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The complete title of this paper should be "The geometry of the constant gravitational field or how to switch from the mechanical Lagrangian to a geometric Lagrangian" and in this abstract we sketch why. To begin with, let us say that Einstein managed to integrate the constant gravitational field in the special theory of relativity, obtaining a metric whose geodesics are locally parabolas. The existence of a similar metric deduced from the considerations of Newtonian mechanics is somehow obstructed by the Lagrangian involved in the description of the constant gravitational field. Therefore, we need to explain how the mechanical Lagrangian above which is not suitable for a metric description of the constant gravitational field can be switched into a geometrical Lagrangian having the same geodesics and suitable for the metric description of the constant gravitational field. The geometric method found by us is related to a parabolic type of transformations. A consequence of the previous method can be applied for the study of bending of light rays in a constant gravitational field. [ABSTRACT FROM AUTHOR]

The concept of a rapidly sign-switching cosmological constant, interpreted as a mirror AdS-dS transition in the late universe and known as the Λ s CDM, has significantly improved the fit to observational data, offering a promising framework for alleviating major cosmological tensions such as the H 0 and S 8 tensions. However, when considered within general relativity, this scenario does not predict any effects on the evolution of the matter density contrast beyond modifications to the background functions. In this work, we propose a new gravitational model in which the background dynamics predicted by the Λ s CDM framework are mapped into f (T) gravity, dubbed f (T) - Λ s CDM, rendering the models indistinguishable at the background level. However, in this new scenario, the sign-switching cosmological constant dynamics modify the evolution of linear matter perturbations through an effective gravitational constant, G eff . We investigate the evolution of the growth rate and derive new observational constraints for this scenario using RSD measurements. We also present new constraints in the standard Λ s CDM case, incorporating the latest Type Ia supernovae data samples available in the literature, along with BAO data from DESI. Our findings indicate that the new corrections expected at the linear perturbative level, as revealed through RSD samples, can provide significant evidence in favor of this new scenario. Additionally, this model may be an excellent candidate for resolving the current S 8 tension. [ABSTRACT FROM AUTHOR]

The aim of this paper is to inspect the geometrical aspects of a perfect fluid spacetime conveying hyperbolic Ricci soliton with torse-forming vector field ξ. Next, we have investigated some physical perceptions of perfect fluid spacetime such as dark fluid spacetime, stiff matter fluid spacetime, dust fluid spacetime and radiation fluid spacetime with hyperbolic Ricci soliton in terms of isotropic pressure, the cosmological constant, energy density and gravitational constant. We have also provided two examples of hyperbolic Ricci soliton and hyperbolic Ricci–Bourguignon soliton. Later, we explore the relativistic magneto-fluid spacetime obeying hyperbolic Ricci soliton along with different vector fields. [ABSTRACT FROM AUTHOR]

Physical properties of the Sun (orientation of rotation axis, oblateness coefficient J 2 ⊙ , and change rate of the gravitational parameter μ ˙ ⊙ ) are determined using a dynamical model describing the motion of the Sun, planets, the Moon, asteroids, and Trans-Neptunian objects (TNOs). Among the many kinds of observations used to determine the orbits and physical properties of the bodies, the most important for our study are precise interplanetary ranging data: Earth–Mercury ranges from MESSENGER spacecraft and Earth–Mars ranges from Odyssey and MRO. The findings allow us to improve the model of the Sun in modern planetary ephemerides. First, the dynamically determined direction of the Sun's pole is ≈2° off the visible axis of rotation of the Sun's surface, which is corroborated by present knowledge of the Sun's interior. Second, the change rate of the Sun's gravitational parameter is found to be smaller (in absolute value) than the nominal value derived from the estimate of mass loss through radiation and solar wind. Possible interpretations are discussed. [ABSTRACT FROM AUTHOR]

We present observations from two field deployments of a calibrated tiltmeter that we name the Self‐Calibrating Tilt Accelerometer (SCTA). The tiltmeter is based upon a triaxial quartz crystal accelerometer; the horizontal channels measure tilt and are periodically rotated into the vertical to obtain a measurement of the acceleration of gravity. Changes in the measured total acceleration are ascribed to drift in the vertical channel and used as calibrations for removing that same drift from the tilt time series observed between calibrations. Changes in the span (sensitivity) of the accelerometer channels can also be measured by calibrating them pointing up and down. A 3‐year test on the seafloor at Axial Seamount show that the calibrations are consistent with a linear‐exponential model of drift to a RMS residual of ∼0.5 μg (μrad). The calibrated tilt time series was impacted by platform settling for the first 2 years, but after repositioning the tiltmeter, the calibrated observations were consistent for the final year with the tilt observed on a nearby LILY tiltmeter, within an assumed level of drift for the unconstrained LILY sensor. A separate 15‐month test in a stable vault at Piñon Flat Observatory was complicated by seasonal temperature variations of >5°C; the calibrations are consistent with a linear‐exponential model of drift to ∼2 μg RMS when temperature and temperature time‐derivative dependence is included. Similarly, the calibrated tilt time series was impacted by thermal deformation of the SCTA assembly. A future test in a thermally and tectonically stable borehole will be required to assess the accuracy of the SCTA. Plain Language Summary: We developed a new instrument for measuring the tilt of a surface to a high degree of accuracy, on the order of a millionth of a radian. This instrument, the Self‐Calibrating Tilt Accelerometer (SCTA), combines three sensor channels that measure acceleration, arranged so that two channels are horizontal at right angles and the other is vertical. Tilting of the ground surface moves the horizontal channels toward alignment with the (vertical) gravitational acceleration, producing an observable signal. The SCTA can rotate to put any of the three channels into the vertical, where they can be calibrated against the full, effectively constant gravitational acceleration. These calibrations correct the horizontal tilt measurements for artificial signals generated within the sensors, yielding reliable measurements of the tilt of the ground surface. We present data from two deployments of the SCTA concept, one land‐based at Piñon Flats Observatory and the other seafloor‐based at Axial Seamount. At Axial, there is ongoing tilting of the seafloor from volcanic inflation that the SCTA measures consistent with a nearby, independent sensor. Piñon Flats should be tectonically stable, but seasonal temperature fluctuations at the site induced apparent tilt signals from internal deformation of the SCTA assembly. Key Points: A 3‐axis quartz crystal accelerometer is calibrated against gravity to remove drift from measurements of tilt in the horizontal channelsCalibrations for separate field tests in a vault and on the seafloor are fit by a linear‐exponential drift model to ∼1 μg residualCalibrations suggest variable span changes by sensor, from approximately 1–5 μg/yr, or 1%–22% of the respective drift rate [ABSTRACT FROM AUTHOR]

Milgrom’s Modified Newtonian Dynamics (MOND) correction to Newtonian gravity is shown to be equivalent to a more fundamental transformation between a non-inertial local reference frame and the fixed background of the observable universe, complying with Mach’s principle. Both Newton’s gravitational constant and Milgrom’s MOND acceleration parameter or scale constant are substituted for the speed of light and two varying and measurable cosmological parameters under the justification of Schrödinger’s and Sciama’s interpretation of Mach’s principle: causally connected mass and size of the universe. This Machian interpretation, free from fundamental constants and parameters with the exception of the speed of light as the speed of gravity, is based on relative field intensities of the small and large scale of the universe. The Machian MOND approximation is a necessary feature of a phenomenological theory of modified inertia which incorporates Mach’s principle in agreement with galaxy rotation curves. [ABSTRACT FROM AUTHOR]

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In this paper, we explore the conformal structure of singularities arising from varying fundamental constants using the method of Penrose diagrams. We employ a specific type of bimetric model featuring two different metrics. One metric describes the causal structure for matter, while the other characterizes the causal structure for gravitational interactions, which is related to variations in fundamental constants such as the gravitational constant and the speed of light. For this reason, we focused on the gravitational metric to calculate the conformal transformation and compose Penrose diagrams for the singularities arising from the varying fundamental constants. We have shown that, in one case, the parameter such as the scale factor, the density and the pressure resemble those of the finite scale factor singularity (FSF). Despite singularity appears in constant conformal time in our case and in the case of FSF the Misner-Sharp horizon looks different. Our another case is similar to sudden future singularity (SFS), but there are differences in the conformal structures. We have also shown that in our cases the behavior of Misner-Sharp horizon strongly depends on initial conditions. The last analytical solution which we introduced is identical to conformal structure of the standard exotic singularity for the matter. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study geometrical aspects of an almost Ricci soliton on (wRs)4 perfect fluid spacetime obeying Einstein’s field equation. Among others, we first find the soliton constant and cosmological constant in terms of scalar curvature and potential vector field in (wRs)4 perfect fluid spacetime. Next, we discuss some physical phenomena related to dust fluid, dark fluid, and radiation era in (wRs)4 perfect fluid spacetime admitting an almost Ricci soliton with potential vector field as solenoidal vector field and basic vector field ρ under matter collineation condition. Further, we find an inequality for soliton constant when (wRs)4 perfect fluid spacetime obeys the timelike convergence condition. Finally, we obtain some results in a (wRs)4 perfect fluid spacetime whose metric represents an almost Ricci soliton when basic vector field and potential vector field both are torseforming vector field ρ. Also, for such spacetime we find the soliton constant in terms of cosmological constant, gravitational constant, energy density, and isotropic pressure. We also provide an example of (wRs)4 spacetime whose metric represents an almost Ricci soliton. [ABSTRACT FROM AUTHOR]

We discuss the quantum-bouncer experiment involving ultracold neutrons in a braneworld scenario. Extra-dimensional theories typically predict the strengthening of gravitational interactions over short distances. In this paper, we specifically study the anomalous gravitational interaction between the bouncing neutron and the reflecting mirror, resulting from hidden dimensions, and investigate the effects of this new interaction on the outcome of the quantum-bouncer experiment in the context of a thick brane model. This analysis allows us to identify which physical quantity of the extra-dimensional theory this neutron experiment is capable of constraining. Based on the experimental data, we found a new and independent empirical bound on the free parameters of the model: the higher-dimensional gravitational constant and a parameter related to a transverse width of the confined matter inside the thickbrane. This new bound is valid in scenarios with an arbitrary number of extra dimensions greater than two. In this manner, by considering the thickness of the brane, we have been able to extend previous studies on this topic, which were limited to models with few codimensions, due to non-computability problems of power-law corrections of the gravitational potential. [ABSTRACT FROM AUTHOR]

In this present paper, we have investigated the dark energy cosmological model in Bianchi-VI0spacetime by considering generalised Brans-Dicke theory, self-interacting potential, and a dynamical coupling parameter. For this purpose, we have utilised a hybrid scale factor to approximate the dynamical behaviour of the deceleration parameter. The deceleration parameter should display distinctive flipping behaviour at the transition redshift since the universe is thought to have changed from an early deceleration to a late temporal acceleration. We have studied six alternative transitioning dark energy models on the basis of observational restrictions on the transition redshift. For each model, the behaviour of the dynamical scalar field, the Brans-Dicke parameter, and the self-interacting potential are examined. On top of that, we used the generalised Brans-Dicke theory to estimate how the Newtonian gravitational constant changes over time. [ABSTRACT FROM AUTHOR]

The present paper dealt with the study of solitons of Lorentzian Kähler space-time manifolds. In this paper, we have discussed different conditions for solitons to be steady, expanding, or shrinking in terms of isotropic pressure, the cosmological constant, energy density, nonlinear equations, and gravitational constant in pseudo-quasi-conformally flat and pseudo-W8 flat Lorentzian Kahler space-time manifolds. [ABSTRACT FROM AUTHOR]

In the context of the minimally extended varying speed of light (meVSL) model, both the absolute magnitude and the luminosity distance of type Ia supernovae (SNe Ia) deviate from those predicted by general relativity (GR). Using data from the Pantheon+ survey, we assess the plausibility of various dark energy models within the framework of meVSL. Both the constant equation of state (EoS) of the dark energy model (ω CDM) and the Chevallier–Polarski–Linder (CPL) parameterization model ( ω = ω 0 + ω a (1 − a) ) indicate potential variations in the cosmic speed of light at the 1 − σ confidence level. For Ω m 0 = 0.30 , 0.31 , and 0.32 with (ω 0 , ω a) = (− 1 , 0) , the 1 − σ range of c ˙ 0 / c 0 (10 − 13 yr − 1) is (−8.76, −0.89), (−11.8, 3.93), and (−14.8, −6.98), respectively. Meanwhile, the 1 − σ range of c ˙ 0 / c 0 (10 − 12 yr − 1) for CPL dark energy models with − 1.05 ≤ ω 0 ≤ − 0.95 and 0.28 ≤ Ω m 0 ≤ 0.32 is (−6.31, −2.98). The value of c at z = 3 can exceed that of the present by 0.2∼3% for ω CDM models and 5∼13% for CPL models. Additionally, for viable models except for the CPL model with Ω m 0 = 0.28 , we find − 25.6 ≤ G ˙ 0 / G 0 (10 − 12 yr − 1) ≤ − 0.36 . For this particular model, we obtain an increasing rate of the gravitational constant within the range 1.65 ≤ G ˙ 0 / G 0 (10 − 12 yr − 1) ≤ 3.79 . We obtain some models that do not require dark matter energy density through statistical interpretation. However, this is merely an effect of the degeneracy between model parameters and energy density and does not imply that dark matter is unnecessary. [ABSTRACT FROM AUTHOR]

Following a recent proposal to describe inelastic eikonal scattering processes in terms of gravitationally dressed elastic eikonal amplitudes, we motivate a collinear double graviton dressing and investigate its properties. This is derived from a generalized Wilson line operator in the worldline formalism by integrating over fluctuations of the eikonal trajectories of external particles in gravitationally interacting theories. The dressing can be expressed as a product of exponential terms — a coherent piece with contributions to all odd orders in the gravitational coupling constant and a term quadratic in graviton modes, with the former providing classical gravitational wave observables. In particular, the coherent dressing involves O κ 3 subleading double graviton corrections to the Weinberg soft factor. We use this dressing to derive expressions for the waveform, radiative momentum spectrum and angular momentum. In a limiting case of the waveform, we derive the nonlinear memory effect resulting from the emission of nearly soft gravitons from a scattering process. [ABSTRACT FROM AUTHOR]

In this work, the hypothesis that the universe is made up of 4-dimensional spheres of space, whose diameter is the. Planck length, allows us to calculate most of the constants used in current physical theories. Calculated constants include: elementary charge, fine structure constant, electron mass, Planck constant, gravitational constant, electrical constant, Boltzmann constant, mass and charge of up and down quarks, mass of second generation quarks: strange and charm, muon mass, Z boson mass and Higgs boson mass. All of them depending on the speed of light and the Planck length, which shows that all the constants are related and not due to chance. [ABSTRACT FROM AUTHOR]

The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction with the rest of the universe. This idea is known today as Mach's principle. We discuss Mach's principle based on transactional gravity, the recently developed connection of entropic gravity to the physics of quantum events, induced by transactions. It is shown that Mach's principle holds and that there is a fundamental relation between the gravitational constant G and the total mass in the causal universe. This relationship, derived by means of entropic principles, is rigorously proven. [ABSTRACT FROM AUTHOR]

The mass (M BH) of a supermassive black hole (SMBH) can be measured using spatially resolved kinematics of the region where the SMBH dominates gravitationally. The most reliable measurements are those that resolve the smallest physical scales around the SMBHs. We consider here three metrics to compare the physical scales probed by kinematic tracers dominated by rotation: the radius of the innermost detected kinematic tracer R min normalized by the SMBH's Schwarzschild radius (R Schw ≡ 2 GM BH/ c 2, where G is the gravitational constant and c the speed of light), sphere-of-influence (SOI) radius (⁠|$R_\mathrm{SOI}\equiv GM_\mathrm{BH}/\sigma _\mathrm{e}^2$|⁠ , where σe is the stellar velocity dispersion within the galaxy's effective radius), and equality radius [the radius R eq at which the SMBH mass equals the enclosed stellar mass, M BH = M *(R eq), where M *(R) is the stellar mass enclosed within the radius R ]. All metrics lead to analogous simple relations between R min and the highest circular velocity probed V c. Adopting these metrics to compare the SMBH mass measurements using molecular gas kinematics to those using megamaser kinematics, we demonstrate that the best molecular gas measurements resolve material that is physically closer to the SMBHs in terms of R Schw but is slightly farther in terms of R SOI and R eq. However, molecular gas observations of nearby galaxies using the most extended configurations of the Atacama Large Millimeter/submillimeter Array can resolve the SOI comparably well and thus enable SMBH mass measurements as precise as the best megamaser measurements. [ABSTRACT FROM AUTHOR]

Aiming at the problem of low operating efficiency and high energy consumption of large pumping stations in China, considering the loss of motor and frequency converter, combined with time-of-use electricity price, a model of minimumdaily operating tariff of pumping stations was established, and artificial electric field algorithm (AEFA) was adopted to solve it. Due to the calculation method for the original gravitational constant leads to premature algorithms and a tendency to fall into local optima, chaotic mapping was introduced for improving the algorithm. Combined with the calculation and solution of a pump station project in Shanxi Province, the results show that the energy saving rate of the artificial electric field algorithm optimization scheme can reach 5.7%-11.3% compared with the actual operation scheme, and the energy saving rate of the improved artificial electric field algorithm optimization scheme can reach 9.9%-28.4% compared with the actual operation scheme. After the improvement of the algorithm, the calculation accuracy, stability and calculation time are better. [ABSTRACT FROM AUTHOR]

We construct a new cosmological model based on relativistic theory of gravity characterized by massive gravitons. The new Friedmann–Robertson–Walker model is characterized by the presence of a static traversable wormhole, massive gravitons, and a variable gravitational coupling constant. To recover the Bianchi identity, a second cosmic fluid is introduced in the theory. Motivated from cosmic dark radiation phenomenological arguments, which suggest that the dynamical component of dark energy could be dominated by a bath of dark radiation, we assume that the original cosmic fluid is radiative, whereas the new cosmic fluid is phantom. The total equation of state of our model is equal to −1. The new model is characterized by an effective Hubble parameter. The solutions of the dynamical equations reveal an accelerated universe with a scale factor of hyperbolic type which allows the deceleration parameter to change sign from a decelerating phase to an accelerating phase. We have evaluated the deceleration parameter, the jerk and the present day variations of the gravitational constant which agree with astronomical observations. [ABSTRACT FROM AUTHOR]

We investigate the dynamics of a sliding top that is a rigid body with an ideal sharp tip moving in a perfectly smooth horizontal plane, so no friction forces act on the body. We prove that this system is integrable only in two cases analogous to the Euler and Lagrange cases of the classical top problem. The cases with the constant gravity field with acceleration g ≠ 0 and without external field g = 0 are considered. The non-integrability proof for g ≠ 0 is based on the fact that the equations of motion for the sliding top are a perturbation of the classical top equations of motion. We show that the integrability of the classical top is a necessary condition for the integrability of the sliding top. Among four integrable classical top cases, the corresponding two cases for the sliding top are also integrable, and for the two remaining cases, we prove their non-integrability by analyzing the differential Galois group of variational equations along a certain particular solution. In the absence of a constant gravitational field g = 0 , the integrability is much more difficult. First, we proved that if the sliding top problem is integrable, then the body is symmetric. In the proof, we applied the Ziglin theorem concerning the splitting of separatrices phenomenon. Then, we prove the non-integrability of the symmetric sliding top using the differential Galois group of variational equations except two the same as for g ≠ 0 cases. The integrability of these cases is also preserved when we add to equations of motion a gyrostatic term. [ABSTRACT FROM AUTHOR]

The current and next observation seasons will detect hundreds of gravitational waves (GWs) from compact binary systems coalescence at cosmological distances. When combined with independent electromagnetic measurements, the source redshift will be known, and we will be able to obtain precise measurements of the Hubble constant H 0 via the distance–redshift relation. However, most observed mergers are not expected to have electromagnetic counterparts, which prevents a direct redshift measurement. In this scenario, one possibility is to use the dark sirens method that statistically marginalizes over all the potential host galaxies within the GW location volume to provide a probabilistic source redshift. Here we presented H 0 measurements using two new dark sirens compared to previous analyses using DECam data: GW190924 |$\_$| 021846 and GW200202 |$\_$| 154313. The photometric redshifts of the possible host galaxies of these two events are acquired from the DECam Local Volume Exploration Survey (DELVE) carried out on the Blanco telescope at Cerro Tololo. The combination of the H 0 posterior from GW190924 |$\_$| 021846 and GW200202 |$\_$| 154313 together with the bright siren GW170817 leads to |$H_{0} = 68.84^{+15.51}_{-7.74}\, \rm {km\, s^{-1}\, Mpc^{-1}}$|⁠. Including these two dark sirens improves the 68  per cent confidence interval (CI) by 7  per cent over GW170817 alone. This demonstrates that the addition of well-localized dark sirens in such analysis improves the precision of cosmological measurements. Using a sample containing 10 well-localized dark sirens observed during the third LIGO/Virgo observation run, without the inclusion of GW170817, we determine a measurement of |$H_{0} = 76.00^{+17.64}_{-13.45}\, \rm {km\, s^{-1}\, Mpc^{-1}}$|⁠. [ABSTRACT FROM AUTHOR]

Exploring the cosmological variations of fundamental dimensionless constants, such as the fine-structure constant, α , the proton-to-electron mass ratio, μ , and the gravitational constant, G, is essential for testing new phenomena beyond the standard cosmological models. This study focuses on investigating the potential variation of constants by analyzing strong gravitational fields associated with white dwarf stars. Utilizing the observed spectrum of G191-B2B, we present a new constraint on the cosmological variation of μ over extended time scales, Δ μ / μ = (0. 0 8 4 ± 1. 0 4 4) × 1 0 − 8 , incorporating the gravitational redshift z ≈ 5 × 1 0 − 5 . This finding represents a new tool for checking the parameters for Grand Unified Theories (GUTs). [ABSTRACT FROM AUTHOR]

There is a strong belief that Allah Almighty could reveal His existence by encoding the laws of nature and their fundamental constants in the Quran with impeccable precision. However, the mathematical frameworks and patterns embedded within the Quranic text to reveal scientific laws and constants may contain minor deviations in numerical values to empower personal exploration, accommodate diverse interpretations, and strengthen faith. This theory is based on the fact that the Quran is the word of Allah Almighty. Consequently, one would anticipate finding evidence suggesting a divine origin. Many scholars and researchers have suggested that this evidence can be found in the mathematical structure of the Quran through patterns, numerical codes, and other mathematical features within the text that are too complex to be simply attributed to human authorship. Therefore, it is believed that the Quran contains within its structure a mathematical encoding of all physical laws and constants. Verses like 20.98, which state, "He encompasses all things in knowledge," are quoted as evidence. According to this perspective, the Quran is assumed to incorporate mathematical miracles, indicating a potential correspondence between its text and the underlying order of the universe. This theory reveals many mathematical frameworks illustrating how the Quran embeds scientific knowledge. These include the identification of frequent occurrences of the golden ratio within the Quranic text and the manifestation of the golden ratio in the human body, alongside the determination of key celestial parameters such as the length of the solar year. Furthermore, this theory uncovers a numerical link between the Quran and fundamental scientific constants, notably the universal gravitational constant, the speed of light, and the Planck constant. Moreover, this theory utilizes numerical analysis to offer a compelling rationale for why the numbers 28 and 114 are used to represent the total number of Arabic letters and chapters in the Quran, respectively. Finally, this theory highlights the Quran's remarkable mathematical architecture, offering indisputable evidence of its divine composition. We behold a mathematical marvel of cosmic scale, a phenomenon defying human intelligence. Indeed, the Quran is a product of a superintelligence exceeding our comprehension. [ABSTRACT FROM AUTHOR]

The internal structure and mass distribution of the terrestrial objects are yet unknown. The 2D gravity model with a constant density of the terrestrial objects can shed light on the surficial or textural heterogeneity due to topographic variations of the terrestrial objects. Three different asteroids, which are Bennu (101955), Itokawa (25143) and Eros (433) are modelled in this study. During the modelling phase, a different number of edges, elements, nodes, and faces are used to describe the 3D models of Bennu, Itokawa, and Eros. These 3D models are used in 2D Non-Uniform Fast Fourier Transform (NU-FFT) applications to obtain gravitational attraction with a constant density polyhedron model. Tensor gradients and tensor invariants of the modelled gravity anomaly are calculated. Three major outcomes are interpreted from tensor gradient and tensor invariants. Firstly, textural heterogeneity due to relatively low topography is detected in the central part of Bennu. Secondly, considerably different properties which can be related to surface variations between the two lobes of Itokawa are observed. Lastly, directional surficial heterogeneities were detected in Eros. [ABSTRACT FROM AUTHOR]

The hybrid flowshop scheduling problem with unrelated parallel machines exists in many industrial manufacturers, which is an NP-hard combinatorial optimisation problem. To solve this problem more effectively, an improved gravitational search (IGS) algorithm is proposed which combines three strategies: generate new individuals using the mutation strategy of the standard differential evolution (DE) algorithm and preserve the optimal solution via a greedy strategy; substitute the exponential gravitational constant of the standard gravitational search (GS) algorithm with a linear function; improve the velocity update formula of the standard GS algorithm by mixing an adaptive weight and the global search strategy of the standard particle swarm optimisation (PSO) algorithm. Benchmark examples are solved to demonstrate the proposed IGS algorithm is superior to the standard genetic algorithm, DE, GS, DE with local search, estimation of distribution algorithm and artificial bee colony algorithms. Two more examples from a real-world water-meter manufacturing enterprise are effectively solved. [ABSTRACT FROM AUTHOR]

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.

The purpose of the present study is to determine the characteristics of time evolution of various cosmological quantities, based on four models constructed for a universe undergoing accelerated expansion. This formulation is done in the framework of Kaluza-Klein space-time, for zero spatial curvature. To solve the field equations, an ansatz is chosen for each model in such a way that it leads to a signature flip of the deceleration parameter, to ensure its consistency with recent astrophysical observations indicating a change from a decelerated expansion to an accelerated expansion of the universe. Based on these four models, time evolutions of several cosmological parameters are obtained and their variations are shown graphically against time. The arbitrary constants, associated with each model, are so tuned that the model correctly predicts the values of the Hubble parameter, deceleration parameter, energy density and gravitational constant at the present time. The findings from these models are consistent with each other, and they are in agreement with the observed features. The gravitational constant (G) shows a rapid fall in the early universe, followed by an extremely slow rise which continues at the present time. Taking (G) as a constant in two of the four models, the cosmological constant is found to be independent of time. A significant finding is that the signature flip of the deceleration parameter almost coincides with the signature flip of the cosmological constant (Λ), pointing towards a relation between the accelerated expansion and the dark energy which is represented by Λ. Other plots with respect to Λ also depict dark energy’s role in governing cosmic evolution. Considering its dynamical nature, Λ is referred to as cosmological term (instead of cosmological constant) in the text. Contrary to the common trend of using arbitrary units, the SI units for all measurable quantities are used.

To solve the problems being easy to fall into local optimum and weak development capability of traditional universal gravitational search algorithm（GSA）, this paper proposed an improved gravity search algorithm with a multistrategy fusion（MFGSA）. Firstly, in order to enhance the exploration capability and convergence precision of the algorithm, the improved algorithm used an update strategy for dynamically adjusting the gravitational constant G.Secondly, in order to preserve the diversity of particles and improve the convergence precision, the improved algorithm proposed a particle crossing processing strategy based on symmetry idea. To accommodate the first two strategies, the improved algorithm used the elitist strategy which is introduced to improve the position of the worst particles with the optimal particles to avoid the algorithm falling into local optimization. At the same time, the improved algorithm proposed a self-adaptive factor to update particle velocity and position strategy to improve the convergence speed of the algorithm. This paper designed a few compared experiments with the traditional universal gravitation search algorithm and other four improved universal gravitation search algorithms on 10 benchmark functions to verify the performance of the improved algorithm, the results show that MFGSA has great advantages in convergence speed and search accuracy, which proves the superiority of MFGSA performance. [ABSTRACT FROM AUTHOR]

We show that the f(R)-gravity theories with constant Ricci scalar in the Jordan/Einstein frame can be described by Einstein or Einstein–Maxwell gravity with a cosmological term and a modified gravitational constant. To obtain the rotating axisymmetric solutions for the Einstein/Einstein–Maxwell gravity with a cosmological constant, we also propose a modified Newmann–Janis algorithm which involves the non-complexification of the radial coordinate and a complexification of the polar coordinate. Using the duality between the two gravity theories we show that the stationary or static solutions for the Einstein/Einstein–Maxwell gravity with a cosmological constant will also be the solutions for the dual f(R)-gravity with constant Ricci scalar. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

MEMS-IMUs are widely used in research, industry, and commerce. A proper calibration technique must reduce their innate errors. In this study, a turntable-based IMU calibration approach was presented. Parameters such as the bias, lever arm, and scale factor, in addition to misalignment, are included in the general nonlinear model of the IMU output. Accelerometer error parameters were estimated using the transformed unscented Kalman filter (TUKF) with triangulation algorithm is suggested for calibrating inertial measurement unit (MPU6050) three-axes accelerometer. In contrast to the present methods, the suggested method uses the gravitational signal as a constant reference and necessitates no external equipment. The technique requires that the sensor be positioned in a rough orientation and that basic rotations be adopted. This technology also offers a quicker and easier calibration. Comparing the experimental findings with other works, Allan deviation shows significant improvements for the bias instability, where a bias instability of (0.116 μg) is achieved at temperatures between (−15°C) and (80°C). [ABSTRACT FROM AUTHOR]

Searching for variations in dimensionless physical constants presents a meaningful characteristic in experimental and observational studies. One of the most valuable explorations of these variations could depend on the evolution of white dwarf stars. By analyzing the spectrum of the white dwarf star G191-B2B, we derive a robust limit on the cosmological variation of the gravitational constant: G ˙ / G = (0.238 ± 2.959) × 10 - 15 yr - 1 . This limit proposes a potential test of the framework of modern unification theories. [ABSTRACT FROM AUTHOR]

In this paper, we report on exact charged black hole solutions in symmergent gravity with Maxwell field. Symmergent gravity induces the gravitational constant G, quadratic curvature coefficient c O , and the vacuum energy V O from the flat spacetime matter loops. In the limit in which all fields are degenerate in mass, the vacuum energy V O can be expressed in terms of G and c O . We parametrize deviation from this limit by a parameter α ˆ such that the black hole spacetime is de Sitter (dS) for α ˆ < 1 and anti-de Sitter (AdS) for α ˆ > 1. In our analysis, we study horizon formation, shadow cast and gravitational lensing as functions of the black hole charge, and find that there is an upper bound on the charge. At relatively low values of charge, applicable to astronomical black holes, we determine constraints on c O and α ˆ using the Event Horizon Telescope (EHT) data from Sgr. A* and M87*. We apply these constraints to reveal how the shadow radius behaves as the observer distance r O varies. It is revealed that black hole charge directly influences the shadow silhouette, but the symmergent parameters have a tenuous effect. We also explored the weak field regime by using the Gauss–Bonnet theorem to study the weak deflection angle caused by the M87* black hole. We have found that impact parameters comparable to the actual distance D = 16.8 Mpc show the potential detectability of such an angle through advanced astronomical telescopes. Overall, our results provide new insights into the behavior of charged black holes in the context of symmergent gravity and offer a new way to test these theories against observational data. [ABSTRACT FROM AUTHOR]

Physics presents us with a symphony of natural constants: , ℏ , , and so forth. Up to this point, constants have received comparatively little philosophical attention. In this article, I provide an account of dimensionful constants, in particular the gravitational constant. I propose that they represent interquantity structure in the form of relations between quantities with different dimensions. I use this account of to settle a debate over whether mass scalings are symmetries of Newtonian gravitation. I argue that they are not, but only if we interpret mass anti-quidditistically. This is analogous to anti-haecceitism in the presence of spacetime symmetries. [ABSTRACT FROM AUTHOR]

Various models of modified gravity invoke 'screening' mechanisms that are sensitive to the value of the local gravitational potential. This could have observable consequences for galaxies. These consequences might be seen by comparing two proxies for galaxy mass – their luminosity and their internal kinematics – as a function of local galaxy density. Motivated by this prospect, we have compared the observed properties of luminous red galaxies (LRGs) inside and outside of voids in the cosmic large scale structure. We used archival measurements of line widths, luminosities, redshifts, colours, and positions of galaxies in conjunction with recent void catalogues to construct comparison LRG samples inside and outside of voids. We fitted these two samples to the well-established fundamental plane of elliptical galaxies to constrain any differences between the inferred value of the Newtonian gravitational constant G for the two samples. We obtained a null result, with an upper limit on any fractional difference in G within and outside of cosmological voids to be α = δ G / G ∼ 40 per cent. This upper bound is dominated by the small-number statistics of our N ∼ 100 within-void LRG sample. With the caveat that environmental effects could influence various parameters such as star formation, we estimate that a 1 per cent statistical limit on α could be attained with data from 105 elliptical galaxies within voids. This is within the reach of future photometric and spectroscopic surveys, both of which are required to pursue this method. [ABSTRACT FROM AUTHOR]

All known planets orbit the Sun so harmoniously that the entire Universe is believed to behave in a rhythmical and fractal way. Titius–Bode law is the main theoretical tool for planetary orbit description. Here we show that planetary sequence follows the Fibonacci-like prime sequence, and we introduce two gravitational spirals to predict orbits for solar members orbiting the Sun. Furthermore, we predict two hypothetical planets as far as 1500 AU and 2300 AU from the Sun, respectively, in our solar system, and some unknown planets in extrasolar planetary systems. Our planetary sequence demonstrates the possible frontier of our solar system, and the theory is also valid for other star systems and planetary systems, giving a simple way to finding the most possible adjacent unknown planets or moons near a known one. We anticipate our sequence can be more sophisticatedly used to search for unknown Universes and to depict the cosmos fully and exclusively, and we conclude that our whole Universe is of fractal property and all celestial bodies are distributed according to Fibonacci sequence. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We consider it worthy if we could construct a realistic model universe that would enable us to identify a clue about the source of dark energy. So, we develop a Scale Covariant Theory model universe considering a 5D spherically symmetric space-time. It is predicted that the constructed model itself behaves as a phantom energy model/ source that tends to a de Sitter phase avoiding the finite-time future singularity (big rip). The model universe is isotropic and is free from an initial singularity. The gravitational constant G decreases with a variation of − 7. 2 × 1 0 − 1 1 yr − 1 and the Hubble parameter is estimated to be H = 6 8. We also provide a thorough analysis of the cosmological findings with graphical representations. [ABSTRACT FROM AUTHOR]

Methods of computer algebra are used to investigate equilibrium orientations of a satellite moving along a circular orbit under the action of gravitational and constant torques. The main focus is placed on the investigation of equilibrium orientations in the cases where the constant torque vector is parallel to the planes formed by the principal central axes of inertia of the satellite. Using methods for Gröbner basis construction, the system of six algebraic equations that determine the equilibrium orientations of the satellite is reduced to one sixth-order algebraic equation in one unknown. Domains with equal numbers of equilibrium solutions are classified using algebraic methods for constructing discriminant hypersurfaces. Bifurcation curves in the space of problem parameters, which define the boundaries of the domains with equal numbers of equilibrium solutions, are constructed. A comparative analysis of the influence of the order of variables in the process of Gröbner basis construction is carried out. Using the proposed approach, it is shown that, under the action of the constant torque, the satellite with unequal principal central moments of inertia has no more than 24 equilibrium orientations in a circular orbit. [ABSTRACT FROM AUTHOR]