arXiv subjects

Alexander Zhuk

Publications and source records attributed to Alexander Zhuk.

At least 37 records · Page 2Linked to original sources

arXiv2019

Weak-field limit of Kaluza-Klein model with non-linear perfect fluid

The main purpose of our paper is to construct a viable Kaluza-Klein model satisfying the observable constraints. To this end, we investigate the six-dimensional model with spherical compactification of the internal space. Background matter is considered in the form of a perfect fluid with non-linear equations of state both in the external/our and internal spaces and the model is set to include an additional bare cosmological constant $Λ_6$. In the weak-field approximation, the background is perturbed by pressureless gravitating mass that is a static point-like particle. The non-linearity of the equations of state of a perfect fluid makes it possible to solve simultaneously a number of problems. The demand that the parameterized post-Newtonian parameter $γ$ be equal to 1 in this configuration, first, ensures compatibility with gravitational tests in the Solar system (deflection of light and time delay of radar echoes) at the same level of accuracy as General Relativity. Second, it translates into the absence of internal space variations so that the gravitational potential coincides exactly with the Newtonian one, securing the absence of the fifth force. Third, the gravitating mass remains pressurless in the external space as in the standard approach to non-relativistic astrophysical objects and meanwhile, acquires effective tension in the internal space.

gr-qc↗

arXiv2019

Effect of the spatial curvature of the Universe on the form of the gravitational potential

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.

gr-qc↗

arXiv2019

Analytic expressions for the second-order scalar perturbations in the $Λ$CDM Universe within the cosmic screening approach

We study the second-order scalar perturbations in the conventional $Λ$CDM Universe within the cosmic screening approach. The analytic expressions for both the velocity-independent and velocity-dependent second-order scalar perturbations are derived. We demonstrate how the Yukawa screening effect, which is inherent in the first-order metric corrections, manifests itself in the second-order ones. It is shown that the obtained formulas for the second-order perturbations are reduced to the known post-Newtonian expressions at distances much smaller than the Yukawa screening length. In the era of precision cosmology, these analytic formulas play an important role since the second-order metric corrections may affect the interpretation of observational data (e.g., the luminosity-redshift relation, gravitational lensing, baryon acoustic oscillations).

gr-qc↗

arXiv2018

Scalar perturbations in cosmological $f(R)$ models: the cosmic screening approach

We investigate cosmological perturbations for nonlinear $f(R)$ models within the cosmic screening approach. Matter is considered both in the form of a set of discrete point-like massive bodies and in the form of a continuous pressureless perfect fluid. We perform full relativistic analysis of the first-order theory of scalar perturbations for arbitrary nonlinear $f(R)$ models and demonstrate that scalar potentials $Φ(t,\mathbf{r})$ and $Ψ(t,\mathbf{r})$ are determined by a system of only two master equations. Our equations are applicable at all spatial scales as long as the approximation $δR/\bar R \ll 1$ (which is usually assumed in studies devoted to cosmological perturbations in $f(R)$ models) works.

gr-qc↗

arXiv2018

Brane world models with bulk perfect fluid and broken 4D Poincare invariance

We consider 5D brane world models with broken global 4D Poincar\a'{e} invariance (4D part of the spacetime metric is not conformal to the Minkowski spacetime). The bulk is filled with the negative cosmological constant and may contain a perfect fluid. In the case of empty bulk (the perfect fluid is absent), it is shown that one brane solution always has either a physical or a coordinate singularity in the bulk. We cut off these singularities in the case of compact two brane model and obtain regular exact solutions for both 4D Poincar\a'{e} broken and restored invariance. When the perfect fluid is present in the bulk, we get the master equation for the metric coefficients in the case of arbitrary bulk perfect fluid equation of state (EoS) parameters. In two particular cases of EoS, we obtain the analytic solutions for thin and thick branes. First one generalizes the well known Randall-Sundrum model with one brane to the case of the bulk anisotropic perfect fluid. In the second solution, the 4D Poincar\a'{e} invariance is restored. Here, the spacetime goes asymptotically to the anti-de Sitter one far from the thick brane.

gr-qc↗

arXiv2018

Black branes and black strings in the astrophysical and cosmological context

We consider Kaluza-Klein models where internal spaces are compact flat or curved Einstein spaces. This background is perturbed by a compact gravitating body with the dust-like equation of state (EoS) in the external/our space and an arbitrary EoS parameter $Ω$ in the internal space. Without imposing any restrictions on the form of the perturbed metric and the distribution of the perturbed energy densities, we perform the general analysis of the Einstein and conservation equations in the weak-field limit. All conclusions follow from this analysis. For example, we demonstrate that the perturbed model is static and perturbed metric preserves the block-diagonal form. In a particular case $Ω=-1/2$, the found solution corresponds to the weak-field limit of the black strings/branes. The black strings/branes are compact gravitating objects which have the topology (four-dimensional Schwarzschild spacetime)$\times$ ($d$-dimensional internal space) with $d\geq 1$. We present the arguments in favour of these objects. First, they satisfy the gravitational tests for the parameterized post-Newtonian parameter $γ$ at the same level of accuracy as General Relativity. Second, they are preferable from the thermodynamical point of view. Third, averaging over the Universe, they do not destroy the stabilization of the internal space. These are the astrophysical and cosmological aspects of the black strings/branes.

gr-qc↗

arXiv2017

Dark and visible matter distribution in Coma cluster: theory vs observations

We investigate dark and visible matter distribution in the Coma cluster in the case of the Navarro-Frenk-White (NFW) profile. A toy model where all galaxies in the cluster are concentrated inside a sphere of an effective radius $R_{\mathrm{eff}}$ is considered. It enables us to obtain the mean velocity dispersion as a function of $R_{\mathrm{eff}}$. We show that, within the observation accuracy of the NFW parameters, the calculated value of $R_{\mathrm{eff}}$ can be rather close to the observable cutoff of the galaxy distribution. Moreover, the comparison of our toy model with the observable data and simulations leads to the following preferable NFW parameters for the Coma cluster: $R_{200} \approx 1.77\,h^{-1} \, \mathrm{Mpc} = 2.61\, \mathrm{Mpc}$, $c=3÷4$ and $M_{200}= 1.29h^{-1}\times10^{15}M_{\odot}$. In the Coma cluster the most of galaxies are concentrated inside a sphere of the effective radius $R_{\mathrm{eff}}\sim 3.7$ Mpc and the line-of-sight velocity dispersion is $1004\, \mathrm{km}\, \mathrm{s}^{-1}$.

astro-ph.CO↗

arXiv2017

Cosmic screening of the gravitational interaction

We study a universe filled with cold dark matter in the form of discrete inhomogeneities (e.g., galaxies) and dark energy in the form of a continuous perfect fluid. We develop a first-order scalar perturbation theory in the weak gravity limit around a spatially flat Friedmann universe. Our approach works at all cosmic scales and incorporates linear and nonlinear effects with respect to energy density fluctuations. The gravitational potential can be split into individual contributions from each matter source. Each potential is characterized by a Yukawa interaction with the same range, which is of the order of 3700 Mpc at the present time. The derived equations can form the theoretical basis for numerical simulations for a wide class of modern cosmological models.

gr-qc↗

arXiv2017

Weak-field limit of Kaluza-Klein models with spherically symmetric static scalar field: observational constraints

In a multidimensional Kaluza-Klein model with Ricci-flat internal space, we study the gravitational field in the weak-field limit. This field is created by two coupled sources. First, this is a point-like massive body which has a dust-like equation of state in the external space and an arbitrary parameter $Ω$ of equation of state in the internal space. The second source is a static spherically symmetric massive scalar field centered at the origin where the point-like massive body is. The found perturbed metric coefficients are used to calculate the parameterized post-Newtonian (PPN) parameter $γ$. We define under which conditions $γ$ can be very close to unity in accordance with the relativistic gravitational tests in the Solar system. This can take place for both massive or massless scalar fields. For example, to have $γ\approx 1$ in the Solar system, the mass of scalar field should be $μ\gtrsim 5.05\times 10^{-49}$g $\sim 2.83\times 10^{-16}$eV. In all cases, we arrive at the same conclusion that to be in agreement with the relativistic gravitational tests, the gravitating mass should have tension: $Ω=-1/2$.

gr-qc↗

arXiv2016

Coupled scalar fields in the late Universe: The mechanical approach and the late cosmic acceleration

In 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 dust-like 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.

gr-qc↗

arXiv2016

Scalar and vector perturbations in a universe with discrete and continuous matter sources

We study a universe filled with dust-like matter in the form of discrete inhomogeneities (e.g., galaxies and their groups and clusters) and two sets of perfect fluids with linear and nonlinear equations of state, respectively. The background spacetime geometry is defined by the FLRW metric. In the weak gravitational field limit, we develop the first-order scalar and vector cosmological perturbation theory. Our approach works at all cosmological scales (i.e. sub-horizon and super-horizon ones) and incorporates linear and nonlinear effects with respect to energy density fluctuations. We demonstrate that the scalar perturbation (i.e. the gravitational potential) as well as the vector perturbation can be split into individual contributions from each matter source. Each of these contributions satisfies its own equation. The velocity-independent parts of the individual gravitational potentials are characterized by a finite time-dependent Yukawa interaction range being the same for each individual contribution. We also obtain the exact form of the gravitational potential and vector perturbation related to the discrete matter sources. The self-consistency of our approach is thoroughly checked. The derived equations can form the theoretical basis for numerical simulations for a wide class of cosmological models.

gr-qc↗

arXiv2016

The late Universe with non-linear interaction in the dark sector: the coincidence problem

We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction $Q = 3\mathcal{H}γ\bar\varepsilon_{\mathrm{DE}} \bar\varepsilon_{\mathrm{DM}} / (\bar\varepsilon_{\mathrm{DE}} + \bar\varepsilon_{\mathrm{DM}})$, where $γ$ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter $w$. In the considered model, the energy densities of the dark sector components present a scaling behaviour with $\bar\varepsilon_{\mathrm{DM}} / \bar\varepsilon_{\mathrm{DE}} \sim \left({a_0} / {a} \right)^{-3(w+γ)}$. We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the former being concentrated around them. To carry our analysis, we consider the theory of scalar perturbations (within the mechanical approach), and obtain the sets of parameters $(w,γ)$ which do not contradict it. We conclude that two sets: $(w=-2/3,γ=1/3)$ and $(w=-1,γ=1/3)$ are of special interest. First, the energy densities of DM and DE on these cases are concentrated around galaxies confirming that they are coupled fluids. Second, we show that for both of them, the coincidence problem is less severe than in the standard $Λ$CDM. Third, the set $(w=-1,γ=1/3)$ is within the observational constraints. Finally, we also obtain an expression for the gravitational potential in the considered model.

gr-qc↗

arXiv2016

$K$-essence model from the mechanical approach point of view: coupled scalar field and the late cosmic acceleration

In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, we can consider the Universe to be filled with dust-like matter in the form of discretely distributed galaxies, a $K$-essence scalar field, playing the role of dark energy, 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 the fluctuations of the other perfect fluids are non-relativistic. Such fluids are designated as coupled because they are concentrated around the inhomogeneities. In the present paper, we investigate the conditions under which the $K$-essence scalar field with the most general form for its action can become coupled. We investigate at the background level three particular examples of the $K$-essence models: (i) the pure kinetic $K$-essence field, (ii) a $K$-essence with a constant speed of sound and (iii) the $K$-essence model with the Lagrangian $bX+cX^2-V(ϕ)$. We demonstrate that if the $K$-essence is coupled, all these $K$-essence models take the form of multicomponent perfect fluids where one of the component is the cosmological constant. Therefore, they can provide the late-time cosmic acceleration and be simultaneously compatible with the mechanical approach.

gr-qc↗

arXiv2016

Perfect fluids coupled to inhomogeneities in the late Universe

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 the groups of galaxies. We also suggest that the Universe is filled with a perfect fluid, and its fluctuations have peculiar velocities of the same (non-relativistic) order of magnitude as for the inhomogeneities. In this sense, the inhomogeneities (e.g. galaxies) and fluctuations of perfect fluids are coupled with each other. We clarify some important points of this approach and present a brief review of previous studies (e.g. CPL model and Chaplygin gas). We demonstrate that considered 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.

gr-qc↗

arXiv2015

Scalar perturbations in the late Universe: viability of the Chaplygin gas models

We study the late-time evolution of the Universe where dark energy (DE) is parametrized by a modified generalized Chaplygin gas (mGCG) on top of cold dark matter (CDM). We also take into account the radiation content of the Universe. In this context, the late stage of the evolution of the universe refers to the epoch where CDM is already clustered into inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Under these conditions, the mechanical approach is an adequate tool to study the Universe deep inside the cell of uniformity. To be more accurate, we study scalar perturbations of the Friedmann-Lemaître-Robertson-Walker metric due to inhomogeneities of CDM as well as fluctuations of radiation and mGCG, the later driving the late-time acceleration of the universe. Our analysis applies as well to the case where mGCG plays the role of DM and DE. We select the sets of parameters of the mGCG that are compatible with the mechanical approach. These sets define prospective mGCG models. By comparing the selected sets of models with some of the latest observational data results, we conclude that the mGCG is in tight agreement with those observations particularly for a mGCG playing the role of DE and DM.

gr-qc↗

arXiv2015

Are dark energy models with variable EoS parameter $w$ compatible with the late inhomogeneous Universe?

We study the late-time evolution of the Universe where dark energy (DE) is presented by a barotropic fluid on top of cold dark matter (CDM). We also take into account the radiation content of the Universe. Here by the late stage of the evolution we refer to the epoch where CDM is already clustered into inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Under this condition the mechanical approach is an adequate tool to study the Universe deep inside the cell of uniformity. More precisely, we study scalar perturbations of the FLRW metric due to inhomogeneities of CDM as well as fluctuations of radiation and DE. For an arbitrary equation of state for DE we obtain a system of equations for the scalar perturbations within the mechanical approach. First, in the case of a constant DE equation of state parameter $w$, we demonstrate that our method singles out the cosmological constant as the only viable dark energy candidate. Then, we apply our approach to variable equation of state parameters in the form of three different linear parametrizations of $w$, e.g., the Chevallier-Polarski-Linder perfect fluid model. We conclude that all these models are incompatible with the theory of scalar perturbations in the late Universe.

gr-qc↗

arXiv2015

Lattice Universe: examples and problems

We consider lattice Universes with spatial topologies $T\times T\times T$, $\; T\times T\times R\; $ and $\; T\times R\times R$. In the Newtonian limit of General Relativity, we solve the Poisson equation for the gravitational potential in the enumerated models. In the case of point-like massive sources in the $T\times T\times T$ model, we demonstrate that the gravitational potential has no definite values on the straight lines joining identical masses in neighboring cells, i.e. at points where masses are absent. Clearly, this is a nonphysical result since the dynamics of cosmic bodies is not determined in such a case. The only way to avoid this problem and get a regular solution at any point of the cell is the smearing of these masses over some region. Therefore, the smearing of gravitating bodies in $N$-body simulations is not only a technical method but also a physically substantiated procedure. In the cases of $\; T\times T\times R\; $ and $\; T\times R\times R$ topologies, there is no way to get any physically reasonable and nontrivial solution. The only solutions we can get here are the ones which reduce these topologies to the $T\times T\times T$ one.

gr-qc↗

arXiv2015

Rigorous theoretical constraint on constant negative EoS parameter $ω$ and its effect for the late Universe

In this paper, we consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies). Supposing that the Universe contains also the cosmological constant and a perfect fluid with a negative constant equation of state (EoS) parameter $ω$ (e.g., quintessence, phantom or frustrated network of topological defects), we investigate scalar perturbations of the FRW metrics due to inhomogeneities. Our analysis shows that, to be compatible with the theory of scalar perturbations, this perfect fluid, first, should be clustered and, second, should have the equation of state parameter $ω=-1/3$. In particular, this value corresponds to the frustrated network of cosmic strings. Therefore, the frustrated network of domain walls with $ω=-2/3$ is ruled out. A perfect fluid with $ω=-1/3$ neither accelerates nor decelerates the Universe. We also obtain the equation for the nonrelativistic gravitational potential created by a system of inhomogeneities. Due to the perfect fluid with $ω= -1/3$, the physically reasonable solutions take place for flat, open and closed Universes. This perfect fluid is concentrated around the inhomogeneities and results in screening of the gravitational potential.

astro-ph.CO↗