Showing papers in "Gravitation & Cosmology in 2016"

On exponential solutions in the Einstein–Gauss–Bonnet cosmology, stability and variation of G

Abstract: A D-dimensional gravitational model with Gauss–Bonnet and cosmological terms is considered. When an ansatz with a diagonal cosmological metric is adopted, we find new examples of solutions for Λ Λ ≠ 0 and D = 8 with an exponential dependence of the scale factors, which describe expansion of our 3D factor-space and contraction of 4D internal space. We also study the stability of the solutions with static Hubble-like parameters hi and prove that two solutions with Λ = 0 in dimensions D = 22, 28, which were found earlier, are stable. For both solutions we find asymptotic relations for the effective gravitational constant.

On stable exponential solutions in Einstein–Gauss–Bonnet cosmology with zero variation of G

Abstract: A D-dimensional gravitational model with a Gauss–Bonnet term and the cosmological constant Λ is considered. Assuming diagonal cosmological metrics, we find, for certain Λ > 0, new examples of solutions with an exponential time dependence of two scale factors, governed by two Hubble-like parameters H > 0 and h < 0, corresponding to submanifolds of dimensions m and l, respectively, with (m, l) = (4, 2), (5, 2), (5, 3), (6, 7), (7, 5), (7, 6) and D = 1 + m + l. Any of these solutions describes an exponential expansion of our 3-dimensional factor space with the Hubble parameter H and zero variation of the effective gravitational constant G. We also prove the stability of these solutions in the class of cosmological solutions with diagonal metrics.

Wormholes leading to extra dimensions

Abstract: In 6D general relativity with a scalar field as a source of gravity, a new type of static wormhole solutions is presented: such wormholes connect our universe with a small 2D extra subspace with a universe where this extra subspace is large, and the whole space-time is effectively 6-dimensional. We consider manifolds with the structure M0 × M1 × M2, where M0 is 2D Lorentzian space-time while each of M1,2 can be a 2-sphere or a 2-torus. After selecting possible asymptotic behaviors of the metric functions compatible with the field equations, we give two explicit examples of wormhole solutions with spherical symmetry in our space-time and toroidal extra dimensions. In one example, with a massless scalar field (it is a special case of a well-known more general solution), the extra dimensions have a large constant size at the “far end”; the other example contains a nonzero potential V(φ) which provides a 6D anti-de Sitter asymptotic, where all spatial dimensions are infinite.

Particle creation in the early Universe: Achievements and problems

Abstract: Results on particle creation from vacuum by the gravitational field of the expanding Friedmann Universe are presented. Finite results for the density of particles and the energy density for created particles are given for different exact solutions and different expansion modes of the Universe. The results are obtained for both conformal and nonconformal particles. The hypothesis on the origin of visible matter from the decay of created from vacuum superheavy particles identified with dark matter is discussed.

Excessive extrapolations in cosmology

Abstract: The current standard cosmological model is based on the normalized Friedmann equation 1 = ΩM +ΩΛ +ΩK, where ΩM is the mass density of dark and baryonic matter, ΩΛ the vacuum energy density, and ΩK is the curvature parameter. We show that the Friedmann equation was derived under excessive extrapolations from Einstein’s equations, which are not scale invariant and are “verified” on much smaller scales. We explain why these extrapolations are incorrect, why the unrestricted use of the term “verified” is questionable, and why dark matter may exist only by definition.

Centenary of Einstein’s general relativity. Its present extensions

Abstract: This paper is a brief review of integrable models of gravitation and cosmology in four and more dimensions which make up one of the proper approaches to studying the basic issues and strong field objects, the early and present Universe, and black hole (BH) physics in particular. The main results within this approach, obtained in the recent years by the research group founded by K.P. Staniukovich, are presented. Absolute G measurements and problems of its possible time and range variations, which are reflections of the unification problem, are discussed within these models. The choice, nature, classification and precision of determination of fundamental physical constants and their role in the expected transition to new definitions of basic SI units, supposed to be based on fundamental physical constants and stable quantum phenomena, are described. A need for further absolute measurements of G, its possible range and time variations is stressed. Themultipurpose space project SEE is shortly described, aimed at measuring G and its stability in space and time with a progress of 2–3 orders of magnitude against the present accuracy. It may answer many important questions posed by gravitation, cosmology and unified theories. A project of a laboratory experiment to test possible deviations from Newton’s law of gravity is also presented.

Naked singularity formation in generalized Vaidya space-time

Abstract: The gravitational collapse in generalized Vaidya space-time is considered. It is known that the end state of gravitational collapse, as to whether a black hole or a naked singularity is formed, depends on the mass function M(v, r). Here we give conditions for the mass function which correspond to the equation of the state P = αρ. where α ∈ (0, 1/3], and according to these conditions we obtain either a black hole or a naked singularity as the end state of gravitational collapse. We also give the conditions for the mass function under which the singularity is gravitationally strong. We present simple examples showing when the result of gravitational collapse is a naked singularity and when this singularity is strong.

A machian request for the equivalence principle in extended gravity and nongeodesic motion

Abstract: Starting from the origin of Einstein’s general relativity (GR), the request of Mach on the theory’s structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of the Equivalence Principle (EP). TheMOND theory byMilgrom proposes a modification of Newtonian dynamics, and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a nongeodesic ratio m i /m g can be fixed and that Milgrom’s acceleration is retrieved at low energies.

On horizons and wormholes in k-essence theories

Abstract: We study the properties of possible static, spherically symmetric configurations in k-essence theories with the Lagrangian functions of the form F(X), X ≡ ϕ,α ϕ,α. A no-go theorem has been proved, claiming that a possible black-hole-like Killing horizon of finite radius cannot exist if the function F(X) is required to have a finite derivative dF/dX. Two exact solutions are obtained for special cases of kessence: one for F(X) = F 0 X 1/3, another for F(X) = F 0|X|1/2 − 2Λ, where F 0 and Λ are constants. Both solutions contain horizons, are not asymptotically flat, and provide illustrations for the obtained nogo theorem. The first solution may be interpreted as describing a black hole in an asymptotically singular space-time, while in the second solution two horizons of infinite area are connected by a wormhole.

Chronometric measurement of orthometric height differences by means of atomic clocks

Abstract: We report on the experimental results of testing a new physical method of determination of the gravitational potential differences and orthometric heights by measuring the relativistic effect of gravitational redshift of frequency by means of atomic clocks. The experiment was performed in the Altai Mountains between two geodetic stations, Shebalino and Sieminski Pass, separated by about 850 meters in altitude. The measured mean value of the frequency shift caused by the change in the gravitational potential between the two stations is (δf/f 0)grav = 7.980 × 10−14, with the dispersion σ f = 7.27 × 10−15 referred to the time interval of the experiment.

Perfect fluids coupled to inhomogeneities in the late Universe

Abstract: We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such scales, the Universe is highly inhomogeneous and is filled with inhomogeneities in the form of galaxies and groups of galaxies. We also suggest that the Universe is filled with a perfect fluid, and its fluctuations have peculiar velocities of the same (nonrelativistic) order of magnitude as for the inhomogeneities. In this sense, the inhomogeneities (e.g., galaxies) and fluctuations of perfect fluids are coupled to each other. We clarify some important points of this approach and present a brief review of previous studies (e.g., the Chevallier-Polarski-Linder (CPL)model and a Chaplygin gas). We demonstrate that the perfect fluids which satisfy our approach are really coupled to galaxies, concentrating around them. The averaged (over the whole Universe) value of their fluctuations is equal to zero.

ΛCDM type Heckmann–Schuking model and Union 2.1 compilation

Abstract: We study a ΛCDM type cosmological model in Heckmann-Schucking space-time, by using 287 high redshift (.3 ≤ z ≤ 1.4) SN Ia data on observed absolute magnitude along with their possible error from Union 2.1 compilation. We use the χ2 test to compare Union 2.1 compilation observed data and the corresponding theoretical values of the apparent magnitude (m). It is found that the best fit value of (Ω m )0, (ΩΛ)0 and (Ω σ )0 are 0.2940, 0.7058 and 0.0002, respectively, and the derived model represents the features of an accelerating universe which is consistent with the recent astrophysical observations.

Dark energy and inflation in a gravitational wave dominated universe

Abstract: The empty space (with no matter fields) is not really empty because of natural metric fluctuations, quantum (gravitons) and classical (gravitational waves). We show that gravitons as well as classical gravitational waves of super-horizon wavelengths are able to form a de Sitter state of the empty homogeneous isotropic Universe. This state is an exact solution to the self-consistent equations of finite one-loop quantum gravity for gravitons in the empty FLRW space. It is also an exact solution to the selfconsistent equations of back-reaction for classical gravitational waves in the same space. Technically, to get this de Sitter solution in both quantum and classical cases, it is necessary to carry out a transition to imaginary time and then to return to real time, which is possible because this de Sitter state is invariant with respect to Wick rotation. Such a procedure means that time was used as a complex variable, and this fact has a deep but still not understood significance. The de Sitter accelerated expansion of the empty Universe naturally explains the origin of dark energy and inflation because the Universe is empty at the start (inflation) and by the end (dark energy) of its evolution. This theory is consistent with the existing observational data. The CMB anisotropy of the order of 10−5 is produced by fluctuations in the number of gravitons. The existence of a threshold and a unique coincidence of topologically impenetrable barriers for tunneling takes place for the matter-dominated epoch and de Sitter State only. These facts provide a solution to the coincidence problem. The theoretical prediction that the equation-of-state parameter should be w > −1 for inflation and w < −1 for dark energy is consistentwith the observational data. To provide the reader with a complete picture, this paper gather together new and some published results of the graviton theory of the origin of inflation and dark energy.

Gauge gravitation theory in Riemann-Cartan space-time and gravitational interaction

Abstract: The place and physical significance of gauge gravitation theory in Riemann-Cartan spacetime (GTRC) in the framework of the gauge approach to gravitation is discussed. Isotropic cosmology built on the basis of GTRC with a general expression of the gravitational Lagrangian with indefinite parameters is considered. The most important physical consequences connected with a change of the gravitational interaction, with possible existence of limiting energy density and gravitational repulsion at extreme conditions, and also with the vacuum repulsion effect are discussed. A solution of the problem of cosmological singularity and the dark energy problem as a result of the change of the gravitational interaction is considered.

Quantum billiards in multidimensional models with fields of forms on a product of Einstein spaces

Abstract: The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an 1-dimensional interval and n oriented Einstein spaces, is chosen, an electromagnetic composite brane ansatz is adopted, and certain restrictions on the branes are imposed, the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDWequation are found in the limit of the formation of billiard walls which reduce the problem to the socalled quantum billiard on (n + l - 1)-dimensional hyperbolic space. Several examples of billiards in the model with {pmn} non-intersecting electric branes, e.g., corresponding to hyperbolic Kac–Moody algebras, are considered. In the classical case, any of these billiards describe a never-ending oscillating behavior of scale factors while approaching to the singularity, which is either spacelike or timelike. For n = 2 the model is completely integrable in the asymptotic regime in the clasical and quantum cases.

Parameters of innermost stable circular orbits of spinning test particles: Numerical and analytical calculations

Abstract: The motion of classical spinning test particles in the equatorial plane of a Kerr black hole is considered for the case where the particle spin is perpendicular to the equatorial plane.We review some results of our recent research of the innermost stable circular orbits (ISCO) [1] and present some new calculations. The ISCO radius, total angular momentum, energy, and orbital angular frequency are considered. We calculate the ISCO parameters numerically for different values of the Kerr parameter a and investigate their dependence on both black hole and test particle spins. Then we describe in detail how to calculate analytically small-spin corrections to the ISCO parameters for an arbitrary values of a. The cases of Schwarzschild, slowly rotating Kerr and extreme Kerr black holes are considered. The use of the orbital angular momentum is discussed. We also consider the ISCO binding energy. It is shown that the efficiency of accretion onto an extreme Kerr black hole can be larger than the maximum known efficiency (42%) if the test body has a spin.

A class of solutions under GUP for a harmonic oscillator and a particle in a box

Abstract: The existence of a minimal observable length is the common prediction of different theories of quantum gravity such as string theory, loop quantum gravity and black hole physics. The ordinary Heisenberg uncertainty principle (HUP) is not compatible with this prediction, so the HUP was generalized to the Generalized Uncertainty Principle (GUP) in literature. The consequences of this generalization are the generalized commutation relations between operators and so the generalized Hamiltonian for systems. In this paper, we represent the solutions of a harmonic oscillator and a particle in a box in the sense of a generalized commutation relation. We show that using of the Hellmann-Feynman (HF) theorem leads to the approximate energy spectrum of a harmonic oscillator and the exact energy spectrum of a particle in a box. In these cases, we do not solve the corresponding generalized Schro¨ dinger equation directly, but the HF theorem exhibit the effect of GUP on the energy spectrum. Also we obtain the uncertainties in both position and momentum for a harmonic oscillator and derive the GUP.

Chameleon scalar field in LRS Bianchi type I cosmological model

Abstract: We consider an anisotropic cosmological model with cold dark matter and a scalar field, where one component of the scale factor is taken in the framework of (i) a logamediate scenario (ii) an intermediate scenario, and (iii) an emergent scenario. In all cases we find expressions for the Chameleon field, Chameleon potential, the statefinder diagnostic pair, i.e., the {r, s} parameters, and the slow-roll parameters. All physical parameters are calculated and discussed in all three cases. It is also shown how the Chameleon field is directly affected by the role of curvature of space time. At large times (t→∞) the models tend asymptotically to an isotropic Friedmann–Robertson–Walker cosmological model.

Spin-2 fields from torsion: Dark energy and bouncing cosmology

Abstract: We study a modified theory of gravitation built on a restricted Riemann–Cartan space-time, characterized by reduction in the number of degrees of freedom of torsion. The dynamics is defined by the Einstein–Cartan action of the Einstein–Cartan–Sciama–Kibble (ECSK) theory, while the kinematical structure is defined in such a way that the general-relativistic kinematics is recovered in the associated Riemannian space-time. In this case, the torsion is automatically decomposed into two spin-2 fields with energies of opposite sign. Investigated is the special case where these spin-2 fields are “sterile” (i.e., only interact with other matter fields through gravitation) and have their number of degrees of freedom further reduced to only one. When these fields are furnished with a conservative self-interaction potential, the spatially homogeneous and isotropic cosmological solution obtained via numerical integration of the field equations exhibits accelerated expansion compatible with the current observational data, while the equation of state of both spin-2 fields have values confined in the interval between −1 and −1/3 during the whole cosmic history. Moreover, the present model exhibits nonsingular (bouncing) cosmological solutions.

Exact solution for a nonstatic cylindrically symmetric perfect fluid distribution in Einstein–Cartan theory

Abstract: We consider a nonstatic, spin-polarized cylindrically symmetric perfect fluid distribution in the Einstein-Cartan theory and obtain the field equations. These field equations are solved using the Ray–Smalley energy-momentum tensor.

An analytical solution in the complex plane for the luminosity distance in flat cosmology

Abstract: We present an analytical solution for the luminosity distance in spatially flat cosmology with pressureless matter and the cosmological constant. The complex analytical solution is made of a real part and a negligible imaginary part. The real part of the luminosity distance allows finding the two parameters H0 and ΩM . A simple expression for the distance modulus for SNs of type Ia is reported in the framework of the mini-max approximation.

Extra-relativistic effects and the Chandrasekhar limit

Abstract: We endeavor to take into account the extra-relativistic effects in the mass-energy relation due to Einstein. We consider a modified mass-energy relation and consequently find a strict bound on the Chandrasekhar limit for a white dwarf star. We find that the said limit gets modified to a certain extent, and we have been able to find the maximum mass of a stable white dwarf star.

Theory of relativity in quaternion spinors

Abstract: It is shown that the theory of relativity, apart from the standard format and the comparatively new quaternion formulation, can also be presented in terms of quaternion spinors. Mathematically, the spinor format is fundamental while technically it is primitive since it links transformations of reference frames (including non-inertial frames) with an instant rotation of a unique vector “about itself.” Such a rotation in its turn can be regarded as a reciprocal change of scales of two orthogonal directions on a 2D plane, in general, a complex number valued one. This allows for considering any transformation of relative groups SO(3,ℂ) and SL(2,ℂ) and the localized Lorentz group as a deformations of the fractal (pregeometric) spin surface.

Macroscopic Einstein equations for a cosmological model with a λ term

Abstract: By averaging the Einstein equations over transverse gravitational perturbations we obtain a closed set of two ordinary differential equations describing the macroscopic cosmological evolution of the isotropic spatially flat Universe filled with gravitational radiation. We have found an asymptotic solution of the evolution equation for the gravitational perturbation amplitude. Substituting this solution to the Einstein equations averaged over gravitational perturbations, we obtain a single nonlinear ordinary differential second-order evolution equation with respect to the macroscopic scale factor. We have also found a solution of the evolution equation for the scale factor in the WKB approximation which analytically describes the process of transformation from the ultrarelativistic mode of cosmological expansion to an inflationary one.

On the equivalence of approximate stationary axially symmetric solutions of the Einstein field equations

Abstract: We study stationary axially symmetric solutions of the Einstein vacuum field equations that can be used to describe the gravitational field of astrophysical compact objects in the limiting case of slow rotation and slight deformation. We derive explicitly the exterior Sedrakyan–Chubaryan approximate solution, and express it in an analytical form, which makes it practical in the context of astrophysical applications. In the limiting case of vanishing angular momentum, the solution reduces to the well-known Schwarzschild solution in vacuum. We demonstrate that the new solution is equivalent to the exterior Hartle–Thorne solution. We establish mathematical equivalence between the Sedrakyan–Chubaryan, Fock–Abdildin and Hartle–Thorne formalisms.

An AP-Structure with Finslerian Flavor: Path Equations

Abstract: The Bazanski approach to deriving paths is applied to Finsler geometry. The approach is generalized and applied to a new developed geometry called “Absolute parallelism with Finslerian Flavor” (FAP). A set of path equations is derived for the FAP. It is a horizontal (h) set. A striking feature in this set is that the coefficient of the torsion term jumps by a step of one-half from one equation to the other. It is tempting to believe that the h-set admits some quantum features. Comparisons with the corresponding sets in other geometries are given. Conditions for reducing the set of path equations obtained to well-known path equations in some geometries are summarized in a schematic diagram.

The effect of universe inhomogeneities on cosmological distance measurements

Abstract: Using the focusing equation, the equation for the cosmological angular diameter distance1 is derived, based on the ideas of Academician Zel’dovich, namely, that the distribution of matter at small angles is not homogeneous, and the light cone is close to being empty. We propose some ways of testing a method for measuring the angular diameter distances and show that the proposed method leads to results that agree better with the experimental data than those obtained by the usual methods.

Relativistic algebra of space-time and algebrodynamics

Abstract: We consider a manifestly Lorentz-invariant form L of the biquaternion algebra and its generalization to the case of a curved manifold. The conditions of L-differentiability of L-functions are formulated and considered as the primary equations for fundamental fields modeled with such functions. The exact form of the effective affine connection induced by L-differentiability equations is obtained for flat and curved manifolds. In the flat case, the integrability conditions of the connection lead to self-duality of the corresponding curvature, thus ensuring that the source-free Maxwell and SL(2,ℂ) Yang-Mills equations hold on the solutions of the L-differentiability equations.

On nonlinear multidimensional gravity and the Casimir effect

Abstract: We study the properties of an effective potential for the scale factor of extra dimensions in a Kaluza-Klein-type model with a spherical extra factor space, including a function of the scalar curvature and other quadratic curvature invariants, taking into account the Casimir energy of massless scalar fields. We demonstrate the existence of a minimum of the potential, able to induce a physically reasonable value of the effective cosmological constant in our space-time. Under the adopted assumptions, it is shown that the huge Casimir energy density can be compensated by the fine-tuned contribution of the curvature-nonlinear terms in the original action.

Can gravity distinguish between Dirac and Majorana neutrinos

Abstract: The interaction of neutrinos with gravitational fields in the weak field regime at one loop to the leading order has been studied by Menon and Thalappilil. They deduced some theoretical differences between the Majorana and Dirac neutrinos. Then they proved that, in spite of these theoretical differences, as far as experiments are concerned, they would be virtually indistinguishable. We study the interaction of neutrinos with weak gravitational fields to the second order (at two loops). We show that there appear new neutrino gravitational form factors which were absent in the first-order calculations, so from a theoretical point of view there are more differences between the two kinds of neutrinos than in the first order, but we show that likewise they are indistinguishable experimentally.