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The existing observational data on possible variations of fundamental physical constants (FPC) confirm more or less confidently only a variability of the fine structure constant $\alpha$ in space and time. A model construction method is described, where variations of $\alpha$ and other FPCs (including the gravitational constant $G$) follow from the dynamics of extra space-time dimensions in the framework of curvature-nonlinear multidimensional theories of gravity. An advantage of this method is a unified approach to variations of different FPCs. A particular model explaining the observable variations of $\alpha$ in space and time has been constructed. It comprises a FRW cosmology with accelerated expansion, perturbed due to slightly inhomogeneous initial data., Comment: 15 pages, 1 figure. Comments and references added

The vacuum cosmological model on the manifold $R \times M_1 \times \ldots \times M_n$ describing the evolution of $n$ Einstein spaces of non-zero curvatures is considered. For $n = 2$ the Einstein equations are reduced to the Abel (ordinary differential) equation and solved, when $(N_1 = $dim $ M_1, N_2 = $ dim$ M_2) = (6,3), (5,5), (8,2)$. The Kasner-like behaviour of the solutions near the singularity $t_s \to +0$ is considered ($t_s$ is synchronous time). The exceptional ("Milne-type") solutions are obtained for arbitrary $n$. For $n=2$ these solutions are attractors for other ones, when $t_s \to + \infty$. For dim $ M = 10, 11$ and $3 \leq n \leq 5$ certain two-parametric families of solutions are obtained from $n=2$ ones using "curvature-splitting" trick. In the case $n=2$, $(N_1, N_2)= (6,3)$ a family of non-singular solutions with the topology $R^7 \times M_2$ is found., Comment: 21 pages, LaTex. 5 figures are available upon request (hard copy). Submitted to Classical and Quantum Gravity

A multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of a multicomponent perfect fluid is considered. When vectors corresponding to the equations of state of the components are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrated and a Kasner-like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda-like system connected with some Lie algebra. PACS numbers: 04.20.J, 04.60.+n, 03.65.Ge

Vacuum cosmological models are considered in the context of a multidimensional theory of gravity with integrable Weyl geometry. A family of exact solutions with a chain of internal spaces is obtained. Models with one internal space are considered in more detail; nonsingular models are selected.

We discuss the dynamics of inhomogeneities of metric in a general solution to D-dimensional Einstein equation with matter sources satisfying the inequality ∊ ≥ p in the vicinity of a cosmological singularity. It is shown that a local behavior of a part of metric functions near the singularity is described by a billiard on a space of a constant negative curvature. If D ≤ 10, the billiard has a finite volume and, consequently, it is a mixing one. It is shown for this case that statistical properties of inhomogeneities of metric admit a complete description. An invariant measure describing statistics of inhomogeneities is obtained and the role of a minimally-coupled scalar field in the dynamics of the inhomogeneities is also considered.

A comparative analysis is made of the most typical projects for experiments to measure the gravitational constant G and other gravitational interaction parameters utilizing artificial satellites, dating from 1967 and performed using state-of-the-art measurement technology.

The multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of multicomponent perfect fluid is considered. When the vectors corresponding to the equations of state of the components are orthogonal with respect to the minisuperspace metric, the Einstein equations are integrated and a Kasner‐like form of the solutions is presented. For special sets of parameters the cosmological model is reduced to the Euclidean Toda‐like system connected with some Lie algebra G. For G=A2 exact solutions are explicitly written. A certain family of wormhole solutions is also obtained.

The equations of multidimensional gravitation are examined for the case of axial symmetry. Exact solutions are obtained in the static and steady-state cases. Solutions that become spherically symmetric are identified.

The evolution of 4-dimensional and (4+D)-dimensional (D=1, 2) cosmological models based on the integrable Weyl geometry are considered numerically both for empty space-time and for scalar field with nonminimal coupling with gravity. In both cases nonsingular solutions exist only for the open exterior space and flat (with torus topology) interior space. It is shown that in the nonsingular case the scenario of dynamical dimension reduction is realized. Some characteristic features of the considered models and their possible generalizations are discussed.

Main stages and scientific results of K.P. Stanyukovich and also of his colleagues after 1989 in gravitation, cosmology and astrophysics are described both in four and arbitrary dimensions.

The dynamics of multidimensional cosmological models based on the Weyl integrable geometry are investigated by means of numerical methods. Models are considered in space and in the presence of matter, the latter modeled by an ideal liquid and a nonminimal scalar field. Sufficient conditions are obtained under which cosmological singularity is absent and the scenario of dynamic dimensional reduction is realized.

A project of the high-resolution magnetic analyzer MAVR is proposed. The analyzer will comprise new magnetic optical and detecting systems for separation and identification of reaction products in a wide range of masses (5-150) and charges (1-60). The magnetic optical system consists of the MSP-144 magnet and a doublet of quadrupole lenses. This will allow the solid angle of the spectrometer to be increased by an order of magnitude up to 30 msr. The magnetic analyzer will have a high momentum resolution (10-4) and high focal-plane dispersion (1.9 m). It will allow products of nuclear reactions at energies up to 30 MeV/nucleon to be detected with the charge resolution ~1/60. Implementation of the project is divided into two stages: conversion of the magnetic analyzer proper and construction of the nuclear reaction products identification system. The MULTI detecting system is being developed for the MAVR magnetic analyzer to allow detection of nuclear reaction products and their identification by charge Q, atomic number Z, and mass A with a high absolute accuracy. The identification will be performed by measuring the energy loss (ΔE), time of flight (TOF), and total kinetic energy (TKE) of reaction products. The particle trajectories in the analyzer will also be determined using the drift chamber developed jointly with GANIL. The MAVR analyzer will operate in both primary beams of heavy ions and beams of radioactive nuclei produced by the U400 - U400M acceleration complex. It will also be used for measuring energy spectra of nuclear reaction products and as an energy monochromator.

Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in D-dimensional gravity with a chain of n Ricci-flat internal spaces are considered. Their special cases and properties are discussed, in particular, the predicted Coulomb law violation. A family of multidimensional dilatonic black-hole solutions is singled out, depending on two integration constants (related to black hole mass and charge) and three free parameters of the theory (the physical and internal space dimensions and the dilaton coupling constant). The black-hole solutions are shown to be stable under small perturbations preserving spherical symmetry, while other solutions, possessing naked singularities, turn out to be catastrophically unstable.

The $n$-time generalization of Schwarzschild solution is considered. The equations of geodesics for the metric are integrated. The multitemporal analogues of Newton laws for the extended objects described by the solution are suggested. The scalar-vacuum generalization of the solution is also presented., 7 pages

Two families of exact solutions in multidimensional gravity with scalar fields and fields of forms are considered: fluxbrane and black brane ones. A brief overview of main results on billiard approach for cosmological-type models with branes is also presented.

Magnetic spectrometers of charged nuclear reaction products, properly matched with an accelerator beam line, have become a very effective setup for the performance of precise nuclear experiments involving ultrasensitive accelerator-based mass spectrometry and investigation of rare events, as well as experiments with radioactive nuclear beams. The procedure for increasing the efficiency and resolution of the available magnetic spectrometer at the Flerov Laboratory of Nuclear Reactions by a few orders of magnitude by means of its matching with the beam line is described.

Recently two methods of measuring the gravitational constant G, possible equivalence principle violation (measured by the Eötvös parameter η) and the hypothetic 5th force parameters α and λ on board a drag-free Earth’s satellite were suggested: SEE (Satellite Energy Exchange) and LPH (Libration Point Hitting). These methods are developed and compared. Various particle trajectories near a heavy ball are studied numerically and analytically. Some basic sources of error are analysed. The G measurement procedure is modelled by noise insertion to a “true” trajectory. It is concluded that the presense knowledge of G, α (for λ≥1 m) and η can be improved by at least two orders of magnitude.

A simulation is described for measuring the newtonian gravitational constant G in the SEE space experiment. Two methods are examined for estimating G: the two-point method and the integral one. When the two-point method is used, to provide an error not more than ΔG/G ≈ 1·10−6 requires path measurements to be performed with an error of not more than 1·10−8 m=λ/50 (λ is the green line wavelength). In the integral method, the same error in estimating G is attained with an error of measurement different by two orders of magnitude, 1·10−6 m.

Problems in fundamental metrology associated with variations in constants and the planned transition to new definitions of SI units based on fixed values of the fundamental physical constants are examined. It is pointed out that all the necessary conditions for such a transition have not yet been satisfied.

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. 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 with intersecting composite branes (e.g., solutions with harmonic functions and black brane ones) with intersection rules related to non-singular Kac-Moody (KM) algebras (e.g. hyperbolic ones) are considered. Some examples of black brane solutions are presented, e.g., those corresponding to hyperbolic KM algebras: H_2(q,q) (q > 2), HA_2^(1) = A_2^{++} and to the Lorentzian KM algebra P_{10}., 16 pages, Latex

Errors affecting the assessment of the attainable accuracy of measurement of Newton's gravitational constant in an experiment performed to observe the relative motion of two bodies housed in a drift-free artificial earth satellite are investigated with a view toward finding a realistic theoretical model.

The results of numerical modeling of the trajectories of motion of a light body (a “particle”) with respect to a heavier body in the orbit of an artificial satellite are presented [1]. Plane circular and elliptic orbits of the heavy body are considered, ignoring the nonsphericity of the gravitational field of the earth, and also plane circular equatorial orbits taking the quadrupole moment of the earth into account. The sensitivity of the trajectories to small variations of the initial conditions and values of the parameters of the gravitational interaction is investigated. It is shown that for the space experiment carried out in [2] to be successful for determining the gravitational constant G and the parameters of the five-force, and to check the principle of equivalence at large distances, the theoretical model of the motion of a “particle/rd must take into account all the perturbations which lead to a displacement of the trajectories of more than 10−4 mm.

We present a new method for the determination of the gravitational constant based on the relative motion of two bodies located at an orbit free of commercial earth satellites, and a probe body located near a libration point. Calculations show a potential for increased accuracy in the determination of G by two orders of magnitude.

An analysis is presented of a space experiment whose purpose is to enhance the accuracy of measurement of the gravitational constant G, improve the estimates of the fifth force parameters α and λ,and finally to verify the equivalence principle. The experiment involves exact measurements of the trajectories of a light body relative to a heavy body on a drag-free Earth satellite. Estimations of the possible effect of various factors on the relative motion trajectory are made. The equations of relative motion are derived for various types of satellite orbits. Some preliminary estimates of the accuracy of the measurements are presented which show that the experiment proposed seems to hold promise.

A generalization of the Tangherlini solution for the case of n internal Ricci-flat spaces is obtained. It is shown that in the (2+d)-dimensional section a horizon exists only in the trivial case when the internal-space factors are constant. The p-adic analog of the solution is also considered., 6 pages, Latex

Main problems of modern physics, gravitation, cosmology and fundamental constants in particular are discussed. Exact solutions with an exponential and power‐law behaviors of scale factors in various models (with perfect fluids, branes) are considered. The metric is defined on the manifold containing a product of several n+1 Ricci‐flat factor spaces. Solutions with accelerated expansion of our 3‐space M0 and a small enough variation of the effective gravitational constant G consistent with present observational and experimental data are given.

We consider the set of gravitational and unified field theories that predict the deviation on Newton's law. The main attention is paid to mechanisms of new forces origin and particles which can be regarded as the mediators of new type of interaction. The all known to us theories are divided into eight classes and relation and discrepancy between them are discussed

A multidimensional cosmological type model with 1-component anisotropic fluid is considered. An exact solution is obtained. This solution is defined on a product manifold containing n Ricci-flat factor spaces. We singled out a special solution governed by the function cosh. It is shown that this special solution has Kasner-like asymptotics in the limits \tau \to + 0 and \tau \to + \infty, where \tau is a synchronous time variable. A relation between two sets of Kasner parameters \alpha_{\infty} and \alpha_{0} is found. This formula (of "scattering law") is coinciding with that obtained earlier for the S-brane solution (when scalar fields are absent)., Comment: 23 pages, 1 figure, Latex

A multidimensional gravitational model containing scalar fields and antisymmetric forms is considered. The manifold is chosen in the form $M = M_0 \times M_1 \times \cdots \times M_n$, where $M_i$ are Einstein spaces ($i \geq 1$). The sigma-model approach and exact solutions with intersecting composite branes (e.g. solutions with harmonic functions, $S$-brane and black brane ones) with intersection rules related to non-singular Kac-Moody (KM) algebras (e.g. hyperbolic ones) are reviewed. Some examples of solutions, e.g. corresponding to hyperbolic KM algebras: $H_2(q,q)$, $AE_3$, $HA_2^{(1)}$, $E_{10}$ and Lorentzian KM algebra $P_{10}$ are presented.

Electric S-brane solutions with two non-composite electric branes and a set of l scalar fields are considered. The intersection rules for branes correspond to Lie algebras A_2, C_2 and G_2. The solutions contain five factor spaces. One of them, M_0, is interpreted as our 3-dimensional space. It is shown that there exists a time interval where accelerated expansion of our 3-dimensional space is compatible with a small enough variation of the effective gravitational constant G(\tau). This interval contains \tau_0, a point of minimum of the function G(\tau). A special solution with two phantom scalar fields is analyzed and it is shown that in the vicinity of the point \tau_0 the time variation of G(\tau) (calculated in the linear approximation) decreases in the sequence of Lie algebras A_2, C_2 and G_2., Comment: 13 pages, LaTex, no figures

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 Mi in the presence of a one‐component perfect fluid. The pressures in all spaces are proportional to the density: pi = wiρ, i = 0,…,n. Solutions with accelerated expansion of our 3‐space M0 and a small enough variation of the gravitational constant G are found.A family of generalized non‐singular 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. The solution possess exponential behaviour of scale factors. These solutions contain a sub‐family 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.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 Mi in the presence of a one‐component perfect fluid. The pressures in all spaces are proportional to the density: pi = wiρ, i = 0,…,n. Solutions with accelerated expansion of our 3‐space M0 and a small enough variation of the gravitational constant G are found.A family of generalized non‐singular 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. The solution possess exponential behaviour of scale factors. These solutions contain a sub‐family 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.

According to the controversial results of recent experiments for fifth force, we present a classification of all possible types of theories leading to non-Newtonian forces. The theoretical analysis shows that if the interaction potential differs from the Newton's law the interactions of macro- and micro-bodies are in general distinguishable. The calculation also shows that Long's result can be improved by several orders if the new method proposed is used.

A generalization of the solution of Tangherlini [1] to the case of internal Ricci plane spaces is obtained. It is shown that a horizon exists in the (2 + d)-dimensional section only in the trivial case where the scale factors of the internal spaces are constant. The p-adic analog of the solution is considered.

The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested.

The integration procedure for multidimensional cosmological models with multicomponent perfect fluid in spaces of constant curvature is developed. Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done. Some known solutions are singled out from those obtained. The existence of the wormholes is proved.

Some methods for the determination and the most precise values of constants of an extended Standard Model, which include the gravitation interaction and massive neutrinos, are presented. Accuracies of constants at different energy scales are compared and the possible manifestations of temporal variations of constants are considered. Theoretical estimations and obtained experimental bounds of variations are listed, that is important as for search of SM generalizations as to account for possible influence on metrological characteristics of measurement standards., Comment: 15 pages

We consider multidimensional gravity with a Lagrangian containing the Ricci tensor squared and the Kretschmann invariant. In a Kaluza-Klein approach with a single compact extra space of arbitrary dimension, with the aid of a slow-change approximation (as compared with the Planck scale), we build a class of spatially flat cosmological models in which both the observed scale factor $a(\tau)$ and the extra-dimensional one, $b(\tau)$, grow exponentially at large times, but $b(\tau)$ grows slowly enough to admit variations of the effective gravitational constant $G$ within observational limits. Such models predict a drastic change in the physical laws of our Universe in the remote future due to further growth of the extra dimensions., Comment: 5 pages, to be published in Grav. Cosmol

A short overview of the billiard approach for cosmological-type models with n Einstein factor-spaces is presented. We start with the billiard representation for pseudo-Euclidean Toda-like systems of cosmological origin. Then we consider cosmological model with multicomponent "perfect-fluid" and cosmological-type model with composite branes. The second one describes cosmological and spherically-symmetric configurations in a theory with scalar fields and fields of forms. The conditions for appearance of asymptotical Kasner-like and oscillating behaviors in the limit \tau \to +0 and \tau \to + \infty (where \tau is a "synchronous-type" variable) are formulated (e.g. in terms of inequalities on Kasner parameters). Examples of billiards related to the hyperbolic Kac-Moody algebras E_{10}, AE_3 and A_{1,II} are given., Comment: 18 pages, Latex, based on plenary report at RUSGRAV-13 (23-28 June, 2008, PFUR, Moscow)

We prove that Gibbons-Maeda reduction of two-component cosmology to the Toda lattice can not be generalyzed for n-component case.

A multidimensional cosmological model with scalar and form fields [1-4] is studied. An exact S-brane solution (either electric or magnetic) in a model with l scalar fields and one antisymmetric form of rank m > 1 is considered. This solution is defined on a product manifold containing n Ricci-flat factor spaces M_1, ..., M_n. In the case when the kinetic term for scalar fields is positive definite we singled out a special solution governed by the function cosh. It is shown that this special solution has Kasner-like asymptotics in the limits \tau \to + 0 and \tau \to + \infty, where \tau is a synchronous time variable. A relation between two sets of Kasner parameters \alpha_{\infty} and \alpha_0 is found. This relation, named as ``scattering law'' (SL) formula, is coinciding with the ``collision law'' (CL) formula obtained previously in [5] in a context of a billiard description of S-brane solutions near the singularity. A geometric sense of SL formula is clarified: it is shown that SL transformation is a map of a ``shadow'' part of the Kasner sphere S^{N-2} (N = n+l) onto ``illuminated'' part. This map is just a (generalized) inversion with respect to a point v located outside the Kasner sphere S^{N-2}. The shadow and illuminated parts of the Kasner sphere are defined with respect to a point-like source of light located at v. Explicit formulae for SL transformations corresponding to SM2- and SM5-brane solutions in 11-dimensional supergravity are presented., Comment: 21 pages, Latex, minor corrections

A scheme for flattening of the ion density distribution on a target is considered. The Xe ion beam extracted from a cyclotron has the following parameters: mass-to-charge ratio is 4.4, the kinetic energy is 4.2 MeV per nucleon, the beam current is 1 muA and the beam emittance is equal to 40 pi mm mrad. The ion beam line consists of quadrupoles doublet and octupole lens. After passing through two quadrupoles the ion beam has large horizontal and small vertical dimensions. After that the octupole makes the ion beam density distribution on the target uniform withing the necessary demands. The geometry of the beam line, the quadrupole and octupole lens parameters are found during simulation. The simulated final beam density distribution on the target is also given.

Main results in obtaining exact solutions for multidimensional models and their application to solving main problems of modern cosmology and black hole physics are described. Some new results on composite fluxbrane and S-brane solutions for a wide class of intersection rules are presented. These solutions are defined on a product manifold R* x M1 x ... x Mn which contains n Ricci-flat spaces M1,...,Mn with 1-dimensional R* and M1. They are defined 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 C2 and G2 are obtained. In these cases the functions Hs(z), s = 1, 2, are polynomials of degrees: (3, 4) and (6, 10), respectively, in agreement with a conjecture suggested earlier. Examples of simple S-brane solutions describing an accelerated expansion of a certain factor-space are given explicitely.

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, Corrected typos, published in Phys. Rev. D72, 103511 (2005)

The discrete spectrum solutions corresponding to dually-charged mesoatom on the space of constant negative curvature are obtained. The discrete spectrum of energies is finite and vanishes, when the magnetic charge of the nucleus exceeds the critical value., 15 pages, LaTex