Noether Symmetry Study in General Scalar Tensor Theory

We present the gravitational coupling function and potential function in a General Scalar Tensor Theory from Noether symmetry approach. Some exact cosmological solutions are presented in the spatially flat, homogeneous and isotropic background. The solutions are exponentially expanding without any graceful exit from inflation. Also the solutions asymptotically reduce to Einstein's theory with finite value of the coupling function supporting the earlier claim of Santiago et al. Further it is shown that in a particular case the effective Newtonian constant is determined by the effective potential of the scalar field.     

Generalized Exact Cosmologies with Interacting Yang-Mills and Nonlinear Scalar Fields

It has been shown that the set of the Einstein-Yang-Mills equations and the nonlinear scalar field have generalized solutions with a homogeneous scalar field, which interacts with the YM field in the Friedmann Universe.     

Evolution of Dynamical Coupling in Scalar Tensor Theory from Noether Symmetry

We present the gravitational coupling function () in the vacuum scalar-tensor theory as allowed by the Noether symmetry. We also obtain some exact cosmological solutions in the spatially homogeneous and isotropic background thereby showing that the attractor mechanism is not effective enough to reduce the theory to Einstein theory. It is observed that, asymptotically, the scalar tensor theory goes over to Einstein theory with a finite value of . This work thus supports earlier works in this direction.     

A Class of Renormalization Group Invariant Scalar Field Cosmologies

We present a class of scalar field cosmologies with a dynamically evolving Newton parameter G and cosmological term . In particular, we discuss a class of solutions which are consistent with a renormalization group scaling for G and near a fixed point. Moreover, we propose a modified action for gravity which includes the effective running of G and near the fixed point. A proper understanding of the associated variational problem is obtained upon considering the four-dimensional gradient of the Newton parameter.     

Plane Symmetric Vacuum Bianchi Type-III Cosmological Model in Brans-Dicke Theory

We have obtained an exact solution of the vacuum Brans-Dicke (Phys. Rev. 124:925, 1961) field equations for the metric tensor of a spatially homogeneous and anisotropic model. Some physical properties of the model are also studied.     

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.     

An isotropic cosmological model in general scalar tensor theory

An isotropic homogeneous cosmological model with Robertson-Walker line element is studied in general scalar tensor theory where the parameterω is a function of the scalar field. The model consists of perfect fluid with the equation of statep=ερ. Exact solutions are obtained in Dicke’s conformally transformed units forε=1 andε=1/3 assuming a functional relationship betweenω and the scalar fieldφ. The properties are compared with vacuum models in this theory.     

Minimal Coupling Method and the Dissipative Scalar Field Theory

Quantum field theory of a damped vibrating string as the simplest dissipative scalar field is investigated by it's coupling to an infinite number of Klein–Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to the velocity is obtained for a special choice of coupling function and quantum dynamics for such a dissipative system is investigated. Some kinematical relations is calculated by tracing out the environment degrees of freedom. The rate of energy flowing between the system and it's environment is obtained.     

Masses and Widths of Light Scalar Mesons in Chiral Perturbation Theory

Based on the diquark model, we assume that the light scalar mesons are q^2q^-2 states rather than qq^-. The chiral effective Lagrangian for the light scalar meson is constructed, and the mass relations are obtained： the isotriplet （a0） and the isosinglet （f0） are the heaviest and are degenerate, the isodoublets （κ） are heavier and the other isosinglet （σ） is the lightest; and 2Mκ^2 = Mα0^2＋ Mσ^2. Using experimental value for a0 and σ mass, we obtain Mκ=794 MeV, which is consistent with the experimental value. Then taking Г（a0^0 →ηπ^0） = 90 MeV and Г（f0→π^0π^0） = 20 MeV, we get the width of σ is： Г（σ0→π^＋π^-）= 150 MeV.     

The Chaotic Mixmaster and the Suppression of Chaos in Scalar–Tensor Cosmologies

We show that there is a threshold in energy for the onset of chaos in cosmology for the Universe described as a dynamical system derived from the Einstein equations of General Relativity (GR). In the case of the mixmaster model (homogeneous and anisotropic cosmology with a Bianchi IX metric), the chaos occurs precisely at the prescribed necessary value H _vac=0 of the GR for the energy of the Universe while the system is found to be regular for H<0 and chaotic for H>0 with respect to its pure vacuum part. In the case of generalized scalar tensor theories within the Bianchi IX model, we show using the ADM formalism and a conformal transformation that the energy of the dynamical system as compared to vacuum lies below the zero energy threshold. The system is thus not exhibiting chaos and the conclusion still holds in the presence of ordinary matter as well. The suppression of chaos occurs in a similar way for stiff matter alone.     

Inconsistencies of the U(1) Theory of Electrodynamics: Stress Energy Momentum Tensor

The internal gauge space of electrodynamics considered as a U(1) gauge field theory is a scalar. This leads to the result that in free space, and for plane waves, the Poynting vector and energy vanish. This result is consistent with the fact that U(1) gauge field theory results in a null third Stokes parameter, meaning again that the field energy vanishes in free space. A self consistent definition of the stress energy momentum tensor is obtained with a Yang Mills theory applied with an O(3) symmetry internal gauge space. This theory produces the third Stokes parameter self consistently in terms of the self-dual Evans-Vigier fields B(3).     

Letter: The Real Scalar Field in Schwarzschild-de Sitter Spacetime

In this paper, the real scalar field equation in Schwarzschild-de Sitter spacetime is solved numerically with high precision. A method called polynomial approximation is introduced to derive the relation between the tortoise coordinate x and the radius r. This method is different from the tangent approximation [1] and leads to more accurate results. The Nariai black hole is then discussed in details. We find that the wave function is harmonic only near the horizons as I. Brevik and B. Simonsen [1] found. However the wave function is not harmonic in the region of the potential peak, with amplitude increasing instead. Furthermore, we also find that, when the cosmological constant decreases, the potential peak increases, and the maximum wave amplitude increases.     

Cosmological Evolution of a Ghost Scalar Field

We consider a scalar field with a negative kinetic term minimally coupled to gravity. We obtain an exact non-static spherically symmetric solution which describes a wormhole in a cosmological setting. The wormhole is shown to connect two homogeneous spatially flat universes expanding with acceleration. Depending on the wormhole's mass parameter m the acceleration can be constant (the de Sitter case) or infinitely growing.     

Inflationary solutions in general scalar tensor theory of gravitation

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.     

Some Bianchi Type Cosmological Models in Bimetric Theory

It is shown that anisotropic spatially homogeneous Bianchi types III and VI₀ cosmological models do not exist in Rosen's [N. Rosen: Gen. Rel. Grav. 4 (1973) 435] bimetric theory when the source of gravitation is governed by either perfect fluid or mesonic perfect fluid. Hence the vacuum models are constructed.     

Plane-Symmetric Solitons of Spinor and Scalar Fields

We consider a system of nonlinear spinor and scalar fields with minimal coupling in general relativity. The nonlinearity in the spinor field Lagrangian is given by an arbitrary function of the invariants generated from the bilinear spinor forms S= and P=i⁵; the scalar Lagrangian is chosen as an arbitrary function of the scalar invariant = _,^,, that becomes linear at 0. The spinor and the scalar fields in question interact with each other by means of a gravitational field which is given by a plane-symmetric metric. Exact plane-symmetric solutions to the gravitational, spinor and scalar field equations have been obtained. Role of gravitational field in the formation of the field configurations with limited total energy, spin and charge has been investigated. Influence of the change of the sign of energy density of the spinor and scalar fields on the properties of the configurations obtained has been examined. It has been established that under the change of the sign of the scalar field energy density the system in question can be realized physically iff the scalar charge does not exceed some critical value. In case of spinor field no such restriction on its parameter occurs. In general it has been shown that the choice of spinor field nonlinearity can lead to the elimination of scalar field contribution to the metric functions, but leaving its contribution to the total energy unaltered.     

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.     

Dynamical Study of the Singularities of Gravity in the Presence of Nonminimally Coupled Scalar Fields

We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action

Scalar Soliton in Newtonian Gravity Modelling Dark Matter Halos

Within standard Newtonian gravity, galactic dark matter is modelled by a scalar field in order to effectively modify Kepler's law. In particular, we show that a solvable toy model with a self-interaction U() borrowed from non-topological solitons produces already qualitatively correct rotation curves. Although relativistic effects in the halo are very small, we indicate corrections arising from the general relativistic formulation.     

Horizon-less Spherically Symmetric Vacuum-Solutions in a Higgs Scalar-Tensor Theory of Gravity

The exact static and spherically symmetric solutions of the vacuum field equations for a Higgs Scalar-Tensor theory (HSTT) are derived in Schwarzschild coordinates. It is shown that in general there exists no Schwarzschild horizon and that the fields are only singular (as naked singularity) at the center (i.e. for the case of a point-particle). However, the Schwarzschild solution as in usual general relativity (GR) is obtained for the vanishing limit of Higgs field excitations.