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Документ A nonlinear multidimensional gravitational model R+R-1 with form fields and stabilized extra dimensions(Madrid : Consejo Superior de Investigaciones Científicas, Instituto Miguel Asín,, 2007) Saidov, T.; Zhuk, AlexanderWe studied multidimensional gravitational models with scalar curvature nonlinearity of the type R−1 and with form fields (fluxes) as a matter source. It is assumed that the higher-dimensional space–time undergoes Freund–Rubin-like spontaneous compactification to a warped product manifold. It is shown that for certain parameter regions the model allows for freezing stabilization of the internal space near the positive minimum of the effective potential, which plays the role of the positive effective cosmological constant. However, the parameters of model should be fine tuned to obtain the observable dark energy.Документ Coupled scalar fields in the late Universe: the mechanical approach and the late cosmic acceleration(IOP Publishing Ltd and Sissa Medialab srl, 2016-09-28) Burgazli, Alvina; Zhuk, Alexander; Morais, Joao; Bouhmadi-L´opezc, Mariam; Kumar, K. SravanIn this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, we consider the Universe to be filled with dustlike matter in the form of discretely distributed galaxies, a minimally coupled scalar field and radiation as matter sources. We investigate such a Universe in the mechanical approach. This means that the peculiar velocities of the inhomogeneities (in the form of galaxies) as well as fluctuations of other perfect fluids are non-relativistic. Such fluids are designated as coupled because they are concentrated around inhomogeneities. In the present paper we investigate the conditions under which a scalar field can become coupled, and show that, at the background level, such coupled scalar field behaves as a two component perfect fluid: a network of frustrated cosmic strings with EoS parameter w = −1/3 and a cosmological constant. The potential of this scalar field is very flat at the present time. Hence, the coupled scalar field can provide the late cosmic acceleration. The fluctuations of the energy density and pressure of this field are concentrated around the galaxies screening their gravitational potentials. Therefore, such scalar fields can be regarded as coupled to the inhomogeneities.Документ Dynamics of cosmic bodies in TNK open Universe(Odessa I.I. Mechnikov National University, 2012) Kudinova, Alexandra; Eingorn, Maxim; Zhuk, AlexanderWe 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 matterДокумент Effective Friedmann model from multidimensional cosmologies(2007) Zhuk, AlexanderWe investigate the possibility of the construction of the conventional Friedmann cosmology for our observable Universe if the underlying theory is the multidimensional Kaluza–Klein model.We show that the effective Friedmann model obtained by dynamic compactification of the multidimensional model is faced with too strong variations in the fundamental constants. On the other hand, models with stable compactification of the internal space are free from this problem and also result in conventional four-dimensonal cosmological behaviour for our Universe. We prove a no-go theorem, which shows that stable compactification of the internal spaces is possible only if the equations of state in the external and internal spaces are properly adjusted to each other. With a proper choice of parameters (fine tuning), the effective cosmological constant in this model provides the late-time acceleration of the Universe.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, AlexanderWe 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.Документ Hubble flows and gravitational potentials in observable Universe(Одеський національний університет імені І. І. Мечникова, 2012) Eingorn, Maxim; Zhuk, AlexanderWe 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.Документ Multidimensional solitons with spherical compactification(Одеський національний університет імені І. І. Мечникова, 2012) Chopovsky, Alexey; Eingorn, Maxim; Zhuk, AlexanderChanging 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.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, AlexanderWe 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.Документ Significance of tension for Kaluza-KIein models: critical remarks(Одеський національний університет імені І. І. Мечникова, 2012) Zhuk, Alexander; Eingorn, MaximWe 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.Документ Sp-branes: integrable multidimensional cosmologies(2007) Baukh, V.; Zhuk, Alexander; Madrid : Consejo Superior de Investigaciones Científicas, Instituto Miguel Asín,We investigate time-dependent solutions (Sp-brane solutions) for product manifolds consisting of factor spaces where only one of them is of a non-Ricci-flat type. Our model contains a minimally coupled free scalar field and form field (flux) as matter sources.We discuss the possibility of generating late-time acceleration of the Universe. For these models, we investigate the variation with time of the effective four-dimensional fundamental ‘constants’. We show that experimental bounds for the fundamental constant variations apply strong restrictions to the considered models.Документ The Shape of Multidimensional Gravity: Non-relativistic Limit(Astroprint, 2009) Zhuk, Alexander; Eingorn, MaximIt 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.