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V. N. Melnikov

Publications and source records attributed to V. N. Melnikov.

At least 37 records · Page 2Linked to original sources
arXiv2008

Multidimensional cosmology with anisotropic fluid: acceleration and variation of G

A multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor-spaces M_i in the presence of a one-component anisotropic fluid is considered. The pressures in all spaces are proportional to the density: p_i = w_i ρ, i = 0,...,n. Solutions with accelerated expansion of our 3-space M_0 and small enough variation of the gravitational constant G are found. These solutions exist for two branches of the parameter w_0. The first branch describes superstiff matter with w_0 > 1, the second one may contain phantom matter with w_0 < - 1, e.g., when G grows with time.

gr-qc↗
arXiv2008

Non-singular solutions in multidimensional cosmology with a perfect fluid: acceleration and variation of G

Exact solutions with an exponential behaviour of the scale factors are considered in a multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor spaces M_i in the presence of a one-component perfect fluid. The pressures in all spaces are proportional to the density: p_i = w_i ρ, i = 0,...,n. Solutions with accelerated expansion of our 3-space M_0 and a small enough variation of the gravitational constant G are found. These solutions exist for two branches of the parameter w_0. The first branch describes superstiff matter with w_0 > 1, the second one may contain phantom matter with w_0 < - 1.

hep-th↗
arXiv2007

Fluxbrane and S-brane solutions with polynomials related to rank-2 Lie algebras

Composite fluxbrane and S-brane solutions for a wide class of intersection rules are considered. These solutions are defined on a product manifold R_{*} x M_1 x ... x M_n which contains n Ricci-flat spaces M_1, ..., M_n with 1-dimensional factor spaces R_{*} and M_1. They are determined up to a set of functions obeying non-linear differential equations equivalent to Toda-type equations with certain boundary conditions imposed. Exact solutions corresponding to configurations with two branes and intersections related to simple Lie algebras C_2 and G_2 are obtained. In these cases, the functions H_s(z), s =1,2, are polynomials of degrees (3, 4) and (6, 10), respectively, in agreement with a conjecture put forward previously in Ref., \cite{Iflux}. The S-brane solutions under consideration, for special choices of the parameters, may describe an accelerating expansion of our 3-dimensional space and a small enough variation of the effective gravitational constant.

math-ph↗
arXiv2007

An S-brane solution with acceleration and small enough variation of G

An S-brane solution with two non-composite electric branes and a set of l scalar fields is considered. The intersection rule for branes corresponds to the Lie algebra A_2. The solution contains five factor spaces with the fifth one interpreted as ``our'' 3-dimensional space. It is shown that there exists a time interval where accelerating expansion of ``our'' 3-dimensional space is compatible with small enough value of effective gravitational ``constant'' variation.

gr-qc↗
arXiv2006

Multidimensional Classical and Quantum Cosmology with Perfect Fluid

A cosmological model describing the evolution of n Ricci-flat spaces (n>1) in the presence of 1-component perfect-fluid and minimally coupled scalar field is considered. When the pressures in all spaces are proportional to the density, the Einstein and Wheeler-DeWitt equations are integrated for a large variety of parameters. Classical and quantum wormhole solutions are obtained for negative density. Some special classes of solutions, e.g. solutions with spontaneous and dynamical compactification, exponential and power-law inflations, are singled out. For positive density a third quantized cosmological model is considered and the Planckian spectrum of ``created universes'' is obtained.

hep-th↗
arXiv2006

S-brane solutions with (anti-)self-dual parallel charge density form on a Ricci-flat submanifold

A D-dimensional cosmological model with several scalar fields and antisymmetric (p+2)-form is considered. For dimensions D = 4m+1 = 5, 9, 13, ... and p = 2m-1 = 1, 3, 5, ... we obtain a family of new cosmological type solutions with 4m-dimensional oriented Ricci-flat submanifold N of Euclidean signature. These solutions are characterized by a self-dual or anti-self-dual parallel charge density form Q of rank 2m defined on N. The (sub)manifold N may be chosen to be K\ddot{a}hler, or hyper-K\ddot{a}hler one, or 8-dimensional manifold of Spin(7) holonomy. The generalization of solutions to a chain of extra marginal) Ricci-flat factor-spaces is also presented. Solutions with accelerated expansion of extra factor-spaces are singled out. Certain examples of new solutions for IIA supergravity and for a chain of B_D-models in dimensions D = 14, 15, ... are considered.

hep-th↗
arXiv2006

Regular black holes and black universes

We give a comparative description of different types of regular static, spherically symmetric black holes (BHs) and discuss in more detail their particular type, which we suggest to call black universes. The latter have a Schwarzschild-like causal structure, but inside the horizon there is an expanding Kantowski-Sachs universe and a de Sitter infinity instead of a singularity. Thus a hypothetic BH explorer gets a chance to survive. Solutions of this kind are naturally obtained if one considers static, spherically symmetric distributions of various (but not all) kinds of phantom matter whose existence is favoured by cosmological observations. It also looks possible that our Universe has originated from phantom-dominated collapse in another universe and underwent isotropization after crossing the horizon. An explicit example of a black-universe solution with positive Schwarzschild mass is discussed.

gr-qc↗
arXiv2006

Electric S-brane solutions with parallel forms on Ricci-flat factor space

In this paper we generalize electric S-brane solutions with maximal number of branes. Previously for the action containing D-dimensional gravity, a scalar field and antisymmetric (p+2)-form we found composite, electric S-brane solutions with all non-zero ``charge'' densities which obeyed self-duality or anti-self-duality relations. These solutions occurred when D = 4m+1 = 5, 9, 13, >... and p = 2m-1 = 1, 3, 5, ... Here we generalize these solutions to the case when the spatial 4m-dimensional submanifold is Ricci-flat rather than simply Euclidean-flat and the charge density form is a parallel self-dual or anti-self-dual form of rank 2m. Also generalizations are found for the case when there is an extra ``internal'' Ricci-flat manifold not covered by the S-branes. In the case when one allows a phantom scalar field a subset of these solutions lead to accelerated expansion of this extra spatial factor space not covered by the S-branes while the other spatial factor space of dimension 4m contracts. Some of these S-brane solutions also provide specific examples of solutions of type IIA supergravity.

hep-th↗
arXiv2006

On the cosmological constant in quantum cosmology

Quantization of a dust-like closed isotropic cosmological model with a cosmological constant is realized by the method of B. DeWitt \cite{1}. It is shown that such quantization leads to interesting results, in particular, to a finite lifetime of the system, and appearance of the Universe in our world as penetration via the barrier. These purely quantum effects appear when $Λ>0$.

gr-qc↗
arXiv2006

On time variation of G in multidimensional models with two curvatures

Expressions for G-dot are considered in a multidimensional model with an Einstein internal space and a multicomponent perfect fluid. In the case of two non-zero curvatures without matter, a mechanism for prediction of small G-dot is suggested. The result is compared with exact (1+3+6)-dimensional solutions. A two-component example with two matter sources (dust + 5-brane) and two Ricci-flat factor spaces is also considered.

gr-qc↗
arXiv2006

Brane world corrections to Newton's law

We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After a brief general exposition, we review in more detail the predicted corrections to Newton's law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein-Gauss-Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton's law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology.

gr-qc↗
arXiv2005

On avoiding cosmological oscillating behavior for S-brane solutions with diagonal metrics

In certain string inspired higher dimensional cosmological models it has been conjectured that there is generic, chaotic oscillating behavior near the initial singularity -- the Kasner parameters which characterize the asymptotic form of the metric "jump" between different, locally constant values and exhibit a never-ending oscillation as one approaches the singularity. In this paper we investigate a class of cosmological solutions with form fields and diagonal metrics which have a "maximal" number of composite electric S-branes. We look at two explicit examples in D=4 and D=5 dimensions that do not have chaotic oscillating behavior near the singularity. When the composite branes are replaced by non-composite branes chaotic oscillating

gr-qc↗
arXiv2005

Composite electric S-brane solutions with maximal number of branes and several scalar fields

A (n+1)-dimensional cosmological model with a set of scalar fields and antisymmetric (p+2)-form is considered. Some of scalar fields may have negative kinetic terms, i.e. they may describe ``phantom'' fields. For certain odd dimensions (D = 4m+1 = 5, 9, 13, ...) and (p+2)-forms (p = 2m-1 = 1, 3, 5, ...) and non-exceptional dilatonic coupling vector $\vecλ$ we obtain cosmological-type solutions to the field equations. These solutions are characterized by self-dual or anti-self-dual charge density forms Q (of rank 2m) and may describe the maximal set of branes (i.e. when all the branes have non-zero charge densities). Some properties of these solutions are considered, e.g. Kasner-like behavior, the existence of non-singular (e.g. bouncing) solutions and those with acceleration. The solutions with bouncing and acceleration take place when at least there is one ``phantom'' field in the model.

hep-th↗
arXiv2005

Non-singular solutions in multidimensional model with scalar fields and exponential potential

Using developed earlier our methods for multidimensional models \cite{M1,M2,M3} a family of cosmological-type solutions in D-dimensional model with two sets of scalar fields \vecϕ and \vecψ and exponential potential depending upon \vecϕ is considered. The solutions are defined on a product of n Ricci-flat spaces. The fields from \vecϕ have positive kinetic terms and \vecψ are "phantom" fields with negative kinetic terms. For vector coupling constant obeying 0< \vecλ^2 < (D-1)/(D-2) a subclass of non-singular solutions is singled out. The solutions from this subclass are regular for all values of synchronous "time" τ\in (- \infty, + \infty). For \vecλ^2 < 1/(D-2) we get an asymptotically accelerated and isotropic expansion for large values of τ.

gr-qc↗
arXiv2005

Exact solutions in multidimensional gravity with antisymmetric forms

This topical review deals with a multidimensional gravitational model containing dilatonic scalar fields and antisymmetric forms. The manifold is chosen in the form M = M_0 x M_1 x ...x M_n, where M_i are Einstein spaces (i >0). The sigma-model approach and exact solutions in the model are reviewed and the solutions with p-branes (e.g. Majumdar-Papapetrou-type, cosmological, spherically symmetric, black-brane and Freund-Rubin-type ones) are considered.

hep-th↗
arXiv2004

Multicomponent perfect fluid with variable parameters in n Ricci-flat spaces

D-dimensional cosmological model describing the evolution of a multicomponent perfect fluid with variable barotropic parameters in n Ricci-flat spaces is investigated. The equations of motion are integrated for the case, when each component possesses an isotropic pressure with respect to all spaces. Exact solutions are presented in the Kasner-like form. Some explicit examples are given: 4-dimensional model with an isotropic accelerated expansion at late times and (4+d)-dimensional model describing a compactification of extra dimensions.

gr-qc↗
arXiv2004

S-brane solutions with acceleration in models with forms and multiple exponential potentials

A family of generalized S-brane solutions with orthogonal intersection rules and n Ricci-flat factor spaces in the theory with several scalar fields, antisymmetric forms and multiple scalar potential is considered. Two subclasses of solutions with power-law and exponential behaviour of scale factors are singled out. These subclasses contain sub-families of solutions with accelerated expansion of certain factor spaces. Some examples of solutions with exponential dependence of one scale factor and constant scale factors of "internal" spaces (e.g. Freund-Rubin type solutions) are also considered.

hep-th↗