Isotropization by scalar field driven inflation and the cosmological quantum boundary

We derive the Wheeler-de Witt equation for the scalar field of mass m > 0 in a Bianchi-type I universe. We argue that classical trajectories become possible at h² ⩽ αt_p^-2, h being the mean Hubble value and t_p the Planck time. We feel justified to set the numerical constant α ≈︁ 1. We discuss this condition in geometrically invariant quantities and compare it with ⩽t_p^-4. The proposed quantum boundary of classical trajectories represents a 3-dimensional sphere in the 4-space of the dynamical system. Equipartition of the initial energy over field (m < m_p) and shear variables at the quantum boundary will cause inflation with a probability p of the order p = 1 - m/m_p thus, p = 1 - 10^-4 for m taken from GUT. In the course of the inflationary stage the initially arbitrarily large shear-anisotropy exponentially decays.     

Geodesics around oscillatons made of exponential scalar field potential

Some of the spherically symmetric solutions to the Einstein–Klein–Gordon (EKG) equations can describe the astronomical soliton objects made of a real time-dependent scalar fields. The solutions are known as oscillatons which are non-singular satisfying the flatness conditions asymptotically with periodic (separated) time-dependency. In this paper, we investigate the geodesic motion around an oscillaton. The Spherically Symmetric Geometry allows the bound orbits in the plan \(\theta=\frac{\pi}{2}\) under a given initial conditions. The potential for the scalar field \(\varPhi=\varPhi(r,t)\), is an exponential function of the form \(V(\varPhi)=V_{0}\exp(\lambda\sqrt{k_{0}}\varPhi)\).     

Nature of singularity formed by the gravitational collapse in Husain space-time with electromagnetic field and scalar field

In this work, we have investigated the outcome of gravitational collapse in Husain space-time in the presence of electro-magnetic and a scalar field with potential. In order to study the nature of the singularity, global behavior of radial null geodesics have been taken into account. The nature of singularities formed has been thoroughly studied for all possible variations of the parameters. These choices of parameters has been presented in tabular form in various dimensions. It is seen that irrespective of whatever values of the parameters chosen, the collapse always results in a naked singularity in all dimensions. There is less possibility of formation of a black hole. Hence this work is a significant counterexample of the cosmic censorship hypothesis.     

Visualization of the solar magnetic field using coefficients of harmonic expansion in the potential approximation

A method for visualization of the solar magnetic field is suggested and implemented. The harmonic expansion coefficients obtained in the potential approximation from magnetic-field observations at the photospheric level are used as an input. Three-dimensional equations for field lines are numerically integrated, and the results are presented in the form of projections onto the picture plane. The density of the line number is assumed to be proportional to the magnetic flux density. The lines of different topological connectedness are differently colored and show areas with open and closed configurations, thus mapping the information about the field direction and magnitude. This method is useful for research and applied studies related to investigation and forecasting of space weather.     

Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues

This note gives a concise algorithm for computing a normal form for a real linear Hamiltonian differential equatin which has purely imaginary eigenvalues. This algorithm is then applied to the differential equation which comes from the quadratic terms of the Hamiltonian of the restricted three body problem at a Lagrange equilateral triangle equilibrium point.     

Non-linear amplification of a magnetic field driven by cosmic ray streaming

One-, two- and three-dimensional numerical results of the non-linear interaction between cosmic rays and a magnetic field are presented. These show that cosmic ray streaming drives large-amplitude Alfvénic waves. The cosmic ray streaming energy is very efficiently transferred to the perturbed magnetic field of the Alfvén waves, and the non-linear time-scale of the growth of the waves is found to be very rapid, of the order of the gyro-period of the cosmic ray. Thus, a magnetic field of interstellar values, assumed in models of supernova remnant blast wave acceleration, would not be appropriate in the region of the shock. The increased magnetic field reduces the cosmic ray acceleration time and so increases the maximum cosmic ray energy, which may provide a simple and elegant resolution to the highest energy Galactic cosmic ray problem, where the cosmic rays themselves provide the fields necessary for their acceleration.     

Multiple expansion of the tidal potential

The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, _E ) Earth spin axis orientation. _E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O     

R-W cosmological models with zero-mass scalar fields for different equations of state

Spatially-flat cosmological models with interacting perfect fluid and zero-mass scalar field have been obtained under different equations of state and in presence of the scalar charge density associated with the Klein-Gordon equation assuming a special law of variation for the Hubble's parameter.     

Cosmological viscous fluid models in the presence of electromagnetic field and zero-mass scalar field

The problem of electromagnetic field interacting with viscous fluid without and with zero-mass scalar field has been studied. It has been shown that electromagnetic field cannot interact with viscous fluid for spherically-symmetric Robertson-Walker metric. Exact solutions corresponding to the problem of electromagnetic field interactions in presence of viscous fluid and zero-mass scalar field have been obtained subject to various physical conditions. It presents a scope for the study of imperfect fluid FRW models showing the existence of the electromagnetic field due to the presence of zero-mass scalar field.     

Diffussion of a scalar field in a compressible turbulent medium

The diffusion of scalar fields (temperature, density number of some admixture) in a compressible medium showing an isotropic, homogeneous and stationary turbulence is considered. The derived formulae for turbulent diffusivity χ_T(ξ) hold up to ξ ≈ 1, where ξ = u₀ τ₀/R₀ (u₀, τ₀, and R₀ are characteristic velocity, life-time, and correlation length of turbulent pulsations, respectively. The velocity field of turbulent motions u(r, t) is assumed to be known and the influence of the scalar field onto u(r, t) is neglected. It is shown that the velocity correlators, which change their signs in dependence on the space corrdinates, may give negative values for ξ_T(ξ) when ξ ≠ 0.     

Magneto-viscous fluid cosmological models in presence of zero-mass scalar field

A viscous fluid cosmological model in presence of magnetic field and zero-mass scalar fields is developed. The non-negativity condition of viscous fluid pressure prescribes a certain minimum value oft vis-a-vis of the scale factorQ(t) and at this epoch the model is found to be singularity free.     

Rotational perturbations of cosmological viscous-fluid Universe with zero-mass scalar field

Certain new analytic solutions for the rotational perturbations of the Robertson-Walker universe are found out to substantiate the possibility of the existence of a rotating viscous universe with zero-mass scalar field. The values for (r, t) which is related to the local dragging of inertial frames are investigated. In all the cases the rotational velocity is found to decay with time. Except for perfect dragging the scalar field is found to have a damping effect on the rotation of matter. The damping effect is found to be roughly analogous to viscosity. In some solutions it is found that the scalar field may exist only during a time period in the course of evolution of the Universe.     

Slow rotation of radiating viscous-fluid Universe coupled with scalar field

One of the models which have stable limit cycles but are very close to the transition of the type I intermittency is examined in some detail. The work integrals are calculated for nonlinear oscillations with various amplitudes. The model reaches its limit cycle by saturation of the driving forces due to the ionized helium (He⁺) ionization. By increasing amplitudes damping becomes superior to the driving forces and so the limit cycle is stable. However, with even larger amplitudes the model becomes pulsational unstable indicating a large positive contribution to the work integral at rather deep interior. Strong luminosity drops are observed in this region during contraction phase. It is shown that the drops come from the neutral helium and hydrogen (He and H) ionization zones moved down to the deep interior at contraction phase with increasing amplitudes. A shock wave is generated by the radiation pressure at the ionization zones and propagates outwards at the phase. The zone between the ionization zones and the detached shock front is compressed locally. Thus, subsequent contraction leads the pressure at the zone becomes very high, causing remarkable enhancement of the opacities. Thus the driving becomes to work efficiently. This is a main driving force with finite amplitudes beyond the limit cycle, and makes the model to have an unstable fixed point beyond it.     

A note on the equation of state of a scalar field

The energy momentum tensor of a scalar field is considered as being that of a perfect fluid with equation of statep=p(). In the extreme case that the field energy is purely kinetic,p=p, whereas if it is purely potential,p=–.     

A new class of relativistic perfect fluid cylinders with expansion proportional to shear scalar

A new class of relativistic perfect fluid cylinders with expansion proportional to shear scalar have been derived by considering the Einstein-Rosen metric. It is shown that the solutions obtained by other workers do not satisfy the isotropy conditions and therefore are erroneous. The solutions derived in this article are analyzed kinematically.     

A light scalar field at the origin of galaxy rotation curves

The nature of the dark matter that binds galaxies remains an open question. It is usually assumed to consist in a gas of massive particles with evanescent interactions; however, such particles—which have never been observed directly—should have a clumpy distribution on scales ≤10⁻² kpc, which may be in contradiction with observations. We focus here on an exotic dark matter candidate: a light non-interacting (or only self-interacting) complex scalar field. We investigate the distribution of the field in gravitational interaction with matter, assuming no singularities (like black holes) at the galaxy center. This simplistic model accounts quite well for the rotation curve of low-luminosity spirals. A chi-squared analysis points towards a preferred mass m∼0.4 to 1.6×10⁻²³ eV in absence of self-interaction. A rough calculation shows that allowing for a quartic self-coupling may shift the upper bound to around 1 eV. We conclude that a scalar field is a promising candidate for galactic dark matter. Our comparison should be extended to other rotation curves in order to derive better constraints on the scalar potential. We finally give a hint of the issues that appear when one tries to implement this scenario on cosmological time scales.     

Rotational perturbations of magneto-viscous fluid universes coupled with zero-mass scalar field

The dynamics of slowly rotating magneto-viscous fluid universe coupled with zero-mass scalar field is investigated, and the rotational perturbations of such models are studied in order to substantiate the possibility that the Universe is endowed with slow rotation, in the course of presentation of several new analytic solutions. Four different cases are taken up in which the nature and role of the metric rotation (r, t) as well as that of the matter rotation(r,t) are discussed. Except for the case of perfect drag, the scalar field is found to have a damping effect on the rotational motion. This damping effect is seen to be roughly analogous to the viscosity. The periods of physical validity of some of the models are also found out. Most of the rotating models obtained here come out to be expanding ones as well which may be taken as good examples of real astrophysical situations.