Dilaton stabilization in string cosmology. II

A mechanism for stabilization of the dilaton field within the framework of low-energy string gravitation with loop corrections to the dilaton coupling function was proposed in the first part of this paper. The mechanism is based on the assumption that loop corrections generate a singular dilaton kinetic function for a certain value of the dilaton field. For a nortgravitational source with a constant barotropic index, the system of cosmological equations reduces to an autonomous, third-order dynamical system. The behavior of the general solution in the vicinity of singularities of the dilaton coupling function is investigated by methods of the qualitative theory of dynamical systems for different values of the singularity index. The conditions under which solutions with a constant dilaton are attractors for a general solution with a variable dilaton are determined. The evolution of models is considered, the corresponding phase diagrams are constructed, and the question of the effectiveness of dilaton stabilization is investigated. Translated from Astrofizika, Vol. 43, No. 2, pp. 313–324, April–June, 2000.     

Qualitative analysis of string cosmology with loop corrections. I

Homogeneous and Isotropic cosmological models of low-energy, string gravitation with loop corrections to the dilaton coupling functions are investigated by methods of the qualitative theory of dynamical systems. An ideal fluid with a barotropic equation of state is considered as the nongravitational source. In the general case of curved models, the cosmological equations are represented in the form of a third-order, autonomous, dynamical system. Phase portraits for different coupling functions are constructed for flat models. The asymptotic behavior of the general solution in limiting regions is investigated. The stabilization of the dilaton is analyzed using the Damour-Polyakov mechanism. Translated from Astrofizika, Vol. 42, No. 1, pp. 117–136, January–March, 1999.     

qualitative analysis of string cosmology with loop corrections. II

Homogeneous and Isotropic cosmological models of effective string theory with a curved space are investigated by the methods of the qualitative theory of dynamical systems. It is shown that for radiation-dominated models, tthe corresponding dynamical system can be integrated exactly for the general case of dilaton coupling functions. Models in the tree approximation with a two-dimensional phase space are considered separately. In the general case of loop corrections, all possible stationary points are found and their character is determined. The results are illustrated using a specific example. Various cases of fixing the dilaton within the framework of the Damour-Polyakov mechanism are considered. Translated from Astrofizika, Vol. 42, No. 2, pp. 295–310, April–June, 1999.     

Cosmological Evolution of String Effective Gravitation with a Dilaton Potential and Higher-Loop Corrections. I

Cosmological evolution is investigated within the framework of low-energy string gravitation with higher-loop corrections to the dilaton coupling functions in the presence of a dilaton potential and a nongravitational source. It is shown that for homogeneous and isotropic models with a flat space, the cosmological system of equations reduces to an autonomous, third-order, dynamical system. Subclasses of models with a constant dilaton, which provide the basis for various cosmological mechanisms of dilaton stabilization, are considered. A class of solutions is distinguished with asymptotic scaling behavior of the energy density of the dilaton field.     

Dilaton Stabilization in String Cosmology. III. Models with Curved Space

Within the framework of the mechanism of dilaton stabilization proposed in Part I of the present work, an analysis of homogeneous and isotropic cosmological models of low-energy string gravitation with loop corrections is continued. The behavior of models with curved space is investigated by methods of the qualitative theory of dynamical systems for different values of the singularity index of the dilaton kinetic function and the barotropic index of nongravitational matter. The conditions under which dilaton stabilization occurs as a result of cosmological expansion are determined, and the corresponding phase diagrams are constructed.     

On string cosmology with a dilaton potential. I

The problems of flat directions and supersymmetry breaking are fundamental problems that are still unsolved in the comparison of string theory with low-energy physics. A possible nonperturbative dilaton potential may play an important role in their solution. In the present paper we consider D-dimensional, low-energy, string cosmological models with a di/aton potential. Exact solutions are written for several simple potentials. The picture of cosmological evolution of a gravi-dilaton model is investigated by methods of the qualitative theory of dynamical systems for different cases of the behavior of the potential in the domain of strong coupling. Features of models having potentials that take negative values in certain ranges of values of the dilaton field are discussed. A specific mechanism of generation of a nonperturbative potential, based on gaugino condensation in the hidden sector of the gauge group, is considered. Translated from Astrofizika, Vol. 40, No. 2, pp. 233–251, April–June, 1997.     

On string cosmology with a dilaton potential. II

Investigations of string cosmology with a nonperturbative dilaton potential, begun in the first part of this work, are continued. The picture of cosmological evolution of an isotropic, gravi-dilaton model for different cases of the behavior of the potential in the region of strong coupling is analyzed by methods of the qualitative theory of dynamical systems. Features of models with potentials that take negative values in certain ranges of values of the dilaton field are discussed. A specific mechanism of generation of the nonperturbative potential, based on gaugino condensation in a hidden sector of the gauge group, is considered. Translated from Astrofizika, Vol. 40, No. 4, pp. 517–534, October-December, 1997.     

Black hole stability in multidimensional gravity theory

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 properties and special cases are discussed. 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 coordinate sphere, internal space dimensions, and the coupling constant). The behaviour of the solutions under small perturbations preserving spherical symmetry, is studied. It is shown that the black-hole solutions without a dilaton field are stable, while other solutions, possessing naked singularities, are catastrophically unstable.     

Gravitational field of a stationary circular cosmic string loop

Gravitational field of a stationary circular cosmic string loop has been studied in the context of full nonlinear Einstein's theory of gravity. It has been assumed that the radial and tangential stresses of the loop are equal to the energy density of the string loop. An exact solution for the system has been presented which has a singularity at a finite distance from the axis, but is regular for any other distances from the axis of the loop. This revised version was published online in July 2006 with corrections to the Cover Date.     

On string cosmology with loop corrections

Homogeneous cosmological models are investigated within the framework of low- energy string gravitation with loop corrections. Various conformai representations of the effective action are considered. Without specifying the correction functions in the Lagrangian, cosmological solutions are found with an arbitrary curvature and with dilaton fields, moduli fields, and Kalb- Ramond fields corresponding to a source with an extremely stiff equation of state. They generalize previously known solutions of the tree approximation. The behavior of the solutions in different asymptotic domains is investigated. Translated from Astrofizika, Vol. 41, No. 2, pp. 277–295, April-June, 1998.     

Chaplygin gas of Tachyon Nature Imposed by Noether Symmetry and constrained via H(z) data

An action of general form is proposed for a Universe containing matter, radiation and dark energy. The latter is interpreted as a tachyon field non-minimally coupled to the scalar curvature. The Palatini approach is used when varying the action so the connection is given by a more generic form. Both the self-interaction potential and the non-minimally coupling function are obtained by constraining the system to present invariability under global point transformation of the fields(Noether Symmetry). The only possible solution is shown to be that of minimal coupling and constant potential(Chaplygin gas). The behavior of the dynamical properties of the system is compared to recent observational data, which infers that the tachyon field must indeed be dynamical.     

Solving the graceful exit problem in superstring cosmology

We briefly review the status of the “graceful exit” problem in superstring cosmology and present a possible resolution. It is shown that there exists a solution to this problem in two-dimensional dilaton gravity provided quantum corrections are incorporated. This is similar to the recently proposed solution of Rey. However, unlike in his case, in our one-loop corrected model the graceful exit problem is solved for any finite number of massless scalar matter fields present in the theory.     

Inflationary Solutions for Higher Dimensional Anisotropic Cosmological Model in Scalar-Tensor Theory II

This is the second paper of the series where we have considered Brans-Dicke (B-D) theory as well as general scalar tensor theory of gravitation in higher dimensional space-time model in the false vacuum state. We have examined whether inflationary solutions are possible both for constant or variable coupling parameter ω. Also the nature of the scalar field and the coupling parameter are discussed in the asymptotic limit. This revised version was published online in July 2006 with corrections to the Cover Date.     

The effect of the dynamical parameters in the motion of the Galilean satellites of Jupiter

The construction of an analytical theory of the motion of the Galilean satellites of Jupiter requires that we keep track of the dynamical parameters, that is, the masses of the satellites, and the harmonic coefficients of the potential of the planet J₂ and J₄. This is realized here. But as in other theories the solution becomes partly numerical from the resolution of an autonomous system. The aim of this paper is to present a method to obtain developped solutions of this autonomous system. In these solutions the proper motions of the pericenters and nodes are obtained as short series developped in the neighbourhood of a numerical solution. We have used these results to obtain complementary terms in the general solution which give a complete representation of the motions with respect to the dynamical parameters.     

Accelerating universe with time variation of G and Λ

We study a gravitational model in which scale transformations play the key role in obtaining dynamical G and Λ. We take a non-scale invariant gravitational action with a cosmological constant and a gravitational coupling constant. Then, by a scale transformation, through a dilaton field, we obtain a new action containing cosmological and gravitational coupling terms which are dynamically dependent on the dilaton field with Higgs type potential. The vacuum expectation value of this dilaton field, through spontaneous symmetry breaking on the basis of anthropic principle, determines the time variations of G and Λ. The relevance of these time variations to the current acceleration of the universe, coincidence problem, Mach’s cosmological coincidence and those problems of standard cosmology addressed by inflationary models, are discussed. The current acceleration of the universe is shown to be a result of phase transition from radiation toward matter dominated eras. No real coincidence problem between matter and vacuum energy densities exists in this model and this apparent coincidence together with Mach’s cosmological coincidence are shown to be simple consequences of a new kind of scale factor dependence of the energy momentum density as ρ∼a ⁻⁴. This model also provides the possibility for a super fast expansion of the scale factor at very early universe by introducing exotic type matter like cosmic strings.     

Anisotropic Fluid Distribution in Bimetric Theory of Relativity

In this paper we have presented a procedure to obtain exact analytical solutions of field equations for spherically symmetric self-gravitating distribution of anisotropic matter in bimetric theory of gravitation. The solution agrees with the Einstein's general relativity for a physical system compared to the size of universe such as the solar system. This revised version was published online in July 2006 with corrections to the Cover Date.     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – I. Formulation of the equations

We present analytic solutions of Maxwell equations in the internal and external background space–time of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat space–time solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections resulting from the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections resulting from both the space–time curvature and the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.     

Nonperturbative corrections to the Kahler potential and the problem of dilaton stabilization

Friedmann-Robertson-Walker gravidilaton cosmological models with a dilaton potential generated by gaugino condensation and by nonperturbative corrections to the Kahler potential are analyzed within the framework of effective string gravitation. The question of dilaton stabilization by such potentials is investigated. It is shown that the existence of a range of dilaton values with a negative definite potential results in the possible existence of mixed expansion-contraction models with aflat space. The corresponding phase portraits are constructed for qualitatively different cases, illustrating the possibility of dilaton stabilization. Translated from Astrofizika, Vol. 42, No. 3, pp. 465–476, July–September, 1999.     

Statefinder diagnostic for dilaton dark energy

Statefinder diagnostic is a useful method which can differ one dark energy model from the others. The Statefinder pair {r,s} is algebraically related to the equation of state of dark energy and its first time derivative. We apply in this paper this method to the dilaton dark energy model based on Weyl-Scaled induced gravitational theory. We investigate the effect of the coupling between matter and dilaton when the potential of dilaton field is taken as the Mexican hat form. We find that the evolving trajectory of our model in the r?s diagram is quite different from those of other dark energy models.     

Axion-Dilaton Coupling and Gamma-Ray Bursts

Axions emitted in supernovae are interesting candidates to account for Gamma-Ray Bursts provided their energy can be effectively converted into electromagnetic energy elsewhere. We point out that this convertion may occur more efficiently if one considers the coupling between intermediate scale axions and the string theory dilaton along with the inclusion of string loops. This revised version was published online in July 2006 with corrections to the Cover Date.