Abstract \(f(R,T)\) gravity is a widely used extended theory of gravity introduced by Harko et al., which is a straightforward generalization of \(f(R)\) gravity. The action in this extended theory of gravity incorporates well-motivated functional forms of the Ricci scalar \(R\) and the trace of the energy momentum tensor \(T\). The present manuscript aims at constraining the most widely used \(f(R

Abstract The reduced vacuum Hamiltonian equations of conformal geometrodynamics of compact manifolds in extrinsic time are written. This is achieved by generalizing the theorem of implicit function derivative to the functional analysis. Under the assumption that constant curvature slicing takes place, York’s field time becomes the global time.

Abstract We review and present full details of the Feynman diagram based and the heat-kernel method based calculations of the simplest nonlocal form factors in the one-loop contributions of a massive scalar field. The paper has pedagogical and introductory purposes and is intended to help the reader in better understanding the existing literature on the subject. The functional calculations are based

Abstract We study the evolution of the universe by assuming an integrated model, which involves interacting dark energy and the holographic principle with the Hubble scale as an IR cutoff. First we determine the interaction rate at which matter is converting to dark energy. At the next step, we evaluate the equation of state parameter which describes the nature of dark energy. Our result predicts that

Abstract Spinning equations of Finslerian gravity, the counterpart of the Mathisson-Papapetrou spinning equations of motion are obtained. Two approaches of Finslerian geometries are formulated and discussed, the Cartan-Rund and Finsler-Cartan ones, as well as their corresponding spinning equations. The significance of the nonlinear connection and its relevance on spinning equations is noticed, and

Abstract We study the accretion of dark matter and dark energy onto \((n+2)\)-dimensional Morris–Thorne wormholes. The wormhole mass and its rate of change have been written in the background of the \((n+2)\)-dimensional Friedmann-Robertson-Walker (FRW) model of the Universe. We have assumed the candidates of dark energy in the form of entropy-corrected holographic dark energy (ECHDE) and entropy-corrected

Abstract Cosmological density perturbations governed by Newtonian and MONDian force laws scenarios for the period from matter domination to recombination have been investigated. Particularly, we find solutions for the density contrast equations obtained for both cases with respect to a homogeneous spatially flat Friedman-Lemaître-Robertson-Walker (FLRW) background using the Lie symmetry approach. Numerical

Abstract We construct a noncommutative gauge theory for the deformed metric corresponding to the modified structure of a gravitational field in the case of noncommutative Yukawa–Schwarzschild space-time. The thermodynamic properties and corrections t o the gravitational force on the horizon of a noncommutative Yukawa–Schwarzschild black hole are analyzed.

Abstract It was suggested in our previous paper [Yu.V. Dumin, Grav. Cosmol. 25, 169 (2019)] that the cosmological Dark Energy might be mediated by the time–energy uncertainty relation in the Mandelstam–Tamm form, which is appropriate for the long-term evolution of quantum systems. The amount of such Dark Energy gradually decays with time, and the corresponding scale factor of the Universe increases

Abstract An axially symmetric nonvacuum solution of the Einstein field equations, regular everywhere and free from curvature divergence is presented. The matter-energy content is a the pure radiation field satisfying the energy conditions, and the metric is of type N in the Petrov classification scheme. The space-time develops circular closed timelike curves everywhere outside a finite region of space

Abstract Based on the macroscopic equations of cosmological evolution obtained earlier by the author, a closed set of macroscopi Einstein equations in the short-wave approximation for perturbations of the scalar Higgs and gravitational fields has been obtained and examined. The resulting exact solutions of the macroscopic equations are determined by three microscopic parameters, depending on the spectrum

Abstract The hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. We discuss static, spherically symmetric vacuum solutions of HMPG with the aid of its scalar-tensor theory (STT) representation. This scalar-tensor theory coincides with general relativity with a conformally coupled

AbstractA new universal method is proposed for obtaining Vlasov–type equations for systems of interacting massive charged particles from the general-relativistic Einstein–Hilbert action. At the same time, a new effective approach to synchronizing the proper times of various particles of a many–particle system has been introduced. A new form of the energy–momentum tensor for matter (and the right-hand

AbstractWe show quantitatively that an exact solution of conformal scalar-tensor gravity can explain very well the galactic rotation curves for a sample of 104 galaxies without the need for dark matter or other exotic modification of gravity. The metric is an overall rescaling of the Schwarzschild-de Sitter space-time as required by Weyl conformal invariance, which has to be spontaneously broken, and

AbstractWe consider a generalization of Higgs inflation, based on cosmology of general relativity (GR), to the case of a two-field model of the tensor-multiscalar theory of gravity (TMS TG). Cosmological solutions are found in the case where a scalar field with the Higgs potential, as a source of TMS TG is in the slow-rolling mode. Solutions with power and exponential-power-law evolution of the scale

AbstractWe build a Kepler model of spacecraft gravity assist maneuver near a Venus-type planet and investigate its sensitivity to changes of the impact parameter. Analytical and numerical computations give similar results indicating a great increase of the trajectory final point shift under a small variation of the assigned spacecraft-planet distance.

AbstractThe goal of the present short letter is to prove, through a specific example (i.e., the class of Ricci-flat, Petrov type D geometries), that the original Newman-Penrose (NP) formalism, seen as an exterior differential system (EDS), suffices to provide the needed syzygies and integrals of the EDS under consideration—without (in principle) the aid of a computer algebra system (CAS).

AbstractWe study the motion of a celestial body under the simultaneous effect of the Newtonian and cosmological fields. The resulting effect is not only interesting by itself, but it could also give a contribution to solving the well-known problem of galactic rotation curves without the assumption of the existence of dark matter. We assume that in the outer regions of galaxies the stars and the hydrogen

AbstractA family of type N exact solutions of the Einstein field equations, regular everywhere except on the symmetry axis, where it possesses a naked curvature singularity, is presented. The stress-energy tensor is that of an anisotropic fluid coupled with a pure radiation field and satisfies different energy conditions, and the physical parameters diverge as \(r\to 0\). The space-time admits a non-expanding

AbstractThe \(f(R,T)\) theory of gravity is an extended theory of gravity in which the gravitational action contains both the Ricci scalar \(R\) and the trace of the energy-momentum tensor \(T\), and hence the cosmological models based on \(f(R,T)\) gravity are eligible to describing the late-time acceleration of the present universe. In this paper, we investigate an accelerating model of a flat universe

AbstractA model of a relativistic process as a finite set of elementary events is considered. General properties of statistics of elementary events are considered. The model has the following properties. Any macroscopic property of any process is a consequence of this statistics. The least action principle means that a macroscopic process chooses a variant with maximum probability. A massive particle

AbstractThe possibility of compensating the atmospheric influence on precision measurement of gravitational ‘‘redshift’’ using the Earth orbiting satellites is discussed. For a communication radio signal propagating from a ground-based tracking station to a spacecraft and back, the interaction with the ionosphere and the troposphere produces a undesirable contribution to the total frequency shift which

AbstractAnalyzing the model of a spinning particle based on the over-rotating Kerr–Newman solution regularized by a supersymmetric bag model, we arrive at the conclusion that a unification of gravity with quantum theory is achieved in this model due to a strong topological influence of the Kerr spinning gravity which occurs on the Compton scale. We obtain that the correct formation of the nonperturbative

AbstractThis article follows a simpler approach (Siddiqui et al. 2011) using the foliation concept with virtual displacement of hypersurfaces near the event horizon to derive the first law of black hole thermodynamics for the Kerr–Newman black hole spacetime.

AbstractAn analysis is presented of the experiment by Datta, Yin and Vargas in the light of the Mbelek–Lachièze-Rey scalar-tensor theory of gravitation, showing that this theory reproduces the magnitude and sign of the measured anomalous weight increment of conducting balls immersed in an inhomogeneous electric field.

AbstractThe article features an interpretation of the cosmic microwave background (CMB) radiation in the framework of the relational approach. The key concept of the proposed interpretation is strongly connected with the ideas on the ‘‘temperature of interstellar space’’ put forward by Weyl, Eddington, Regener and Nernst in the 1920s–1930s. In accordance with the relational justification of the cosmological

AbstractWe study a \(D\)-dimensional Einstein–Gauss–Bonnet gravitational model including the Gauss-Bonnet term and the cosmological constant \(\Lambda\). We find a class of cosmological type solutions with exponential dependence of two scale factors on the variable \(u\) (either cosmological time or a spatial coordinate), governed by two Hubble-like parameters \(H\neq 0\) and \(h\), corresponding to

AbstractThe purpose of this paper is to investigate if the weak field lensing (WFL) observables can distinguish between three physically distinct lenses, mathematically connected by a combination of real and complex transformations. All three kinds of lenses have been discussed in the literature in the strong field limit, but since the weak field light deflection does not follow as a PPN expansion

AbstractWe study the accretion of dark matter and DE onto \((n+2)\)-dimensional Schwarzschild black holes. Since, due to the accretion process, the mass of the black hole is dynamical, so the mass and its changing rate for \((n+2)\)-dimensional Schwarzschild black holes have been found. We assume a general form of holographic DE where the dimensionless model parameter \(c\) is assumed to be variable

AbstractThe theory of direct particle interaction proposed in our previous works is further developed. In this theory, the electromagnetic interaction is primary whereas the emergence of particle masses and gravity are its consequences. The equation of motion is generalized to arbitrary velocities of the selected particle (rather than small ones). With the introduction of an effective metric, a correspondence

AbstractWe consider two most popular definitions of velocities of remote objects in General Relativity. Our work has two motivations. From a research point of view, we generalize the formula connecting these two velocities in FRW metrics found by Chodorowski to arbitrary synchronous spherically symmetric metrics. From a methodological point of view, our goal is to outline certain counter-intuitive

AbstractThe existence of Lyra’s cosmology is studied with the least interaction between normal matter and dark energy using Bianchi-III space-time in a nonsingular hybrid universe. The model explains the phase transition of the universe from deceleration to acceleration in the presence of a perfect fluid and naturewise anisotropic dark energy interacting very minimally to keep the energy-momentum tensors

AbstractThe Newtonian gravity force is massless and decreases as \(1/r^{2}\), too steeply to explain the flat rotation curves of spiral galaxies. Massive gravity, on the other hand, drops as \(1/r\) and is capable of doing the job. Massive fields have a respected record in the history of field theories. We follow the suit and add a ‘‘mass term’’ to the field equation of Newtonian gravity, which, to

AbstractA revision of the author’s results concerning the possible existence of the so-called Euclidean cycles in cosmological evolution of a system of Higgs scalar fields is being performed. The assumption of a nonnegative velocity of the Universe expansion, which in certain cases contradicts the complete set of the Einstein equations, is removed. It is shown that in the cases where the effective

AbstractBeing convinced in global generalities of Nature’s fundamental principles, phenomena and processes on all cosmic scales, and taking a broad view on the phenomenon of photons’ entanglement, here one postulates the phenomenon of large-scale entanglement of gravitons. This original phenomenon might play a major role in justifying the networks of galaxies and their clusters. The mechanism of entangled

—The paper is devoted to some of the difficulties which the Wheeler-DeWitt quantum geometrodynamics encountered, in particular, a strong mathematical proof that this theory is gauge-invariant, the definition of the wave function of the Universe through a path integral and the illegality of asymptotic boundary conditions in quantum gravity, the derivation of the Wheeler-DeWitt equation from the path

One of the most accepted ideas in modern cosmology to explain a number of puzzling astronomical observations is the existence of Dark Matter in the Universe, even though it has not been directly observed. We recall the motivation for its existence according to its influence on visible matter and its characteristics in terms of famous candidate particles.

To give a possible explanation of the 3-dimensionality of space, a matrix version of the Wheeler-DeWitt equation for quantum gravity is developed. In this equation, the number of spatial dimensions D is associated with a discrete variable. In this framework, a toy quantum-cosmological model for the birth of the universe from nothing is constructed. Here, nothing means a precosmic state with no classical

The paper studies the influence of periodically changing boundary conditions on the motion of a test null string “inside” an axially symmetric null string domain that has a layered structure and preserves its size. It is shown that the action of the gravitational field of the null string domain on a test null string whose size (radius) is smaller than the size of the domain, under any initial conditions

The main purpose of our paper is to construct a viable Kaluza-Klein model satisfying the observational constraints. To this end, we investigate a six-dimensional model with spherical compactification of the internal space. Background matter is considered in the form of a perfect fluid with nonlinear equations of state both in the external/our and internal spaces, and the model is set to include an

The article discusses and substantiates a self-consistent approach to the macroscopic description of systems with gravitational interaction. Corrections to the equation of state of the fluid are found, based on the macroscopic Einstein equations which were obtained by averaging over microscopic spherically symmetric metric fluctuations created by primordial black holes in a fluid medium. It is shown

This study links the fractal structure of physical space-time to quantum-mechanical laws. It is shown that primitive distortions of the pregeometric surface, a fractal cell of 3D space, gives birth to a condition eliminating the metric defect while providing “eternal validity” of the exclusive algebras (of real, complex, and quaternion numbers). Written in the physical units typical for the micro-world

The so-called hybrid metric-Palatini theory of gravity (HMPG), proposed in 2012 by T. Harko et al., is known to successfully describe both local (solar-system) and cosmological observations. This paper gives a complete description of static, spherically symmetric vacuum solutions of HMPG in the simplest case where its scalar-tensor representation has a zero scalar field potential V(ϕ), and both Riemannian

An anthropic explanation of the evident smallness of the dark energy (DE) density value implies the existence of a time-dependent component of the scalar field, serving, together with a negative-valued cosmological constant, as one of two components to the overall DE density. The observers (i.e. us) might then only evolve in those regions of the universe where the sum of those two components (the positive

In the framework of the Stueckelberg-Wheeler-Feynman concept of a “one-electron Universe” we consider a world line implicitly defined by a system of algebraic (precisely, polynomial) equations. A collection of pointlike “particles” of two kinds on the world line (or its complex extension) is defined by the real (complex conjugate) roots of the polynomial system and is detected then by an external inertial

We analyze two branches of five-dimensional theories from a methodological point of view: Kaluza’s theory and the Klein-Fock-Rumer (KFR) 5-optics, aimed at a geometric description of electromagnetism and masses of elementary particles, respectively. These two theories have a number of problematic points such as the Planckian masses in Kaluza’s theory, or appearing of a configuration space in the KFR

Using variable gravitational and cosmological constants, the mechanism of particle creation in the universe is studied for Friedmann–Robertson–Walker (FRW) space-times at high dimensions to explain the early deceleration and present accelerating phases. To investigate the dynamics of these phases, we consider two scale factor of the forms \(a(t)=\sqrt{t^\alpha{e^t}}\) and \(a(t)=\sqrt[m]{{\rm{sin}}h(kt)}\)

A Bianchi type IX cosmological model with expansion and rotation has been constructed in the framework of general relativity. The model comprises the Friedmannian stages of the Universe evolution including the subsequent transition to accelerated exponential expansion observed nowadays. The gravitational field sources of the model are ultrarelativistic matter, dust and a comoving anisotropic rotating

In the recent years, it was found that the energy Ec.m. in the center of mass frame of two colliding particles can be unbounded near black holes. If a collision occurs precisely on the horizon, Ec.m. is formally infinite. However, in any physically reasonable situation this is impossible. We collect different scenarios of this kind and show why in every act of collision Ec.m. is indeed finite (although

Dilatonic black hole dyon-like solutions are overviewed in the gravitational 4D model with a scalar field, two 2-forms, two dilatonic coupling constants λi ≠ 0, i = 1, 2, obeying λ1 ≠ − λ2, and the sign parameter ε = ±1 before the scalar field kinetic term. Here ε = −1 corresponds to a phantom scalar field. The solutions are defined up to solutions of two master equations for two moduli functions,

We consider modified f(R) gravity with a kinetic curvature scalar, which can be reduced to a chiral cosmological model of special kind. A detailed derivation is presented for the action of a chiral cosmological model as an equivalent to a gravitational model with higher derivatives with respect to the Ricci scalar using Lagrange multipliers and a transition from the Jordan frame to the Einstein one

In the recent years, the interest in modifications of the Einstein theory of gravitation has seriously increased due to the unsolved problem of dark energy. One of them was suggested in our earlier publications where a generalization of the Einstein gravitational theory with Weyl’s connection was studied. In the generalization, the Weyl vector potentials were regarded as a weak field giving small corrections

We consider numerically the dynamics of a flat anisotropic Universe in Einstein—Gauss—Bonnet gravity with positive Λ in dimensions 5 + 1 and 6 + 1. We identify three possible outcomes of the evolution, one singular and two nonsingular ones. The first nonsingular outcome is oscillatory. The second one is the known exponential solution. Its simplest version is the isotropic de Sitter solution. In Gauss—Bonnet

Introducing an additional symmetry (δ symmetry) in the Einstein-Hilbert action, we obtain a gravitational field model (δ gravity) based on two symmetric tensors, gμv and ̃gμv where an effective metric, given by gμv = gμv + ̃gμv must be defined to describe the trajectories of massless particles. In previous papers, a truncated versions of δ gravity applied to cosmology was presented, where the δ symmetry

Dark matter (DM) may be studied through the motion of objects following nongeodesic trajectories either due to the existence of an extra mass as a projection of higher dimensions onto lower ones or as motion of dipolar particles and fluids in the halos of spiral galaxies. The effect of DM has been extended nearby the core of the galaxy by means of the excess of mass appearing in the motion of fluids

A certain approach to solving the Wheeler-DeWitt equation in quantum cosmology, based on a type of super-selection rule by which negative frequency solutions are discarded, is discussed. In a preliminary analysis: we recall well-known results in relativistic quantum field theory, showing that adopting this approach of super-selection by discarding a sector of the frequencies does not lead to acceptable

The Unruh effect for a massless scalar field in (1 + 1)D space-time is considered. It is shown that, under some natural assumptions like finiteness of the integration volume or finiteness of the interaction (propagation of information) speed, the Unruh effect should be anisotropic. This property is not connected with a particular detector design but is fundamental like the Unruh effect itself. This

As one knows, strong discrepancies are found between the different precise measurements of the gravitational constant carried out in Earth-based laboratories. While the precision is increasing in different laboratories and with various methods, these measurements are even more and more discordant. We have shown since 2002 that an improved 5D Kaluza-Klein (KK) theory may provide a satisfactory explanation

Using the Newman-Penrose-Jogia-Griffith spin coefficients approach, we obtain an exact solution for a Bianchi Type-I metric for a nonvanishing component of spin with torsion in the context of the Einstein–Cartan theory, and the solution is found to be Petrov type D. It is observed that in the absence of torsion the solution reduces to Petrov type O.

The dark energy (DE) model of a complementary gravitational field is used to address the entropy-corrected cosmological model. The dominant DE universe can originate from an indirect coupling between vacuum energy and another complementary gravitational field. This idea is used together with entropy-corrected models to study the evolution of DE in the universe. The zero point energy is calculated from