arXiv subjects

Maxim Eingorn

Publications and source records attributed to Maxim Eingorn.

At least 37 records · Page 2Linked to original sources

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↗

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

Perfect fluids with $ω=\mathrm{const}$ as sources of scalar cosmological perturbations

We make a generalization of a self-consistent first-order perturbation scheme, being suitable for all (sub-horizon and super-horizon) scales, which has been recently constructed for the concordance cosmological model and discrete presentation of matter sources, to the case of extended models with extra perfect fluids and continuous presentation. Namely, we derive a single equation determining the scalar perturbation and covering the whole space as well as define the corresponding universal Yukawa interaction range. We also demonstrate explicitly that the structure growth is suppressed at distances exceeding this fundamental range.

gr-qc↗

arXiv2017

Second-order Cosmological Perturbations Engendered by Point-like Masses

In the $Λ$CDM framework, presenting nonrelativistic matter inhomogeneities as discrete massive particles, we develop the second-order cosmological perturbation theory. Our approach relies on the weak gravitational field limit. The derived equations for the second-order scalar, vector and tensor metric corrections are suitable at arbitrary distances including regions with nonlinear contrasts of the matter density. We thoroughly verify fulfilment of all Einstein equations as well as self-consistency of order assignments. In addition, we achieve logical positive results in the Minkowski background limit. Feasible investigations of the cosmological backreaction manifestations by means of relativistic simulations are also outlined.

gr-qc↗

arXiv2017

Cosmological law of universal gravitation

Without exceeding the limits of the conventional $Λ$CDM paradigm, we argue for Yukawa law of interparticle interaction as the law of gravitation in the real expanding inhomogeneous Universe. It covers the whole space and comes up to take place of Newtonian gravity, which is restricted exclusively to sub-horizon distances. The large-scale screening of gravitational interaction between every two nonrelativistic massive particles is ensured by the homogeneous cosmological background (specifically, by the nonzero average rest mass density of nonrelativistic matter). We take advantage of the uniform matter distribution case (i.e. the homogeneous Universe limit) to demonstrate superiority of Yukawa gravity. Attention is also devoted to the concrete particular case of inhomogeneity.

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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.

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arXiv2016

First-order Cosmological Perturbations Engendered by Point-like Masses

In the framework of the concordance cosmological model the first-order scalar and vector perturbations of the homogeneous background are derived in the weak gravitational field limit without any supplementary approximations. The sources of these perturbations (inhomogeneities) are presented in the discrete form of a system of separate point-like gravitating masses. The found expressions for the metric corrections are valid at all (sub-horizon and super-horizon) scales and converge at all points except at locations of the sources. The average values of these metric corrections are zero (thus, first-order backreaction effects are absent). Both the Minkowski background limit and the Newtonian cosmological approximation are reached under certain well-defined conditions. An important feature of the velocity-independent part of the scalar perturbation is revealed: up to an additive constant this part represents a sum of Yukawa potentials produced by inhomogeneities with the same finite time-dependent Yukawa interaction range. The suggested connection between this range and the homogeneity scale is briefly discussed along with other possible physical implications.

gr-qc↗

arXiv2015

Uniformity of Cosmic Microwave Background as a Non-Inflationary Geometrical Effect

The conventional $Λ$CDM cosmological model supplemented by the inflation concept describes the Universe very well. However, there are still a few concerns: new Planck data impose constraints on the shape of the inflaton potential, which exclude a lot of inflationary models; dark matter is not detected directly, and dark energy is not understood theoretically on a satisfactory level. In this brief sketch we investigate an alternative cosmological model with spherical spatial geometry and an additional perfect fluid with the constant parameter $ω=-1/3$ in the linear equation of state. It is demonstrated explicitly that in the framework of such a model it is possible to satisfy the supernovae data at the same level of accuracy as within the $Λ$CDM model and at the same time suppose that the observed cosmic microwave background (CMB) radiation originates from a very limited space region. This is ensured by introducing an additional condition of light propagation between the antipodal points during the age of the Universe. Consequently, the CMB uniformity can be explained without the inflation scenario. The corresponding drawbacks of the model with respect to its comparison with the CMB data are also discussed.

astro-ph.CO↗

arXiv2015

Zero average values of cosmological perturbations as an indispensable condition for the theory and simulations

We point out a weak side of the commonly used determination of scalar cosmological perturbations lying in the fact that their average values can be nonzero for some matter distributions. It is shown that introduction of the finite-range gravitational potential instead of the infinite-range one resolves this problem. The concrete illustrative density profile is investigated in detail in this connection.

astro-ph.CO↗

arXiv2015

Scalar perturbations in cosmological models with dark energy - dark matter interaction

Scalar cosmological perturbations are investigated in the framework of a model with interacting dark energy and dark matter. In addition to these constituents, the inhomogeneous Universe is supposed to be filled with the standard noninteracting constituents corresponding to the conventional $Λ$CDM model. The interaction term is chosen in the form of a linear combination of dark sector energy densities with evolving coefficients. The methods of discrete cosmology are applied, and strong theoretical constraints on the parameters of the model are derived. A brief comparison with observational data is performed.

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.

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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↗

arXiv2015

Gurzadyan's Problem 5 and improvement of softenings for cosmological simulations using the PP method

This paper is devoted to different modifications of two standard softenings of the gravitational attraction (namely the Plummer and Hernquist softenings), which are commonly used in cosmological simulations based on the particle-particle (PP) method, and their comparison. It is demonstrated that some of the proposed alternatives lead to almost the same accuracy as in the case of the pure Newtonian interaction, even despite the fact that the force resolution is allowed to equal half the minimum interparticle distance. The revealed way of precision improvement gives an opportunity to succeed in solving Gurzadyan's Problem 5 and bring modern computer codes up to a higher standard.

astro-ph.CO↗

arXiv2014

$f(R)$ gravity: scalar perturbations in the late Universe

In this paper we study scalar perturbations of the metric for nonlinear $f(R)$ models. We consider the Universe at the late stage of its evolution and deep inside the cell of uniformity. We investigate the astrophysical approach in the case of Minkowski spacetime background and two cases in the cosmological approach, the large scalaron mass approximation and the quasi-static approximation, getting explicit expressions for scalar perturbations for both these cases. In the most interesting quasi-static approximation, the scalar perturbation functions depend on both the nonlinearity function $f(R)$ and the scale factor $a$. Hence, we can study the dynamical behavior of the inhomogeneities (e.g., galaxies and dwarf galaxies) including into consideration their gravitational attraction and the cosmological expansion, and also taking into account the effects of nonlinearity. Our investigation is valid for functions $f(R)$ which have stable de Sitter points in future with respect to the present time, that is typical for the most popular $f(R)$ models.

astro-ph.CO↗

arXiv2014

Scalar perturbations in cosmological models with quark nuggets

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 a small fraction of colored objects escaped hadronization and survived up to now in the form of quark-gluon nuggets (QNs), and also taking into account radiation, we investigate scalar perturbations of the FRW metrics due to inhomogeneities of dustlike matter as well as fluctuations of QNs and radiation. In particular, we demonstrate that the nonrelativistic gravitational potential is defined by the distribution of inhomogeneities/fluctuations of both dustlike matter and QNs. Consequently, QNs can be distributed around the baryonic inhomogeneities (e.g., galaxies) in such a way that it can solve the problem of the flatness of the rotation curves. We also show that the fluctuations of radiation are caused by both the inhomogeneities in the form of galaxies and the fluctuations of quark-gluon nuggets. Therefore, if QNs exist, the CMB anisotropy should contain also the contributions from QNs. Additionally, the spatial distribution of the radiation fluctuations is defined by the gravitational potential. All these results look physically reasonable.

astro-ph.CO↗

arXiv2014

Problematic aspects of Kaluza-Klein excitations in multidimensional models with Einstein internal spaces

We consider Kaluza-Klein (KK) models where internal spaces are compact Einstein spaces. These spaces are stabilized by background matter (e.g., monopole form-fields). We perturb this background by a compact matter source (e.g., the system of gravitating masses) with the zero pressure in the external/our space and an arbitrary pressure in the internal space. We show that the Einstein equations are compatible only if the matter source is smeared over the internal space and perturbed metric components do not depend on coordinates of extra dimensions. The latter means the absence of KK modes corresponding to the metric fluctuations. Maybe, the absence of KK particles in LHC experiments is explained by such mechanism.

gr-qc↗