each with opposite spin projections, can be understood as being triggered by the action of a unitary transformation resembling the Hadamard gate.

Plane Symmetric Cosmological Model with Strange Quark Matter in f(R,T) Gravity

A plane symmetric Bianchi-I model filled with strange quark matter (SQM) was explored in f(R,T)=R+2λT gravity, where R is the Ricci scalar, T is the trace of the energy-momentum tensor, and λ is an arbitrary constant. Three different types of solutions were obtained. In each model, comparisons of the outcomes in f(R,T) gravity and bag constant were made to comprehend their roles. The first power-law solution was obtained by assuming that the expansion scalar is proportional to the shear scalar. This solution was compared with a similar one obtained earlier. The second solution was derived by assuming a constant deceleration parameter q. This led to two solutions: one power-law and the other exponential. Just as in the case of general relativity, we can obtain solutions for each of the different eras of the universe, but we cannot obtain a model which shows transitional behavior from deceleration to acceleration. However, the third solution is a hybrid solution, which shows the required transition. The models start off with anisotropy, but are shear free at late times. In general relativity, the effect of SQM is to accelerate the universe, so we expect the same in f(R,T) gravity.

Atom Interferometry with Rb Blue Transitions.

We demonstrate a novel scheme for Raman-pulse and Bragg-pulse atom interferometry based on the 5S-6P blue transitions of ^{87}Rb that provides an increase by a factor ∼2 of the interferometer phase due to accelerations with respect to the commonly used infrared transition at 780nm. A narrow-linewidth laser system generating more than 1W of light in the 420-422nm range was developed for this purpose. Used as a cold-atom gravity gradiometer, our Raman interferometer attains a stability to differential acceleration measurements of 1×10^{-8} g at 1s and 2×10^{-10} g after 2000s of integration time. When operated on first-order Bragg transitions, the interferometer shows a stability of 6×10^{-8} g at 1s, averaging to 1×10^{-9} g after 2000s of integration time. The instrument sensitivity, currently limited by the noise due to spontaneous emission, can be further improved by increasing the laser power and the detuning from the atomic resonance. The present scheme is attractive for high-precision experiments as, in particular, for the determination of the Newtonian gravitational constant.

A Study of Evolution of Cosmological Parameters Based on a Dark Energy Model in the Framework of Brans-Dicke Gravity

The objective of the present study is to find the characteristics of evolution of a homogeneous and isotropic universe in the framework of Brans-Dicke (BD) theory of gravity. FLRW space-time, with zero spatial curvature, has been used to obtain BD field equations. Scale factor and Hubble parameter have been obtained from an ansatz for the deceleration parameter, assumed on the basis of its property of signature flip indicating a change of phase from deceleration to acceleration. Validation of the model has been achieved by a suitable parametrization of that ansatz. Expressions for energy density, pressure, equation of state (EoS) parameter, cosmological constant, gravitational constant have been derived and depicted graphically. The gravitational constant is found to decrease with time at a gradually decreasing rate. The Hubble parameter, deceleration parameter and energy density decrease with time, which is in agreement with many other studies. The value of the EoS parameter at the present epoch is negative, and it becomes more negative with time. The cosmological constant increases very rapidly in the early universe from negative to smaller negative values, becoming positive finally, with a much slower change thereafter. A cosmographic and a geometrical analysis have been carried out. It is observed that a gradual transition takes place from a regime of quintessence to phantom dark energy. An important finding of this study is that the signature flip of the deceleration parameter takes place almost simultaneously with the signature flip of the cosmological constant, implying a connection between accelerated expansion and dark energy, which is represented here by the cosmological constant. Unlike the common practice of using arbitrary units, proper SI units for all measurable quantities have been used. This theoretical investigation provides the reader with a simple method to formulate models in the framework of BD theory.

Enhanced Modeling of Crumple Zone in Vehicle Crash Simulation Using Modified Kamal Model Optimized with Gravitational Search Algorithm

The effectiveness of a vehicle crash system depends on how well it can simulate the behavior of a real vehicle in a crash scenario and accurately identifies the correct working limits of the model parameters, including mass, spring, and damper. Therefore, this study explores the modelling vehicle front crumple zone to represent the behaviors of real crash scenario. The modelling process using Kamal approach is used to develop a precise vehicle crash model for analyzing the impact of a collision on both the vehicle and its passengers. In this study, a complex mass-spring-damper system representing the front crumple zone of an actual car is re-designed to modify the existing vehicle crash model. The gravitational search algorithm (GSA) is implemented in the simulation model's code to obtain optimized values of damping coefficient (c) and spring constant (k). The simulation results show that the deformation response of crumple zone and the deceleration response of vehicle body match the experimental results, indicating the model's accuracy. Additionally, this study investigates the effects of varying the GSA parameters' number of agents (N), the beta parameter (β), and the gravitational constant (G) to improve the model's accuracy by minimizing the root mean square error (RMSE) between model response and crash test data. The optimal GSA parameter chosen in this study were N = 50, β = 0.3, and G = 20 with the lowest RMSE of 22.3874, 22.26664, and 23.86638 respectively.

The electromagnetic origin of gravity

Under the condition of the expansion of the universe and all masses with their charges in it, the electromagnetic origin of the gravitational force is determined with the help of the Lorentz force. Basic physical relations to the interactions of the basic forces of nature are established. This includes calculation formulas for the gravitational constant, the proton radius and the age of the universe.

Gravitational waves from walls bounded by strings in SO(10) model of pseudo-Goldstone dark matter

We explore the gravitational wave spectrum generated by string-wall structures in an SO(10) (Spin(10)) based scenario of pseudo-Goldstone boson dark matter (pGDM) particle. This dark matter candidate is a linear combination of the Standard Model (SM) singlets present in the 126 and 16 dimensional Higgs fields. The Higgs 126-plet vacuum expectation value (VEV) 〈126H〉 leaves unbroken the Z2 subgroup of Z4, the center of SO(10). Among other things, this yields topologically stable cosmic strings with a string tension μ∼〈126H〉2. The subsequent (spontaneous) breaking of Z2 at a significantly lower scale by the 16-plet VEV 〈16H〉 leads to the appearance of domain walls bounded by the strings produced earlier. We display the gravitational wave spectrum for Gμ values varying between 10−15 and 10−9 (〈126H〉∼1011 - 1014 GeV), and 〈16H〉∼0.1 - 102 TeV range (G denotes Newton's constant.) These predictions can be tested, as we show, by a variety of (proposed) experiments including LISA, ET, CE and others.

Revisiting the thermodynamics of the BTZ black hole with a variable gravitational constant* *Supported by the National Natural Science Foundation of China (12275216, 12105222, 12247103)

The thermodynamics of BTZ black holes are revisited with a variable gravitational constant. A new pair of conjugated thermodynamic variables are introduced, including the central charge C and chemical potential μ. The first law of thermodynamics and the Euler relationship, instead of the Smarr relationship in the extended phase space formalism, are matched perfectly in the proposed formalism. Compatible with the standard extensive thermodynamics of an ordinary system, the black hole mass is verified to be a first order homogeneous function of the related extensive variables, and restores the role of internal energy. In addition, the heat capacity has also resulted in a first order homogeneous function using this formalism, and asymptotic behavior is demonstrated at the high temperature limit. The non-negativity of the heat capacity indicates that the rotating and charged BTZ black holes are thermodynamically stable.

The effect of the gravitational constant variation on the propagation of gravitational waves

Since the first detection of gravitational waves, they have been used to investigate various fundamental problems, including the variation of physical constants. Regarding the gravitational constant, previous works focused on the effect of the gravitational constant variation on the gravitational wave generation. In this paper, we investigate the effect of the gravitational constant variation on the gravitational wave propagation. The Maxwell-like equation that describes the propagation of gravitational waves is extended in this paper to account for situations where the gravitational constant varies. Based on this equation, we find that the amplitude of gravitational waves will be corrected. Consequently the estimated distance to the gravitational wave source without considering such a correction may be biased. Applying our correction result to the well known binary neutron star coalescence event GW170817, we get a constraint on the variation of the gravitational constant. Relating our result to the Yukawa deviation of gravity, we for the first time get the constraint of the Yukawa parameters in 10 Mpc scale. This scale corresponds to a graviton mass mg∼10−31 eV.

Cosmology in holographic non-minimal derivative coupling theory: Constraints from inflation and variation of gravitational constant

We consider a cosmological model of non-minimal derivative coupling (NMDC) to gravity with holographic effect from Bekenstein–Hawking entropy using Hubble horizon IR cutoff. Holographic parameter c is considered constant with value in a range, 0≤c<1. The NMDC effect is considered either as modification in kinetic scalar field or in gravitational constant. The NMDC effect allows gravitational constant to be time-varying. Since the NMDC effect is cosmological, definition of holographic density should include time-varying part of the gravitational constant. The NMDC part reduces strength of gravitational constant for κ>0 and opposite for κ<0. The holographic part enhances gravitational strength. Slow-roll parameters are derived. We use spectral index and tensor-to-scalar ratio to test the model against CMB constraint. Number of e-folding is chosen to be N≥60. Power-law scalar potentials, V=V0ϕn with n=2,4, and exponential potential, V=V0exp(−βϕ) are considered. Combined parametric plots of κ and ϕ show that the allowed regions of the power spectrum index and of the tensor-to-scalar ratio are not overlapping. NMDC inflation is ruled out and the holographic NMDC inflation is also ruled out for 0<c<1. NMDC significantly changes major anatomy of the dynamics, i.e. it gives new late-time attractor trajectories in acceleration regions. The holographic part clearly affects pattern of trajectories. However, for the holographic part to affect shape of the acceleration region, the NMDC field must be in presence. To constrain the model at late time, variation of gravitational constant is considered. Gravitational-wave standard sirens and supernovae data give a constraint, Ġ/G|t0≲3×10−12year−1 (Zhao et al., 2018) which, for this model, results in 10−12year−1≳−κϕ̇ϕ̈/MP2. Positive κ is favored and greater c2 results in lifting up lower bound of κ.