Effective Action for Scalar Fields in Two-Dimensional Gravity

We consider a general two-dimensional gravity model minimally or nonminimally coupled to a scalar field. The canonical form of the model is elucidated, and a general solution of the equations of motion in the massless case is reviewed. In the presence of a scalar field all geometric fields (zweibein and Lorentz connection) are excluded from the model by solving exactly their Hamiltonian equations of motion. In this way the effective equations of motion and the corresponding effective action for a scalar field are obtained. It is written in a Minkowskian space-time and does not include any geometric variables. The effective action arises as a boundary term and is nontrivial both for open and closed universes. The reason is that unphysical degrees of freedom cannot be compactly supported because they must satisfy the constraint equation. As an example we consider spherically reduced gravity minimally coupled to a massless scalar field. The effective action is used to reproduce the Fisher and Roberts solutions.     

Letter: An Exact Solution for the Fluctuations of an FRW Cosmology with n Scalar Fields, for an Arbitrary Potential

In this work we rigorously study the fluctuations in FRW models coupled with n neutral scalar fields, minimally coupled to the gravitational field. We find the exact solutions and the asymptotic behavior for the fluctuation around the critical point of the background for an arbitrary potential.     

Late-time acceleration and phantom divide line crossing with?non-minimal coupling and Lorentz-invariance violation

We consider two alternative dark-energy models: a Lorentz-invariance preserving model with a non-minimally coupled scalar field and a Lorentz-invariance violating model with a minimally coupled scalar field. We study accelerated expansion and the dynamics of the equation of state parameter in these scenarios. While a minimally coupled scalar field does not have the capability to be a successful dark-energy candidate with line crossing of the cosmological constant, a non-minimally coupled scalar field in the presence of Lorentz invariance or a minimally coupled scalar field with Lorentz-invariance violation have this capability. In the latter case, accelerated expansion and phantom divide line crossing are the results of the interactive nature of this Lorentz-violating scenario.     

Exact Solutions for the Fluctuations in a Flat FRW Universe Coupled to a Scalar Field

Some exact solutions for the small-first-order perturbations of an FRW metric minimally coupled to a neutral massive scalar field are presented.     

Conformally related metrics and Lagrangians and their physical interpretation in cosmology

Conformally related metrics and Lagrangians are considered in the context of scalar–tensor gravity cosmology. After the discussion of the problem, we pose a lemma in which we show that the field equations of two conformally related Lagrangians are also conformally related if and only if the corresponding Hamiltonian vanishes. Then we prove that to every non-minimally coupled scalar field, we may associate a unique minimally coupled scalar field in a conformally related space with an appropriate potential. The latter result implies that the field equations of a non-minimally coupled scalar field are the same at the conformal level with the field equations of the minimally coupled scalar field. This fact is relevant in order to select physical variables among conformally equivalent systems. Finally, we find that the above propositions can be extended to a general Riemannian space of $n$ n -dimensions.     

The Cauchy problem for coupled Yang-Mills and scalar fields in the temporal gauge

We study the Cauchy problem for minimally coupled classical Yang-Mills and scalar fields inn+1 dimensional space-time in the temporal gauge. We prove the existence and uniqueness of solutions for small time intervals and for anyn. We then develop a general theory of solutions in local spaces and extend the previous local (in time) results to this more general setting. In space-time dimensions two and three, we prove the existence of global (in time) solutions by the method of a priori estimates, both in global and local spaces. In space-time dimension four, our estimates yield only partial results on the global existence problem.Laboratoire associé au Centre National de la Recherche Scientifique     

Isotropisation of flat homogeneous Bianchi type <Emphasis Type="Italic">I</Emphasis> model with a non minimally coupled and massive scalar field

In previous works, we studied the isotropisation of some Bianchi class A models with a minimally coupled scalar field. In this paper we extend these results, in the special case of a Bianchi type I model, to a non minimally coupled scalar field. The Universe isotropisation for the Brans-Dicke and low energy string theories are studied.     

The role of a scalar-field potential in the Einstein-Kartan cosmology

Flat space isotropic cosmological models including a nonminimally coupled scalar field with a nonlinear potential are studied within the Einstein-Kartan theory. The exact general solutions for various types of scalar fields are derived for arbitrary values of the coupling constant ξ. It is shown that both singular and nonsingular models are feasible. The spectral values of ξ and restriction on ξ are found for the foregoing solutions. The cosmological consequence of taking into account the scalar-field potential is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 67–71, June, 2006.     

Static Plane-Symmetric Nonlinear Spinor and Scalar Fields in GR

We consider a system of minimally coupled nonlinear spinor and scalar fields within the scope of a plane-symmetric gravitational field. The gravitational field plays crucial role in the formation of soliton-like solutions, i.e., solutions with limited total energy, spin, and charge. The change of the sign of the scalar field energy density of the system in question realizes physically if and only if the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. The choice of spinor field nonlinearity leads to the elimination of scalar field contribution to the metric functions, but leaves its contribution to the total energy unaltered. The spinor field is more sensitive to the gravitational field than the scalar field.     

Qualitative Properties of Scalar-Tensor Theories of Gravity

The qualitative properties of spatiallyhomogeneous stiff perfect fluid and minimally coupledmassless scalar field models within general relativityare discussed. Consequently, by exploiting the formal equivalence under conformal transformations and field redefinitions of certain classes of theories ofgravity, the asymptotic properties of spatiallyhomogeneous models in a class of scalar-tensor theories of gravity that includes the Brans-Dicke theory can be determined. For example, exact solutions are presented, which are analogues of the general relativistic Jacobs stiff perfect fluid solutions andvacuum plane wave solutions, which act as past andfuture attractors in the class of spatially homogeneousmodels in Brans-Dicke theory.     

Spherically symmetric configurations of General Relativity in presence of scalar fields: separation of circular orbits

We show that the test body stable circular orbits around the spherically symmetric black hole (BH) configuration can form disjoint structures in presence of a minimally coupled nonlinear scalar field. General conditions for the disjoint structures to exist are formulated. To present examples we construct a two-parametric family of exact solutions to Einstein equations with scalar fields for appropriate self-interaction potentials. For different values of the family parameters the solutions describe either BH or naked singularity (NS). We found numerically regions of the parameters when there exist two disjoint regions of stable circular orbits; such nonconnected structures indeed can exist in case of both BH and NS solutions.     

Quantization of Kantowski-Sachs Model and the Wave Function

In this paper, we consider Kantowski-Sachs (ks)minisuperspace model with a minimally coupled masslessscalar field. A canonical transformation is performed onthe phase space to simplify the scalar constraint.Then the quantization programme for this modelhas been developed using the standard general procedureby Ashtekar and co-workers. Finally, the wave functionfor this model has been evaluated in the pathintegral formalism.     

Coupling Parameters and the Form of the Potential via Noether Symmetry

We explore the conditions for the existence of Noether symmetries in the dynamics of FRW metric, non minimally coupled with a scalar field, in the most general situation, and with nonzero spatial curvature. When such symmetries are present we find a general exact solution for the Einstein equations. We also show that non Noether symmetries can be found. Finally, we present an extension of the procedure to the Kantowski-Sachs metric which is particularly interesting in the case of degenerate Lagrangian.     

Nonminimally coupled scalar field and perfect fluid in Einstein–Cartan cosmology

Exact general solutions to the Einstein–Cartan equations are obtained for spatially flat isotropic and homogeneous cosmologies with a nonminimally coupled scalar field and perfect fluid. Some effects of torsion are revealed by solving an analogous problem in general relativity. A comparative analysis of the cosmological models with and without perfect fluid is carried out in context of the Einstein–Cartan theory. The role of perfect fluid in the dynamics of models is discussed.     

The Countable Number of Models in the Cosmology with Nonminimal Coupling and Torsion

Cosmological models of flat space with a nonminimally coupled scalar field and ultrarelativistic gas are studied within the Einstein–Kartan theory. Exact general solutions are derived for two-component models and those containing only scalar field for an arbitrary coupling constant . It is shown that both singular and countable number of nonsingular models is possible depending on the type of scalar field and the sign of . The special values of and restrictions on are found for the above solutions. The role of relativistic gas in the evolution of models is revealed.     

Collapse of non-spherically symmetric scalar field distributions

In the present work the collapse scenario of some exact non-spherical models with a minimally coupled scalar field is studied. Scalar field collapse with planar as well as toroidal, cylindrical and pseudoplanar symmetries have been investigated. It is shown that the scalar field may have collapsing modes even if it has the equation of state corresponding to that of a dark energy.     

Kantowski-Sacks Bulk Viscous String Cosmological Models in the Presence of Zero-Mass Scalar Fields

The Kantowski-Sachs cosmological solutions of massive strings have been studied in the presence of zero-mass scalar field coupled with bulk viscosity. It is assumed that the coefficient of bulk viscosity is a power function of energy density of massive strings. Further we have considered the cosmological parameter as a function of cosmic time. We obtained the general solution of the field equations in polynomial and exponential forms respectively. The behaviors of these models are also discussed in the presence as well as in the absence of bulk.     

Euclidean Wormholes with Phantom Field and Phantom Field Accompanied by Perfect Fluid

We study the classical Euclidean wormhole solutions for the gravitational systems with minimally coupled pure Phantom field and minimally coupled Phantom field accompanied by perfect fluid. It is shown that such solutions do exist and then the general forms of the Phantom field potential are obtained for which there are classical Euclidean wormhole solutions.     

Scalar field cosmology in phase space

Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaître-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time quintessence eras. Focussing on the spatially flat case, we examine the geometrical structure of the phase space, locate the equilibrium points of the system (de Sitter spaces with a constant scalar field), study their stability through both a third-order perturbation analysis and Lyapunov functions, and discuss the late-time asymptotics. As we do not specify the scalar field’s origin or its potential, the results are independent of the high-energy model.     

Homogenization and isotropization of an inflationary cosmological model

A member of the class of anisotropic and inhomogeneous cosmological models constructed by Wainwright and Goode is investigated. It is shown to describe a universe containing a scalar field which is minimally coupled to gravitation and a positive cosmological constant. It is shown that this cosmological model evolves exponentially rapidly towards the homogeneous and isotropic de Sitter universe model.