Gravitational Coupling Constant Research Articles

Next-to-eikonal corrected double graviton dressing and gravitational wave observables at OG2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({G}^2\\right) $$\\end{document}

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 Oκ3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O}\\left({\\kappa}^3\\right) $$\\end{document} 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.

Probing Weyl-type [formula omitted] gravity: Cosmological implications and constraints

In this paper, we investigate the cosmological implications and constraints of Weyl-type f(Q,T) gravity. This theory introduces a coupling between the non-metricity Q and the trace T of the energy–momentum tensor, using the principles of proper Weyl geometry. In this geometry, the scalar non-metricity Q, which characterizes the deviations from Riemannian geometry, is expressed in its standard Weyl form ∇μgαβ=−wμgαβ and is determined by a vector field wμ. To study the implications of this theory, we propose a deceleration parameter with a single unknown parameter χ, which we constrain by using the latest cosmological data. By solving the field equations derived from Weyl-type f(Q,T) gravity, we aim to understand the behavior of the energy conditions within this framework. In the present work, we consider two well-motivated forms of the function f(Q,T): (i) the linear model represented by f(Q,T)=αQ+β6κ2T, and (ii) the coupling model represented by f(Q,T)=γ6H02κ2QT, where α, β, and γ are free parameters. Here, κ2=116πG represents the gravitational coupling constant. In both of the models considered, the strong energy condition is violated, indicating consistency with the present accelerated expansion. However, the null, weak, and dominant energy conditions are satisfied in these models.

Black strings in asymptotically safe gravity

In this paper, we study black strings in asymptotic safety gravity (ASG) scenario. The ASG approach is introduced by implementing gravitational and cosmological running coupling constants directly in the black string metric. We calculate the Hawking temperature, entropy, and heat capacity of the improved black string metric in two cases: considering the cosmological constant fixed in some fixed point and the general case where both Newton’s constant and cosmological constant are improved. For the identification of the scale moment we used an general inverse law setting k(r) ∼ 1/r n . We show that improving only the Newton’s constant the problem of singularity is solved for the identifications with n > 1. However, if the cosmological constant is also running the singularity persists in the solution. Also, we show that the ASG effects predicts the presence of a remnant mass in the final evaporation process. Besides that, a logarithmic correction is observed in the entropy. However, a running cosmological constant introduces new correction terms to the entropy beyond that. We show that the improved black string solution remains stable, as in the usual case. Phase transitions are not observed in both cases studied here.

Traversable wormhole model with massive gravitons, two fluids, and a variable gravity

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.

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.

Gravitational response of topological quantum states of matter

Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee their imperviousness to realistic imperfections, disorder and environmental disturbances. Is the gravitational coupling coefficient of topological quantum states of matter a promising candidate? Substantially building on well established results for quantum Hall states, using disclinations as tools for controlled creation of pristine spatial curvature free of undesirable artifacts such as would interfere with the electronic motion of interest, herein we report that a large class of lattice topological states of matter exhibit gravitational response, i.e., charge response to intrinsic spatial curvature. This phenomenon is characterized by a topologically quantized coupling constant. Remarkably, the charge-gravity relationship remains linear in the curvature, up to the maximum curvature achievable on the lattice, demonstrating absence of higher order nonlinear response. Our findings facilitate articulating the physical principles underlying the topological quantization of the gravitational coupling constant, in analogy with the insights offered by the Chern number description of the quantized Hall conductance.

Gravitational corrections to electroweak vacuum decay: metric vs. Palatini

We consider the standard Einstein-Hilbert-Higgs action where the Higgs field couples nonminimally with gravity via the term ξh2R, and investigate the stability of the electroweak vacuum in the presence of gravitational corrections in both the metric and Palatini formulations of gravity. In order to identify the differences between the two formalisms analytically, we follow a perturbative approach in which the gravitational corrections are taken into consideration via a leading order expansion in the gravitational coupling constant. Our analysis shows that in the Palatini formalism, the well-known effect of gravity suppressing the vacuum decay probability, becomes milder in comparison with the metric case for any value of the nonminimal coupling ξ. Furthermore, we have found that in the Palatini formalism, the positivity of the gravitational corrections, which is a necessary requirement for the unitarity of the theory, entails the lower bound ξ>−1/12.

Neutron stars in modified teleparallel gravity

We investigate compact objects in modified teleparallel gravity with realistic equations of state. We propose a modification of Teleparallel Equivalent to General Relativity, then an appropriate tetrad is applied to the field equations. A specific set of relations showing an equivalency between our gravitational model and the New General Relativity is found. The conservation equation implies that our Tolman-Oppenheimer-Volkoff equations are presented with an effective gravitational coupling constant. Numerical analysis using realistic equations of state is made, and the behavior of mass, radius, and the relation mass-radius as functions of a free parameter of our model is also investigated.

Geometric response of quantum Hall states to electric fields

Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the characteristic geometry of electronic motion in the presence of magnetic and electric fields. The geometric picture we provide motivates the following conjecture: non-uniform electric fields mimic the presence of spatial curvature. Consequently, the gravitational coupling constant also appears in the charge response to non-uniform electric fields.

Unity Formula that connect the Fine Structure constant and the Proton to Electron Mass Ratio

In this paper will be presented the unity Formulas that connect the Fine Structure constant α and the Proton to Electron Mass Ratio μ. The equations are simple,elegant and symmetrical in a great physical meaning. At the beginning we will make a review of the last works. We will suggest the exact formula for the Fine Structure constant α with the Golden Angle and the Fifth Power of the Golden Mean and αlso we propose a simple and accurate expression for the Fine Structure constant α in terms of the Archimedes constant π. After we propose two exact mathematical expressions for the Proton to Electron Mass Ratio. It will be presented the mathematical Formula that connects the Proton to Electron Mass Ratio μ,the Fine-structure constant α,the ratio Ν1 of electric force to gravitational force between electron and proton,the Avogadro number NA,the Gravitational coupling constant αG for the electron and the gravitational coupling constant of proton αG(p). Also we will find a new formula for the Avogadro number NA and a new formula for Gravitational Constant G. Ιt will be explained that the product μ⋅α-1 is one of the roots of the following trigonometric equation: 2·102⋅cos(μ⋅α-1)+132=0 (1) It will also be shown that another way to show this equation is the following exponential form of the equation: 102⋅(eiμ/α+e-iμ/α)+132=0 (2) This exponential form can also be written with the form: 102⋅(eiμ/α+e-iμ/α)=132⋅eiπ (3) So the beautiful formula that connect the Fine Structure constant,the Proton to Electron Mass Ratio and the Fifth Power of the Golden Mean is: 52⋅(5∙φ-2+φ-5)2⋅(eiμ/α+e-iμ/α)+(5∙φ2-φ-5)2=0 (4) Also the formula that connect the Fine Structure constant,the Proton to Electron Mass Ratio and Mathematical constants π,φ,e,i is: 102⋅(eiμ/α+e-iμ/α)=(5∙φ2-φ-5)2⋅eiπ (5) Also the unity Formula can also be written in the form: 10⋅(eiμ/α+e-iμ/α)1/2=13⋅i (6) Finally we will show that the radio ω=(c/υs)2 of the speed of light and the maximum speed of sound depends only from the Fine Structure constant α and not from the Proton to Electron Mass Ratio μ: 102⋅(eiωα/2+e-iωα/2)+132=0 (7) All these equations are simple,elegant and symmetrical in a great physical meaning.

Dynamical analysis of Brans–Dicke universe with inverse power-law effective potential

We study Brans–Dicke cosmology with an inverse power-law effective potential. By using dynamical analyses, we search for fixed points corresponding to the radiation-like matter and dark energy-dominated era of our Universe, and the stability of fixed points is also investigated. We find phase space trajectories which are attracted to the stable point of the dark energy-dominated era from unstable fixed points like matter-dominated era of the Universe. The dark energy comes from effective potentials of the Brans–Dicke field, whose variation (related to the time-variation of the gravitational coupling constant) is shown to be in good agreement with observational data.

A connection between Rastall-type and f(R, T) gravities

Recently a Lagrangian formulation for Rastall Gravity (RG) has been proposed in the framework of f(R, T) gravity. In the present work we obtain Lagrangian formulation for the standard Rastall theory assuming the matter content is a perfect fluid with linear Equation of State (EoS). We therefore find a relation between the coupling constant of the Lagrangian, the Rastall gravitational coupling constant and the EoS parameter. We also propose a Lagrangian for the Generalized Rastall Gravity (GRG). In this case the Rastall parameter which is a constant is replaced by a variable one. More exactly, it appears as a function of the Ricci scalar and the trace of the Energy Momentum Tensor (EMT). In both mentioned models, the Lagrangians are constructed by a linear function of R and T.

On the impact of Majorana masses in gravity-matter systems

We investigate the Higgs-Yukawa system with Majorana masses of a fermion within asymptotically safe quantum gravity. Using the functional renormalization group method we derive the beta functions of the Majorana masses and the Yukawa coupling constant and discuss the possibility of a non-trivial fixed point for the Yukawa coupling constant. In the gravitational sector we take into account higher derivative terms such as R2 and RμνRμν in addition to the Einstein-Hilbert term for our truncation. For a certain value of the gravitational coupling constants and the Majorana masses, the Yukawa coupling constant has a non-trivial fixed point value and becomes an irrelevant parameter being thus a prediction of the theory. We also discuss consequences due to the Majorana mass terms to the running of the quartic coupling constant in the scalar sector.

4-Index theory of gravity and its relation with the violation of the energy–momentum conservation law

Recently, a 4-index generalization of the Einstein theory has been proposed by Moulin [F. Moulin, Eur. Phys. J. C 77, 878 (2017)]. Using this method, we find the most general 2-index field equations derivable from the Einstein–Hilbert action. The application of Newtonian limit, the role of gravitational coupling constant and the effects of the properties of ordinary energy–momentum tensor in obtaining a 4-index gravity theory have been studied. We also address the results of building Weyl free 4-index gravity theory. Our study displays that both the Einstein and Rastall theories can be obtained as the subclasses of a 4-index gravity theory which shows the power of 4-index method in unifying various gravitational theories. It is also obtained that the violation of the energy–momentum conservation law may be allowed in 4-index gravity theory, and moreover, the contraction of 4-index theory generally admits a non-minimal coupling between geometry and matter field in the Rastall way. This study also shows that, unlike the Einstein case, the gravitational coupling constant of 4-index Rastall theory generally differs from that of the ordinary 2-index Rastall theory.

What if Newton’s Gravitational Constant Was Negative?

In this work, we seek a cosmological mechanism that may define the sign of the effective gravitational coupling constant, G. To this end, we consider general scalar-tensor gravity theories as they provide the field theory natural framework for the variation of the gravitational coupling. We find that models with a quadratic potential naturally stabilize the value of G into the positive branch of the evolution and further, that de Sitter inflation and a relaxation to General Relativity is easily attained.

Nonlocal generalized uncertainty principle and its implications in gravity and entropic Verlinde holographic approach

Recently, a nonlocal generalized uncertainty principle was derived based on the new notion of quantum acceleratum operator within the framework of nonlocal-maximal quantum mechanics. In this study, we discuss some of its properties and some of its implications in Newtonian gravity theory and Verlinde’s entropic holographic approach. A number of features were revealed; in particular, the emergence of a logarithmic correction to the gravitational Newtonian potential, a minimum energy and a minimum mass which depend on the gravitational coupling constant. Based on the concept of holographic principle, Verlinde’s conjecture and equipartition rule, a quantized Newton’s force law of gravity for a particle of mass m gravitating around a Planck mass is derived.

How Problematic is the Near-Euclidean Spatial Geometry of the Large-Scale Universe?

Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called "flatness problem", which is widely perceived to be a major outstanding problem of modern cosmology and as such forms one of the prime motivations behind inflationary models. An inspection of the literature and some further critical reflection however quickly reveals that the typical formulation of this putative problem is fraught with questionable arguments and misconceptions and that it is moreover imperative to distinguish between different varieties of problem. It is shown that the observational fact that the large-scale Universe is so nearly flat is ultimately no more puzzling than similar "anthropic coincidences", such as the specific (orders of magnitude of the) values of the gravitational and electromagnetic coupling constants. In particular, there is no fine-tuning problem in connection to flatness of the kind usually argued for. The arguments regarding flatness and particle horizons typically found in cosmological discourses in fact address a mere $single$ issue underlying the standard FLRW cosmologies, namely the $extreme$ improbability of these models with respect to any "reasonable measure" on the "space of all spacetimes". This issue may be expressed in different ways and a phase space formulation, due to Penrose, is presented here. A horizon problem only arises when additional assumptions - which are usually kept implicit and at any rate seem rather speculative - are made.

Stationary Solutions of Second-Order Equations for Fermions in Reissner–Nordström Space-Time

Existence of degenerate stationary bound states with square integrable radial wave functions was proved when second-order equations are used with the effective potential of the Reissner-Nordstr\"{o}m (RN) field with two event horizons for charged and uncharged fermions. The fermions in such states are localized near event horizons within the ranges from zero to several fractions of Compton wave length of fermions versus the values of gravitational and electromagnetic coupling constants and the values of angular and orbital momenta $j,l$. In case of extreme RN fields, absence of stationary bound states of fermions with the energies of $E<mc^{2}$ is shown for solutions of the second-order equation for any value of gravitational and electromagnetic coupling constants. Existence of the discrete energy spectrum is shown for the naked RN singularity due to solution of the second-order equation at definite values of physical parameters. The discrete spectrum exists for both charged and uncharged fermions. The naked RN singularity in quantum mechanics with the second-order equation for half-spin particles poses no threat to cosmic censorship since it is covered with an infinitely large potential barrier. Electrically neutral systems of atomic type (RN collapsars with the definite number of fermions in degenerate bound states) are proposed to consider as particles of dark matter.

Stationary Solutions of Second-Order Equations for Point Fermions in the Schwarzschild Gravitational Field

When using a second-order Schr\"odinger-type equation with the effective potential of the Schwarzschild field, existence of a stationary state of half-spin particles with energy $E=0$ is proved. For each of the values of quantum numbers $j,l$, the physically meaningful energy $E=0$ (the binding energy is $E_{b}=mc^{2}$) is implemented at the value of the gravitational coupling constant $\alpha\geq\alpha_{min}$. The particles with $E=0$ are, with the overwhelming probability, at some distance from the event horizon within the range from zero to several fractions of Compton wavelength of a fermion depending on value of the gravitational coupling constants and values $j,l$. In this paper, similar solutions of the second-order equation are announced for bound states of fermions in the Reissner-Nordstr\"om, Kerr, Kerr-Newman fields. Atomic-type systems: collapsars with fermions in bound states are proposed as particles of dark matter.

Atomic Systems with Bound States of Fermions in the Schwarzschild, Reissner–Nordström Fields as Candidates for the Role of Dark Matters Particles

After transition from the Dirac equation to the Schr\"{o}dinger-type relativistic equation with effective potentials of the Schwarzschild and Reissner-Nordstr\"{o}m (RN) fields, the existence of the stationary state of fermions with real square-integrable radial wave functions is proved. The fermions are localized near the event horizon within the range from zero to several fractions or a few units of the Compton wavelength of a fermion as a function of the gravitational and electromagnetic coupling constants and the angular and orbital momenta j,l. Electrically neutral atomic-type systems (Schwarzschild and RN collapsars with fermions in bound states) are proposed as particles of dark matter.