Showing papers in "Gravitation & Cosmology in 2020"

Hybrid metric-Palatini gravity: black holes, wormholes, singularities and instabilities

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 scalar field (which can be canonical or phantom), therefore the known solutions of this theory are re-interpreted in terms of HMPG. In particular, in the case of zero scalar field potential $$V(\phi)$$ , such that both Riemannian and Palatini Ricci scalars are zero, generic asymptotically flat solutions either contain naked singularities or describe traversable wormholes, and there are only special cases of black hole solutions with extremal horizons. There is also a one-parameter family of solutions with an infinite number of extremal horizons between static regions. Examples of analytical solutions with nonzero potentials $$V(\phi)$$ are also described, among them black hole solutions with simple horizons which are generic but, for canonical scalars, they require (at least partly) negative potentials. With phantom scalars there are “black universe” solutions that lead beyond the horizon to an expanding universe instead of a singularity. Most of the solutions under consideration turn out to be unstable under scalar monopole perturbations, but some special black hole solutions are stable.

Galactic Rotation Curves in Conformal Scalar-Tensor Gravity

Abstract: We 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 the velocity of the stars depends only on two fixed universal parameters. Using the Monte Carlo Markov Chain (MCMC) method, we make a fit of the observational rotation curves in order to get the mass-to-light ratio for each galaxy. Finally, we analytically compare our model with the modified Newtonian dynamics (MOND) and the metric skew tensor gravity (MSTG) showing that the three theories have a very different behavior at very large distances.

A Complete Model of Cosmological Evolution of a Scalar Field with Higgs Potential and Euclidean Cycles

Abstract: A 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 energy of the system tends to zero, happens a smooth transition of the model to the range of negative values of the expansion rate, i.e., there is a transition to a collapsing stage rather than winding of the phase trajectories on the boundary of prohibited area. This process is studied with the help of numerical simulation methods for a model based on a classical scalar Higgs field.

The Kerr–Newman Black Hole Solution as Strong Gravity for Elementary Particles

Abstract: Analyzing 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 bag model requires the use of the supersymmetric Landau–Ginzburg field model. We obtain that one of the most important gravitational phenomena in particle physics is the appearance of the quantum Wilson loop caused by the effect of frame-dragging related to the spin. Being located on the sharp border of the bag, the Wilson loop has a strong influence on the circular D-string structure located there.

Cosmological Evolution of a Scalar-Charged Degenerate Cosmological Plasma with Higgs Scalar Fields

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.

Constraints from observational data for a running cosmological constant and warm dark matter with curvature

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 of their power spectrum are constructed and analyzed.

Accelerating Model of a Flat Universe in $$\boldsymbol{f(R,T)}$$ Gravity

Abstract: The $$f(R,T)$$ 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 with a linearly varying deceleration parameter (LVDP). We apply the linear time-varying law for the deceleration parameter that generates a model of a transition from an early decelerating phase to the current accelerating phase. We carry out the state-finder and Om(z) analysis, and obtain that the LVDP model has a consistency with the astrophysical observations. We also profoundly discuss a violation of the energy-momentum conservation law in $$f(R,T)$$ gravity and the dynamic behavior of the model.

Sensitivity of the Gravity Assist to Variations of the Impact Parameter

Abstract: We 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.

Can Weak Field Lensing Distinguish Between a Naked Singularity, an Ellis-Bronnikov Regular Wormhole and a Black Hole?

Abstract: The 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 from the strong field deflection due to a logarithmic divergence at the photon sphere, the WFL requires a separate investigation that has not yet been done adequately. This paper attempts to fill this gap by calculating the WFL observables such as the position, magnification and differential time delay of the images using the Keeton-Petters method. We shall, for illustration, assume the lens to be the compact object SgrA* and compare the WFL signatures with those of the Schwarzschild black hole. It is shown that, while the zeroth-order observables for the three classes of lenses are indistinguishable from those of the Schwarzschild black hole, higher-order correction terms are theoretically distinguishable for different lenses, and future accurate measurements might constrain the parameter $$\gamma$$ of the solutions.

Bianchi–III Transitioning Space-Time in a Nonsingular Hybrid Universe within Lyra’s Cosmology

Abstract: The 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 conserved independently. We take the hybrid average scale factor as $$a=(t^{m}e^{\lambda t})^{1/n}$$, where $$m,\lambda,n$$ are positive constants, which, with a time-varying deceleration parameter, describes both the early and late time features of universe. The time-varying displacement $$\beta(t)$$ of Lyra’s manifold used in the present model correlates with the nature of the cosmological constant $$\Lambda(t)$$. The physical and geometric properties of the model for a nonuniformly accelerated universe are also discussed with a comparison with other models.

One-Loop Effective Action: Nonlocal Form Factors and Renormalization Group

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 on the solution by Avramidi and Barvinsky and Vilkovisky for the heat kernel and are performed in curved space-time. One of the important points is that the main structure of nonlocalities is the same as in the flat background.

Interacting Holographic Dark Energy, the Present Accelerated Expansion and Black Holes

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 the present state of the universe is dominated by quintessence type dark energy, and it will become phantom dominated in the near future. Again, our analysis successfully addresses the problem of present accelerated expansion of the universe and softens the coincidence problem. We also find that the universe was previously undergoing a decelerated phase of expansion and a transition from deceleration to acceleration should have occurred at a time $$t_{q=0}=0.732t_{0}$$ , where $$t_{0}$$ is the present age of the universe. Finally, we discuss the evolution of black holes in this environment.

Axially Symmetric Type N Space-Time with a Naked Curvature Singularity and Closed Timelike Curves

Abstract: A 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, non-twisting, and shear-free geodesic null congruence and belongs to a special class of type N Kundt metrics. The space-time is geodesically complete along the radial direction in the constant $$z$$ planes and exhibits geometrically different properties from the known $$pp$$ -wave space-times. The present family of solutions admits closed timelike curves (CTC) which appear after a certain time instant, and the present metric is a four-dimensional generalization of the Misner space metric in curved space-time.

Accretion of Some Classes of Holographic DE onto Higher-Dimensional Schwarzschild Black Holes

Abstract: We 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, i.e., $$c$$ is a function of redshift $$z$$ . We also assume seven types of parametrizations of $$c(z)$$ , and they are: model I (linear type), model II (CPL type), model III (JBP type), model IV (Wetterich type), model V (Efstathiou type), model VI (Ma-Jhang type), and model VII (ASSS type). The black hole mass is calculated in terms of redshift when dark matter and a general form of holographic DE accrete onto the black hole. We show that the black hole mass increases for all types of holographic dark energy candidates. The mass increasing rate sensitively depends on the space-time dimension.

Axially Symmetric Type N Space-Time with Causality Violating Curves and the von Zeipel Cylinder

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 i.e., beyond a null curve. Furthermore, the physical interpretation of the solution based on the study of the equations of geodesic deviation is presented. Finally, the von Zeipel cylinders with respect to the Zero Angular Momentum Observers (ZAMOs) is discussed. In addition, circular null and timelike geodesic of pace-time are also presented.

Temperature of Interstellar Space Revisited by Relational Approach

Abstract: The 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 redshift and modern data on stellar luminosities, a new estimate of the CMB temperature is obtained.

The Second Post-Newtonian Motion in Schwarzschild Spacetime

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.

Early Inflationary Phase with Canonical and Noncanonical Scalar Fields: A Symmetry-Based Approach

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 Lagrangian densities and find only a one-parameter Lie point symmetry for both canonical and noncanonical scalar field equations. We use the Lie symmetry generator to obtain an exact analytical group-invariant solution of the homogeneous scalar field equations from an invariant curve condition. The solutions obtained are consistent and satisfy the Friedmann equations subject to constraint conditions on the potential parameter $$\lambda$$ for the canonical case and on the parameter $$\mu$$ for the noncanonical case. In this scenario, we obtain the values of various inflationary parameters and make useful checks on the observational constraints on the parameters from Planck data by imposing a set of bounds on the parameters $$\lambda$$ and $$\mu$$ . The results for the scalar spectral index ( $$n_{S}$$ ) and the tensor-to-scalar ratio ( $$r$$ ) are presented in the $$(n_{S},r)$$ plane in the background of Planck-2015 and Planck-2018 data for noncanonical cases and are in good agreement with cosmological observations. For theoretical completeness of the noncanonical models, we verify that the noncanonical models under consideration are free from ghosts and Laplacian instabilities. We also treat the noncanonical scalar field model equations for two power-law (kinetic) corrections by the dynamical system theory. We provide useful checks on the stability of the critical points for both cases and show that the group-invariant analytical noncanonical inflation solutions are stable attractors in phase space.

Constraining $$\boldsymbol{f(R,T)}$$ Gravity from the Dark Energy Density Parameter $$\boldsymbol{\Omega}_{\boldsymbol{\Lambda}}$$

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 $$f(R,T)$$ gravity model of the form $$f(R+2\lambda T)$$ to understand its coherency and applicability in cosmology. We communicate here a novel method to find a lower bound on the model parameter $$\lambda\gtrsim-1.9\times 10^{-8}$$ through the equation relating the cosmological constant ( $$\Lambda$$ ) and the critical density of the universe ( $$\rho_{\textrm{cr}}$$ ).

Lambda Perturbations of Keplerian Orbits in the Expanding Universe

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 the problem—the initial radius of the orbit, the Schwarzschild and de Sitter radii—a specific secular perturbation caused by $$\Lambda$$ -term becomes significant, i.e., can reach the rate of the standard Hubble flow. This fact is interesting both by itself and may have important consequences for the long-term dynamics of planets and stellar binary systems.

Thermodynamic Properties of a Yukawa–Schwarzschild Black Hole in Noncommutative Gauge Gravity

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.

Nonzero Gravitational Force Exerted by a Spherical Shell on a Body Moving Inside It, and Cosmological Implications

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 their relative motion. In this work, I develop a direct closed-form evaluation of the integral of the elements of force to show that Weber-like interactions, which take into account the relative motion between the body and the shell, yield a nonzero force opposite to the acceleration of the body with respect to the shell, whatever be its position and velocity. For gravitational interactions, this nonzero force is relevant in cosmology since it can be identified with the force of inertia, as caused by the celestial sphere (i.e., the set of distant stars), which allows for a full mathematical implementation of Mach’s principle.

On Stability of Exponential Cosmological Type Solutions with Two Factor Spaces in the Einstein–Gauss–Bonnet Model with a $$\boldsymbol{\Lambda}$$ -Term

Abstract: We 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 $$H eq 0$$ and $$h$$, corresponding to factor spaces of dimensions $$m>2$$ and $$l>2$$, respectively, and depending on the sign parameter $$\varepsilon=\pm 1$$ ($$\varepsilon=1$$ corresponds to cosmological solutions and $$\varepsilon=-1$$ to static ones). These solutions are governed by a certain master equation $$\Lambda\alpha=\lambda(x)$$ and the restriction $$\alpha\varepsilon(x-x_{+})(x-x_{-})<0$$ ($$x_{-}

Velocities of distant objects in General Relativity revisited

Abstract: We 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 properties of the definitions in question, which would allow us to use them when it is reasonable and to avoid incorrect statements, based on inappropriate use of the intuition.

A Model of the Big Bang and Universe Expansion in General Relativity with Spread of a Gas Mass from a Point to Empty Space

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. At first sight, such a spread, like a spread of the singularity of a black hole, is impossible. However, a fundamental difference is that a black hole results from a collapse of a massive star after complete burning of its thermonuclear fuel. Therefore, although at a collapse the temperature, pressure and density grow infinitely, this growth is such that the gravitational forces in the course of compression are always larger than the resisting high pressure. Everything is the opposite at a spread of the initial hot singularity because of the huge (at the beginning of the spread) energy and pressure of all kinds of massless (with zero rest mass) and massive particles and antiparticles, under a negligible contribution of the excess (over antibaryons and positrons) baryons and electrons. In the process of spreading, the situation changes, and the energy of the atoms formed by these baryons and electrons becomes dominant.

Nature of Higher-Dimensional Wormhole Mass Due to Accretion of Entropy Corrected Holographic and New Agegraphic Dark Energies

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 new agegraphic dark energy (ECNADE) with its logarithmic and power-law versions. For these different dark energy models, the wormhole mass has been calculated in terms of the redshift when dark matter and the above types of dark energies accrete onto the wormhole. For this purpose, we have taken two classes of scale factors, where in class I the scale factor describes a future singularity while class II follows from an initial singularity. We graphically present the nature of the wormhole mass in different dimensions (4D, 5D, 6D) for ECHDE and ECNADE accretion. In the class I scale factor, we observe that the wormhole mass increases during the evolution of the Universe in both ECHDE and ECNADE models in both the power-law and logarithmic versions. Also, with the class II scale factor, we see that the wormhole mass decreases during the evolution of the Universe for ECHDE in both power-law and logarithmic versions, and for ECNADE with power law models, while the wormhole mass increases during the evolution of the Universe for ECNADE in its logarithmic version.

The Effect of Interplay between the Newtonian Gravitational Field and the Cosmological Expansion

Abstract: We 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 clouds follow not only the geodesics of the central field, but also the Hubble flow. By a simple application of the classical kinematics of relative motions, we analyze the effects of the composition of these two motions, and we find an increase of the rotation speed with respect to the galactic center that could be the cause of the non-Newtonian behavior of the rotation curves.

Cosmological Density Perturbations from Matter Domination to Recombination in Newtonian and MONDian Gravity Scenarios

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-Lemaitre-Robertson-Walker (FLRW) background using the Lie symmetry approach. Numerical solutions of the density contrast equations for both cases also have been provided in order to study the evolution of the density contrast. For the Newtonian case we find a limiting mass that dictates whether the growth of the density contrast is possible or not. Interestingly, in the Newtonian case, physical growth of the density contrast is not possible since the horizon mass is smaller than the limiting mass. On the other hand, growth of the density contrast is possible depending on the initial condition and the fluctuation mass of the MOND-dominated region despite the radiation pressure that leads to future structure formation.

Cosmological Solutions in the Tensor-Multi-Scalar Theory of Gravity with the Higgs Potential

Abstract: We 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 factor are obtained for various limiting forms of the Higgs potential.

Massive Gravity as an Alternative Gravity

Abstract: The 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 begin with, is static. Next, we use the observation-based Tully-Fisher relation to determine the nature and characteristics of the added mass term. We are able to produce the rotation curves flat enough to justify the observational data up to several optical radii of the galaxies, where observations are both abundant and reliable. At very far distances, however, massive gravity goes through a sequence of intermittently attractive and repulsive phases. This is a welcome novelty. It may enable one to address the wavy fluctuations and patchy voids that are not uncommon in the archives of observed rotation curves. With a stretch of imagination, massive gravity may find an observational support in the Oort clouds, a stipulated spherical shell of debris at farthest outreaches of the Solar system.