Generalized de Sitter solution in multi-dimensional cosmology with static internal spaces

A multi-dimensional cosmological model with space-time consisting of n(n ≥ 2) Einstein spaces M_i is investigated in the presence of a cosmological constant λ and a homogeneous minimally coupled free scalar field. A generalized de Sitter solution was found for λ > 0 and a Ricci-flat external space for the case of static internal spaces with fine tuning of parameters.     

Kasner-like,inflationary and steady-state solutions in multi-dimensional cosmology

Multi-dimensional cosmological models with n(n > 1) Ricci-flat spaces and a scalar field are discussed classically and with respect to canonical quantization. These models are integrable. Two classes of solutions are obtained. One class of solutions generalizes the Kasner solutions. For special additional conditions we find another solution describing extended inflation connected with a constant volume of the whole multidimensional space (steady-state).     

Non-Existence Of <Emphasis Type="Italic">N</Emphasis>-Dimensional Static Plane Symmetric Solutions In Bimetric Relativity Theory

A problem of static plane symmetric metric in the perfect fluid, the mesonic massive scalar field and in their coupling is studied in Rosen’s (1973) bimetric theory of relativity. It was found that the matter field like either perfect fluid or mesonic massive scalar field or their coupling does not survive in bimetric theory of gravitation when the space–time is governed by n-dimensional static plane symmetric metric.     

Global stability analysis for scalar-tensor models

The phase space of a cosmological model with a scalar field coupled to curvature is discussed in detail for any value of the coupling constant ξ and any power law (ϕ²ⁿ) potential. The results obtained generalize previous studies with minimal coupling (ξ = 0) and quadratic or quartic potentials to the entire parameter space (ξ, n). In many cases one finds global attractors and inflationary trajectories, with or without the correct Friedmannian limit. If the coupling constant is positive, a forbidden region cuts out a large part of the phase space, while, if it is negative, escaping regions may occur. Semi-classical instability of vacuum states and singularity-free trajectories are also discussed.     

Some Bianchi type cosmological models in f(R) gravity

The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. In this context, we study the exact vacuum solutions of Bianchi type I, III and Kantowski-Sachs spacetimes in the metric version of f(R) gravity. The field equations are solved by taking expansion scalar θ proportional to shear scalar σ which gives A=B ⁿ , where A and B are the metric coefficients. The physical behavior of the solutions has been discussed using some physical quantities. Also, the function of the Ricci scalar is evaluated in each case.     

Tachyonic teleparallel dark energy

Teleparallel gravity is an equivalent formulation of general relativity in which instead of the Ricci scalar R, one uses the torsion scalar T for the Lagrangian density. Recently teleparallel dark energy has been proposed by Geng et al. (in Phys. Lett. B 704, 384, 2011). They have added quintessence scalar field, allowing also a non-minimal coupling with gravity in the Lagrangian of teleparallel gravity and found that such a non-minimally coupled quintessence theory has a richer structure than the same one in the frame work of general relativity. In the present work we are interested in tachyonic teleparallel dark energy in which scalar field is responsible for dark energy in the frame work of torsion gravity. We find that such a non-minimally coupled tachyon gravity can realize the crossing of the phantom divide line for the effective equation of state. Using the numerical calculations we display such a behavior of the model explicitly.     

Dark Matter from the inflaton field

We present a model where inflation and Dark Matter takes place via a single scalar field ?. Without introducing any new parameters we are able unify inflation and Dark Matter using a scalar field ? that accounts for inflation at an early epoch while it gives a Dark Matter WIMP particle at low energies. After inflation our universe must be reheated and we must have a long period of radiation dominated before the epoch of Dark Matter. Typically the inflaton decays while it oscillates around the minimum of its potential. If the inflaton decay is not complete or sufficient then the remaining energy density of the inflaton after reheating must be fine tuned to give the correct amount of Dark Matter. An essential feature here, is that Dark Matter-Inflaton particle is produced at low energies without fine tuning or new parameters. This process uses the same coupling g as for the inflaton decay. Once the field ? becomes non-relativistic it will decouple as any WIMP particle, since n_? is exponentially suppressed. The correct amount of Dark Matter determines the cross section and we have a constraint between the coupling g and the mass m_o of ?. The unification scheme we present here has four free parameters, two for the scalar potential V(?) given by the inflation parameter λ of the quartic term and the mass m_o. The other two parameters are the coupling g between the inflaton ? and a scalar filed φ and the coupling h between φ with standard model particles ψ or χ. These four parameters are already present in models of inflation and reheating process, without considering Dark Matter. Therefore, our unification scheme does not increase the number of parameters and it accomplishes the desired unification between the inflaton and Dark Matter for free.     

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.     

Phase transition in Schwarzschild-de Sitter spacetime

Using a static massive spherically symmetric scalar field coupled to gravity in the Schwarzschild-de Sitter (SdS) background, first we consider some asymptotic solutions near horizon and their local equations of state (E.O.S.) on them. We show that near cosmological and event horizons our scalar field behaves as a dust. At the next step near two pure de Sitter or Schwarzschild horizons we obtain a coupling dependent pressure to energy density ratio. In the case of a minimally coupling this ratio is ?1 which springs to the mind thermodynamical behavior of dark energy. If having a negative pressure behavior near these horizons we concluded that the coupling constant must be ξ<¼. Therefore we derive a new constraint on the value of our coupling ξ. These two different behaviors of unique matter in the distinct regions of spacetime at present era can be interpreted as a phase transition from dark matter to dark energy in the cosmic scales and construct a unified scenario.     

Formation of stars by implosion of a gas cloud

In the standard Friedmann cosmology the black-body radiation spectrum is usually taken (without explicit proof as far as we know) to have the same familiarT ⁴-form that it has in a flat space. With explicit use of the equation of motion of a quantized massless field propagating in a curved background Robertson-Walker metric we show (for the readily tractable scalar field case) that the assumption is in fact true for an open Universe. For a closed Universe, we find that there is an in principle modification to theT ⁴-law. Unfortunately, the correction turns out to be too small to be experimentally detectable. In passing, we also obtain a simple derivation for the cosmological red shift of frequencies.     

Cosmological scalar fields that mimic the ΛCDM cosmological model

We look for cosmologies with a scalar field (dark energy without cosmological constant), which mimic the standard ΛCDM cosmological model yielding exactly the same large-scale geometry described by the evolution of the Hubble parameter (i.e. photometric distance and angular diameter distance as functions on z). Asymptotic behavior of the field solutions is studied in the case of spatially flat Universe with pressureless matter and separable scalar field Lagrangians; the cases of power-law kinetic term and power-law potential are considered. Exact analytic solutions are found in some special cases. A number of models have the field solutions with infinite behavior in the past or even singular behavior at finite redshifts. We point out that introduction of the cosmological scalar field involves some degeneracy leading to lower precision in determination of Ω _m . To remove this degeneracy additional information is needed besides the data on large-scale geometry. The article is published in the original.     

Massless scalar field in Robertson-Walker space-time

Recently, exact spatially-homogeneous solutions have been found for a conformally invariant massless scalar fieldS(t) coupled to a Robertson-Walker geometry. We investigate extending these solutions to inhomogeneous scalar fieldsS(t, x ^l ). For an isotropic scalar fieldS(t, r) we find a solution satisfying three of the five field equations. If we use REDUCE, we show that the remaining equations forceS=S(t).     

L.R.S. Bianchi Type I string dust magnetized cosmological models

L.R.S. Bianchi Type I string dust cosmological models with and without magnetic field following the techniques used by Letelier and Stachel, is investigated. To get a determinate solution, we assume a conditionσ is proportional to scalar of expansion θ where σ is shear and θ is scalar of expansion and which leads to A=ℓ B ⁿwhere n is a constant and ℓ is proportionality constant. Some special models are also investigated by introducing the transformation, , which leads to Riccati type differential equation. The physical and geometrical aspects of the models are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

LRS Bianchi-I anisotropic cosmological model with dominance of dark energy

The present study deals with spatially homogeneous and anisotropic locally rotationally symmetric (LRS) Bianchi type I cosmological model with dominance of dark energy. To get the deterministic model of Universe, we assume that the shear scalar (σ) in the model is proportional to expansion scalar (θ). This condition leads to A=B ⁿ , where A, B are metric potential and n is positive constant. It has been found that the anisotropic distribution of dark energy leads to the present accelerated expansion of Universe. The physical behavior of the Universe has been discussed in detail.     

(Non-)geodesic motion in chameleon Brans Dicke model

Based on Das and Banerjee (Phys. Rev D 78:043512, 2008), we assume there is a non-minimal coupling between scalar field and matter in the Brans-Dicke model. We analyzes the motion of different matter such as, massless scalar field, photon, massless perfect fluid (dust), massive perfect fluid and point particle matter in this study. We show that the motion of massless scalar field and photon can satisfy null geodesic motion only in high frequency limit. Also we find that the motion of the dust and massive perfect fluid is geodesic for L _m =?P and it is non-geodesic for L _m =ρ. Finally, we study the motion of point particle and show that the motion of this kind of matter is like massive perfect fluid.     

Cosmological models with the variable gravitational and cosmological constants

Cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einsteins theory is considered. A general method of solving the field equations is given. Exact solution for Zeldovich fluid satisfying G=G ₀(R/R ₀) ⁿ is given.     

Emergent universe with scalar (or tachyonic) field in higher derivative theory

We consider a spatially homogeneous and isotropic flat Robertson-Walker model filled with a scalar (or tachyonic) field minimally coupled to gravity in the framework of higher derivative theory. We discuss the possibility of the emergent universe with normal and phantom scalar fields (or normal and phantom tachynoic fields) in higher derivative theory. We find the exact solution of field equations in normal and phantom scalar fields and observe that the emergent universe is not possible in normal scalar field as the kinetic term is negative. However, the emergent universe exists in phantom scalar field in which the model has no time-like singularity at infinite past. The model evolves into an inflationary stage and finally admits an accelerating phase at late time. The equation of state parameter is found to be less than −1 in early time and tends to −1 in late time of the evolution. The scalar potential increases from zero at infinite past to a flat potential in late time. More precisely, we discuss the particular case for phantom field in detail. We also carry out a similar analysis in case of normal and phantom tachyonic field and observe that only phantom tachyonic field solution represents an emergent universe. We find that the coupling parameter of higher order correction affects the evolution of the emergent universe. The stability of solutions and their physical behaviors are discussed in detail.     

Harmonic maps from spacetimes and their coupling to gravitation

The paper focusses on harmonic maps f from an m-dimensional space-time or Lorentzian manifold into an n-dimensional properly Riemannian field manifold: the energy-momenturn tensor of f, the coupling of f to a gravitational field, and the Cauchy problem to the harmonic map equations are studied.     

Cosmological models with generalised gravitational and cosmological constants

We consider cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einstein’s theory. A general method of solving the field equations is given. We study here the exact solutions for negative pressure models satisfying G=G ₀(R/R ₀) ⁿ .     

Slowly rotating perfect-fluid universes coupled with zero-mass scalar field

Certain new analytic solutions for rotating perfect-fluid spheres in the Robertson-Walker universe are found out to substantiate the possibility of the existence of rotating cosmological objects coupled with zero-mass scalar field. Exact solutions for the metric rotation (r, t) and the matter rotation (r, t) under different conditions are obtained and their nature and role are investigated. Except for perfect dragging the scalar field is found to have a damping effect on the rotation of matter. In some solutions we find out the restrictions on the radii of the models for realistic astrophysical situations. Rotating models which can also be expanding are also obtained, in which case the rotational velocities are found to decay with the time; and these models may be taken as examples of real astrophysical objects in the Universe.