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Документ Dynamics of cosmic bodies in TNK open Universe(Odessa I.I. Mechnikov National University, 2012) Kudinova, Alexandra; Eingorn, Maxim; Zhuk, AlexanderПоказати більше We develop the dynamical approach in this model and investigate nonrelativistic motion of two, three and even more cosmic bodies against the cosmological background, perturbed locally by density inhomogeneities (namely, galaxies). For arbitrary initial conditions, we get solutions of equations of motion (trajectories), demonstrating most important features of the cosmological expansion, only slightly restrained by gravitational attraction. Our methods can be used for indirect observations of dark energy and dark matterПоказати більше Документ Effect of the Cubic Torus Topology on Cosmological Perturbations(2021) Eingorn, Maxim; Canay, Ezgi; Metcalf, Jacob M.; Brilenkov, Maksym; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр ИвановичПоказати більше We study the effect of the cubic torus topology of the Universe on scalar cosmological perturbations which define the gravitational potential. We obtain three alternative forms of the solution for both the gravitational potential produced by point-like masses, and the corresponding force. The first solution includes the expansion of delta-functions into Fourier series, exploiting periodic boundary conditions. The second one is composed of summed solutions of the Helmholtz equation for the original mass and its images. Each of these summed solutions is the Yukawa potential. In the third formula, we express the Yukawa potentials via Ewald sums. We show that for the present Universe, both the bare summation of Yukawa potentials and the Yukawa-Ewald sums require smaller numbers of terms to yield the numerical values of the potential and the force up to desired accuracy. Nevertheless, the Yukawa formula is yet preferable owing to its much simpler structure.Показати більше Документ Effect of the spatial curvature of the Universe on the form of the gravitational potential(2019) Eingorn, Maxim; Yükselci, A. Emrah; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр ИвановичПоказати більше Within the cosmic screening approach, we obtain the exact formulas for the velocity-independent gravitational potentials produced by matter in the form of discrete sources distributed in the open and closed Universes. These formulas demonstrate that spatial curvature of the Universe considerably affect the form of the potentials and forces.While in the open Universe the gravitational force undergoes exponential suppression at cosmological distances, in the closed Universe the force induced by an individual mass is equal to zero at the antipodal point with respect to this mass. The derived formulas are applicable for investigations of the motion of astrophysical objects (e.g., galaxies) in the open and closed Universes, and for simulations of the large scale structure formation.Показати більше Документ Effects of nonlinearity of f (R) gravity and perfect fluid in Kaluza–Klein models with spherical compactification(2020) Canay, Ezgi; Eingorn, Maxim; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр ИвановичПоказати більше We study the effects associated with nonlinearity of f (R) gravity and of the background perfect fluid manifested in the Kaluza–Klein model with spherical compactification. The background space-time is perturbed by a massive gravitating source which is pressureless in the external space but has an arbitrary equation of state (EoS) parameter in the internal space. As characteristics of a nonlinear perfect fluid, the squared speeds of sound are not equal to the background EoS parameters in the external and internal spaces. In this setting, we find exact solutions to the linearized Einstein equations for the perturbed metric coefficients. For nonlinear models with f (R0) = 0, we show that these coefficients acquire correction terms in the form of two summed Yukawa potentials and that in the degenerated case, the solutions are reduced to a single Yukawa potential with some “corrupted” prefactor (in front of the exponential function), which, in addition to the standard 1/r term, contains a contribution independent of the three-dimensional distance r . In the linear f (R) = 0 model, we generalize the previous studies to the case of an arbitrary nonlinear perfect fluid. We also investigate the particular case of the nonlinear background perfect fluid with zero speed of sound in the external space and demonstrate that a non-trivial solution exists only in the case of f (R0) = 0.Показати більше Документ Fine tuning problem avoidance in five-dimensional brane world models(Одеський національний університет імені І. І. Мечникова, 2012) Fakhr, Seyed Hossein; Eingorn, Maxim; Zhuk, AlexanderПоказати більше We avoid this problem of naturalness, introducing a perfect fluid with arbitrary equations of state in both three-dimensional external and one-dimensional internal spaces parallel with the cosmological constant.Показати більше Документ Gravitational Interaction in the Chimney Lattice Universe †(2021) Eingorn, Maxim; McLaughlin II, Andrew; Canay, Ezgi; Brilenkov, Maksym; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр ИвановичПоказати більше We investigate the influence of the chimney topology T T R of the Universe on the gravitational potential and force that are generated by point-like massive bodies. We obtain three distinct expressions for the solutions. One follows from Fourier expansion of delta functions into series using periodicity in two toroidal dimensions. The second one is the summation of solutions of the Helmholtz equation, for a source mass and its infinitely many images, which are in the form of Yukawa potentials. The third alternative solution for the potential is formulated via the Ewald sums method applied to Yukawa-type potentials. We show that, for the present Universe, the formulas involving plain summation of Yukawa potentials are preferable for computational purposes, as they require a smaller number of terms in the series to reach adequate precision.Показати більше Документ Hubble flows and gravitational potentials in observable Universe(Одеський національний університет імені І. І. Мечникова, 2012) Eingorn, Maxim; Zhuk, AlexanderПоказати більше We consider the Universe deep inside of (he cell of uniformity. At these scales, the Universe is tilled with inhomogeneousiy distributed discrete structures (such as galaxies, their groups and clusters). These inhomogeneities perturb the homogeneous background, described satisfactorily by the Friedmann mode.Показати більше Документ Implementation of gravitational potential screening on large scales in an N-body code(2019) Baldi, Marco; Burgazli, Alvina; Eingorn, Maxim; Жук, Олександр Іванович; Жук, Александр Иванович; Zhuk, Oleksandr I.Показати більше There was considered the Universe filled with cold dark matter in the form of discrete inhomogeneities (e.g., galax-ies) and dark energy in the form of arbitrary continuous per-fect fluids. The background space-time geometry is defined by the Friedmann metric.Показати більше Документ Multidimensional solitons with spherical compactification(Одеський національний університет імені І. І. Мечникова, 2012) Chopovsky, Alexey; Eingorn, Maxim; Zhuk, AlexanderПоказати більше Changing the compactification type, we construct exact and approximate soliton solutions, when the internal space represents a sphere of some finite radius. We investigate these solutions concerning their compatibility with the experimental data and establish restrictions on their parameters.Показати більше Документ Quintessence and phantom energy inhomogeneities at late stages of universe evolution(Одеський національний університет імені І. І. Мечникова, 2012) Burgazli, Alvina; Eingorn, Maxim; Zhuk, AlexanderПоказати більше We demonstrate that -1/3 is the only admissible negative parameter in the non-vacuum equation of state, determine the corresponding gravitational potentials and discuss their main properties.Показати більше Документ Scalar and vector perturbations in a universe with nonlinear perfect fluid(2021) Canay, Ezgi; Ruslan, Brilenkov; Eingorn, Maxim; Arapo˘glu, A. Savas; Zhuk, Oleksandr I.; Жук, Олександр Іванович; Жук, Александр ИвановичПоказати більше We study a three-component universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies) and perfect fluids characterized by linear and nonlinear equations of state. Within the cosmic screening approach, we develop the theory of scalar and vector perturbations. None of the energy density contrasts associated with the distinct components is treated as small. Consequently, the derived equations are valid at both sub- and super-horizon scales and enable simulations for a variety of cosmological models.Показати більше Документ Significance of tension for Kaluza-KIein models: critical remarks(Одеський національний університет імені І. І. Мечникова, 2012) Zhuk, Alexander; Eingorn, MaximПоказати більше We clarify the problematic aspects of gravitational interaction in the weak field limit of Kaluza-KIein models. We explain why some models meet the classical gravitational tests, while the others do not. We show that variation of the total volume of the internal spaces generates the fifth force. This is the main reason of the problem. It happens for all considered models (linear with respect to the scalar curvature and nonlinear f(R), with toroidal and spherical compactifications). We explicitly single out the contribution of the fifth force to nonrelativistic gravitational potentials.Показати більше Документ The Shape of Multidimensional Gravity: Non-relativistic Limit(Astroprint, 2009) Zhuk, Alexander; Eingorn, MaximПоказати більше It is found the exact solution of the Poisson equation for the multidimensional space with topology M3+d = R3 ×Td. This solution describes smooth transition from the Newtonian behavior 1/r3 for distances bigger than periods of tori (the extra dimension sizes) to multidimensional behavior 1/r1+d 3+d in opposite limit. In the case of one extra dimension d = 1, the gravitational potential is expressed via compact and elegant formula. Obtained formula is applied to an infinitesimally thin shell, a shell, a sphere and two spheres to show deviations from the Newtonian expressions. It is shown that the corrections to the gravitational constant in the Cavendish-type experiment can be within the measurement accuracy of Newton’s gravitational constant GN. It is proposed models where the test masses are smeared over some (or all) extra dimensions. In 10-dimensional spacetime with 3 smeared extra dimensions, it is shown that the size of 3 rest extra dimensions can be enlarged up to submillimeter for the case of 1TeV fundamental Planck scale MPl(10). In the models where all extra dimensions are smeared, the gravitational potential exactly coincides with the Newtonian one. Nevertheless, the hierarchy problem can be solved in these models.Показати більше