Abstract We want to briefly review the cosmological perturbations with some reflections about vorticity. Indeed, vorticity has rarely been studied in the early Universe and in cosmology. This topic has become a subject of study only in the recent years. Starting from a Gamow reflection, we assume that the space of the newborn and hot Universe may have had turbulent areas. These regions could represent

Abstract The observable effects of large-scale (non-quantum) fluctuations of dark energy (DE) are discussed within the framework of classical general relativity. The paper is focused on different local rates of the cosmological expansion (the phenomenon known as the Hubble constant tension) and the contribution of DE fluctuations to the anisotropy of the cosmic microwave background radiation; other

Abstract We use the canonical formalism of classical mechanics together with the first law of thermodynamics to unveil a differential equation for a minimally coupled canonical scalar field which should be solved simultaneously with the Klein–Gordon equation. This equation was obtained by realizing that the thermodynamic work is equal to the work done by the generalized force to increase the scalar

Abstract A mathematical model of the evolution of plane perturbations in a cosmological statistical system of completely degenerated scalar-charged fermions with the Higgs scalar interaction is formulated. A complete closed system of differential equations describing the unperturbed state of a homogeneous and isotropic system and a system of self-consistent equations describing the evolution of small

Abstract We seek the cosmological outcome of a ghost dark energy (GDE) model with sign-changeable interaction in \(f(R,T)\) modified theory of gravity. We assume that the universe is filled with two fluid, a barotropic fluid, and ghost dark energy. With the particular choice of the functional \(f(R,T)=R+2f(T)\), where \(R\) is the Ricci scalar and \(T\) is the trace of the stress-energy tensor, we

Abstract We solve the Klein–Gordon equation subject to a homogeneous magnetic field including a quantum flux under the influence of a scalar and vector potential of Coulomb types in a cosmic string space-time, and analyze the relativistic analogue of the Aharonov–Bohm effect for bound states.

Abstract A mathematical model is formulated for the evolution of plane perturbations in the cosmological statistical system of completely degenerate scalarly charged fermions with Higgs scalar interaction for short-wave perturbations. These disturbance modes have been found and investigated. It is shown that in such a model an additional oscillation mode arises, which is associated directly with degenerate

Abstract We revisit the variable \(\Lambda\) theory recently developed by Alexander et al. [1, 2]. We implement it to explain the current expansion of the Universe. The varying \(\Lambda\) theory reduces one degree of freedom. The varying \(\Lambda\) term (cosmological term) follows the energy density of the Universe. We consider such a theory which does not respect self-dual symmetry. The Bianchi

Abstract The gravitational field with torsion is being constructed by using the parametrized absolute parallelism geometry. A generalized law of variation of Hubble’s parameter in evolutionary cosmological models is used. The cosmological models under the influence of the gravitational field with torsion are obtained and discussed. A new model of the Universe is presented using a special class of Riemann–Cartan

Abstract A Hayward black hole and a magnetically charged black hole based on rational nonlinear electrodynamics with the Lagrangian \({\mathcal{L}}={-}{\mathcal{F}}/(1+2\beta{\mathcal{F}})\) (\({\mathcal{F}}\) is the field invariant) are considered. It is shown that the metric function in both models possesses a de Sitter core without singularities as \(r\to 0\). The behavior of the Hawking temperature

Abstract The process of generating gravitational waves by a standing electromagnetic wave is considered. The description of gravitational waves coupled with the electromagnetic field is carried out on the basis of linearized Einstein gravity. It is shown that such gravitational-electromagnetic waves inside a Fabry-Perrot resonator lead to generation of the usual high-frequency transverse-traceless

Abstract The Bakry-Émery Ricci tensor gives an analogue of the Ricci tensor for a Riemannian manifold with a smooth function. This notion motivates a new version of Einstein’s field equation in which the mass becomes part of geometry. This new field equation is purely geometric and is obtained from an action principle which is formed naturally by the scalar curvature associated with the Bakry-Émery

Abstract We consider, within the framework of an improved \(5D\) Kaluza-Klein theory (KK\(\psi\)), the set of twenty most precise values ever published of Earth-based gravitational constant measurements. We take into account the possibility of a jump discontinuity into the geomagnetic potential in connection with the spin crossover of the iron (III) complex ions migrating from the Earth’s outer core

Abstract A mathematical model of the cosmological evolution of statistical systems of scalarly charged particles with Higgs scalar interaction is formulated and investigated. Examples are given of numerical modeling of such systems, revealing their very remarkable properties, in particular, the formation of paired bursts of cosmological acceleration.

Abstract A new model is constructed for the Big Bang and the expansion of the Universe, based on a description of a spread of a finite mass of ideal (nonviscous and non-heat-conducting) gas from a point (“initial hot singularity”) to empty space in the framework of general and special relativity (GR and SR). That is, the expansion began inside the sphere with the gravitational radius of the Universe

Abstract We study the early inflationary phase of the universe driven by noncanonical scalar field models using an exponential potential. The noncanonical scalar field models are represented by Lagrangian densities containing square and square-root kinetic corrections to the canonical Lagrangian density. We investigate the Lie symmetry of the homogeneous scalar field equations obtained from noncanonical

Abstract It is known than the inclusion of spatial curvature can modify the evolution of matter perturbations and affect the Large Scale Structure (LSS) formation. We quantify the effects of the nonzero spatial curvature in terms of LSS formation for a cosmological model with a running vacuum energy density and a warm dark matter component. The evolution of density perturbations and the modified shape

Abstract We propose a possibility of qualitatively taking into account the mutual influence of two gravitationally interacting null strings (thin tubes of a massless scalar field) on the motion of each of them. It is shown that it is possible to implement a self-consistent motion of two null strings in which their mutual gravitational influence leads to vibrations of each string inside a bounded spatial

Abstract We use the dynamical system method in order to investigate the dynamics of a non-minimally coupled tachyon field within induced gravity on the brane in a holographic cosmological context. Assuming an exponential potential and a monomial form of the nonminimal coupling function, we construct the phase space of the model. Two possible cases, namely, the minimal and nonminimal coupling, are investigated

Abstract We investigate the Universe at the late stage of its evolution and inside the cell of uniformity, 150–370 Mpc. We consider the Universe to be filled at these scales with dustlike matter, a minimally coupled Galileon field and radiation. We use the mechanical approach. Therefore, the peculiar velocities of the inhomogeneities as well as the fluctuations of other perfect fluids can be considered

Abstract We present the second-order post-Newtonian solution for the quasi-Keplerian motion in the Schwarzschild space-time under the Wagoner-Will-Epstein-Haugan representation. Detailed derivations are provided for readers’ convenience.

Abstract The shell theorem, proved by Newton in his Principia (1687), states that the net force exerted by a uniform spherical shell on a body located anywhere inside it is zero, as long as the force is proportional to the inverse square of the distance between the interacting bodies. This null result remains valid whenever the interaction depends only on the distance between the bodies, but not on

Abstract To estimate the influence of “dark energy” on Keplerian orbits, we solve the general-relativistic equations of motion of a test particle in the field of a pointlike mass embedded in the cosmological background formed by the cosmological constant with realistic cosmological Robertson–Walker asymptotics at infinity. It is found that under certain relations between three crucial parameters of

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.