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.     

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.     

Dilaton stabilization in string cosmology. I

A new mechanism is proposed for stabilization of the scalar dilaton field within the framework of lowenergy string gravitation with loop corrections to the dilaton coupling functions. It is based on the assumption that the loop corrections generate a kinetic dilaton function, which is singular for some finite value of the dilaton field. For a nongravitational source of the barotropic type, the system of equations describing the evolution of homogeneous and isotropic cosmological models is represented in the form of a thirdorder, autonomous, 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. It is shown that there is a class of solutions, different from solutions of the general theory of relativity, with a constant dilaton. The conditions under which these solutions are an attractor for a general solution with a variable dilaton are determined. Translated from Astrofizika, Vol. 43, No. 1, pp. 123-136, January–March, 2000.     

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.     

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.     

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 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.     

Viscous ΛCDM universe models

We explore flat ΛCDM models with bulk viscosity, and study the role of the bulk viscosity in the evolution of these universe models. The dynamical equations for these models are obtained and solved for some cases of bulk viscosity. We obtain differential equations for the Hubble parameter H and the energy density of dark matter ρ _m , for which we give analytical solutions for some cases and for the general case we give a numerical solution. Also we calculate the statefinder parameters for these models and display them in the s–r-plane.     

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.     

Bianchi Type-1 vacuum models in modified theory of general relativity

In this paper, the problem of spatially homogeneous and an isotropic Bianchi type-1 space time with perfect fluid distribution is considered in Barber's second theory of gravitation. To obtain determinate solutions, we have assumed the equation of statep= γρ, 0 ≤ γ ≤ 1. It is observed that the general fluid distribution degenerates isotropic vacuum model whenγ = 1 and Λ < 0. Further it is observed that the vacuum model obtained in case of γ = 0, ρ = 0 andΛ = 0, reduces to well known Kasner model in Einstein's theory. Some physical and geometrical aspects of the models together with singularities in the models are also discussed This revised version was published online in July 2006 with corrections to the Cover Date.     

On Einstein–Rosen Cosmic Strings in a Scalar Tensor Theory of Gravitation

Explicit field equations of a scalar tensor theory of gravitation proposed by Saez and Ballester are obtained with the aid of Einstein–Rosen cylindrically symmetric metric in the presence of cosmic string source. The field equations being highly non–linear static and non–static cases have been considered separately. It is observed that in the static case the geometric strings do not exist while in the non–static case cosmological model does not exist in this theory.     

Multi-dimensional cosmological models in effective string gravitation. I

We consider multi-dimensional cosmological models in the low-energy field theory of strings with a boson gravitational sector containing a metric, dilaton field, and antisymmetric Kalb-Ramon field. We study the conformal properties of the action and show that in the general conformal representation the theory is equivalent to a generalized scalar-tensor theory with a Lagrangian of nongravitating matter dependent on the dilaton. We find exact solutions of the flat homogeneous anisotropic model with structure R×M¹×...×Mⁿ and with equation of state p_i=a_i in the space Mⁱ. We discuss the picture of cosmological evolution in different conformal representations.Translated fromAstrofizika, Vol. 38, No. 2, 1995.     

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.     

String effective gravitation and extended inflation

The low-energy string gravitation is investigated for the case of reduction with a variable (in string units) inner space. A flat cosmological model of the corresponding four-dimensional theory is constructed. The model equations are analyzed qualitatively for a potential-dominated scalar field as the source. It is demonstrated that an extended inflation stage with one purely scalar dilaton field is possible here, in contrast with the case of a constant inner space. The pattern of cosmological evolution in various conformal representations is discussed.Translated from Astrofizika, Vol. 38, No. 1, pp. 99–119, January–March, 1995.     

Variant of the bimetric theory of gravitation. I. Parameterized post-newtonian formalism

A bimetric theory of gravitation with a Lagrangian that is quadratic with respect to “intensities” is considered. All the post-Newtonian parameters are determined and it is shown that they coincide with the respective parameters of the general theory of relativity. Translated from Astrofizika, Vol. 43, No. 2, pp. 303-312, April–June, 2000.     

Absorption probability and dynamical evolution of scalar field with nonminimal derivative coupling in Garfinkle-Horowitz-Strominger dilaton spacetime

In Garfinkle-Horowitz-Strominger dilaton spacetime, we study the property of coupling Scalar field with coupling term R∂ ^μ ψ∂ _μ ψ, and the results show that as the charge term ξ increases, the absorption probability at weak coupling case decreases, but the absorption probability is enhanced at strong coupling case. Next, we investigate the dynamical evolution of coupling field in this spacetime, and we find that the effect of coupling field leads to the damping of the quasinormal modes at a slightly rapider rate.     

Nonlinear dynamical analysis for displaced orbits above a planet

Nonlinear dynamical analysis and the control problem for a displaced orbit above a planet are discussed. It is indicated that there are two equilibria for the system, one hyperbolic (saddle) and one elliptic (center), except for the degenerate h _z ^max, a saddle-node bifurcation point. Motions near the equilibria for the nonresonance case are investigated by means of the Birkhoff normal form and dynamical system techniques. The Kolmogorov–Arnold–Moser (KAM) torus filled with quasiperiodic trajectories is measured in the τ ₁ and τ ₂ directions, and a rough algorithm for calculating τ ₁ and τ ₂ is proposed. A general iterative algorithm to generate periodic Lyapunov orbits is also presented. Transitions in the neck region are demonstrated, respectively, in the nonresonance, resonance, and degradation cases. One of the important contributions of the paper is to derive necessary and sufficiency conditions for stability of the motion near the equilibria. Another contribution is to demonstrate numerically that the critical KAM torus of nontransition is filled with the (1,1)-homoclinic orbits of the Lyapunov orbit.     

Theory of relaxation of pulsar angular velocity within the framework of the general theory of relativity

The dynamics of the rotation of a two-component system in a neutron star is considered within the framework of the general theory of relativity. Equations for the angular velocities of the normal and superfluid components are obtained in the W approximation. It is shown that the solutions of these equations can describe the relaxation of pulsar angular velocity after a glitch. Translated from Astrofizika, Vol. 42, No. 1, pp. 89–100, January–March, 1999.