Gravitational stability of dark energy in galaxies and clusters of galaxies

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. It was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations, it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was also illustrated that the “accretion” of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities-the regions with negative amplitude of density perturbations of dark energy.     

Theory of linear cosmological perturbations in flat space-time theory of gravitation

Covariant linear cosmological perturbations are considered in flat space-time theory of gravitation. The background metric is not altered. The perturbed energy-momentum is given. The basic equations for the propagation of the perturbations are presented. The perturbed equations for a homogeneous, isotropic universe are stated.     

Linearized treatment of scalar perturbations in the Asymptotic Cosmological Model

In this paper the implications of a recently proposed phenomenological model of cosmology, the Asymptotic Cosmological Model (ACM), on the behavior of scalar perturbations are studied. Firstly we discuss new fits of the ACM at the homogeneous level, including fits to the Type Ia Supernovae UNION dataset, first CMB peak of WMAP5 and BAOs. The linearized equations of scalar perturbations in the FRW metric are derived. A simple model is used to compute the CMB temperature perturbation spectrum. The results are compared with the treatment of perturbations in other approaches to the problem of the accelerated expansion of the universe.     

Nodal and periastron precession of inclined orbits in the field of a rapidly rotating neutron star

We derive a formula for the nodal precession frequency and the Keplerian period of a particle at an arbitrary orbital inclination (with a minimum latitudinal angle reached at the orbit) in the post-Newtonian approximation in the external field of an oblate rotating neutron star (NS). We also derive formulas for the nodal precession and periastron rotation frequencies of slightly inclined low-eccentricity orbits in the field of a rapidly rotating NS in the form of asymptotic expansions whose first terms are given by the Okazaki-Kato formulas. The NS gravitational field is described by the exact solution of the Einstein equation that includes the NS quadrupole moment induced by rapid rotation. Convenient asymptotic formulas are given for the metric coefficients of the corresponding space-time in the form of Kerr metric perturbations in Boyer-Lindquist coordinates.     

The largest scale perturbations: A window on the physics of the beginning

I present results of new statistical techniques for the interpretation of the temperature and polarization maps and power spectra of the cosmic microwave background. We show that the power deficit at low ℓ in the WMAP1 data is consistent with a statistical fluctuation at the 10% level; that future high S/N maps of the temperature and polarization anisotropies can be combined into a reconstruction of the metric perturbations imprinted during inflation; and that machine learning techniques can accelerate cosmological parameter estimation by orders of magnitude while being highly accurate and robust.     

Turbulence in cosmology

The influence of short-wave turbulence on the expansion of a homogeneous and, on average, isotropic Universe was studied in Papers I–III. In the present paper we study the influence on the manner of expansion, for a complete spectrum of wavelengths, of scalar, tensor and vector perturbations. Ast»0, all waves become long (greater than the horizon); therefore, a knowledge of their influence on the averaged metric is required. It is shown that the long-wave modes of scalar and tensor perturbations which remain finite ast»0 deflect the metric for a homogeneous and, on average, isotropic Universe from the Friedmannian, giving it a form coinciding with the average quasi-isotropic solution of Lifshitz and Khalatnikov (1963). Ast»0 their contribution to the solution tends to zero. What remains to be determined is the contribution of those modes of scalar, tensor and vector perturbations which diverge ast»0. Att=0 the proposed solution for such modes becomes inapplicable. The behaviour of the metric of a homogeneous and, on average, isotropic Universe under the influence of all waves and all modes of perturbation is shown in Figure 1–3.     

Initial Data Set for Cosmology

The method of conformal metric is used to find an analytic set of consistent initial data for the linearized Einstein field equations. We discuss the relation between independent degrees of freedom and perturbations. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytical study of the Earth's shadowing effects on satellite orbits

In this paper a new mathematical model is proposed for the study of the effects of the direct solar radiation pressure on the orbit of an artificial Earth satellite. The equations for the first order effects become canonical when a different definition for the orders of magnitude is adopted. This enables us the utilization of the method of Von Zeipel to eliminate all periodic terms. The model leads to the non-existence of pure secular perturbations owing to the direct solar radiation pressure on the metric elements: semi-major axis, eccentricity and inclination. Numerical examples built with an approximation for the shadow function show that the secular inequalities on the angle variables—longitude, perigee and node—are very small.     

Testing cosmological structure formation using redshift-space distortions

Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure. In this paper, we develop and test a new statistic based on anisotropies in the measured galaxy power spectrum, which is independent of galaxy bias and matches the matter power spectrum shape on large scales. The amplitude provides a constraint on the derivative of the linear growth rate through   f σ₈(mass)  . This demonstrates that spectroscopic galaxy surveys offer many of the same advantages as weak lensing surveys, in that they both use galaxies as test particles to probe all matter in the Universe. They are complementary as redshift-space distortions probe non-relativistic velocities and therefore the temporal metric perturbations, while weak lensing tests the sum of the temporal and spatial metric perturbations. The degree to which our estimator can be pushed into the non-linear regime is considered and we show that a simple Gaussian damping model, similar to that previously used to model the behaviour of the power spectrum on very small scales, can also model the quasi-linear behaviour of our estimator. This enhances the information that can be extracted from surveys for Λ cold dark matter (ΛCDM) models.     

Use of Roche coordinates in the problems of small oscillations of tidally-distorted stellar models

Kopal's method of Roche coordinates used by us in an earlier paper (Mohan and Singh, 1978) to study the problems of small oscillations of tidally-distorted stars has been extended further to take into account the effect of second-order terms in tidal distortion. Our results show that the effect of including terms of second order of smallness in tidal distortion in the metric coefficients of the Roche coordinates of tidally distorted stars is quite significant, especially in case of stars with extended envelopes and (or) larger values of the mass ratio of the companion star producing tidal distortion. Some of the models which were earlier found stable against small perturbations now become dynamically unstable with the inclusion of the terms of second order of smallness in tidal effects.At present on leave of absence with the department of Mathematics, College of Science, Baghdad, Iraq.     

Critical properties of spherically symmetric accretion in a fractal medium

Spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. The stationary transonic solution is greatly sensitive to infinitesimal deviations in the outer boundary condition, but the flow becomes transonic and stable when its evolution is followed through time. The evolution towards transonicity is more pronounced for a fractal medium than it is for a continuum, and in the former case the static sonic condition is met on relatively larger length scales. The dynamic approach also shows that there is a remarkable closeness between an equation  of motion for a perturbation in the flow, and the metric of an analogue acoustic black hole. The stationary inflow solutions of a fractal medium are as much stable under the influence of linearized perturbations as they are for the fluid continuum.     

The scalar, vector and tensor contributions of a stochastic background of magnetic fields to cosmic microwave background anisotropies

We study the contribution of a stochastic background (SB) of primordial magnetic fields (PMFs) on the anisotropies in temperature and polarization of the cosmic microwave background (CMB) radiation. A SB of PMF modelled as a fully inhomogeneous component induces non-Gaussian scalar, vector and tensor metric linear perturbations. We give the exact expressions for the Fourier spectra of the relevant energy–momentum components of such a SB, given a power-law dependence parametrized by a spectral index   n_B   for the magnetic field power spectrum cut at a damping scale k _D. For all the values of   n_B   considered here, the contribution to the CMB temperature pattern by such a SB is dominated by the scalar contribution and then by the vector one at higher multipoles. We also give an analytic estimate of the scalar contribution to the CMB temperature pattern.     

The linear stability of the post-Newtonian triangular equilibrium in the three-body problem

Continuing a work initiated in an earlier publication (Yamada et al. in Phys Rev D 91:124016, 2015), we reexamine the linear stability of the triangular solution in the relativistic three-body problem for general masses by the standard linear algebraic analysis. In this paper, we start with the Einstein–Infeld–Hoffmann form of equations of motion for N-body systems in the uniformly rotating frame. As an extension of the previous work, we consider general perturbations to the equilibrium, i.e., we take account of perturbations orthogonal to the orbital plane, as well as perturbations lying on it. It is found that the orthogonal perturbations depend on each other by the first post-Newtonian (1PN) three-body interactions, though these are independent of the lying ones likewise the Newtonian case. We also show that the orthogonal perturbations do not affect the condition of stability. This is because these do not grow with time, but always precess with two frequency modes, namely, the same with the orbital frequency and the slightly different one due to the 1PN effect. The condition of stability, which is identical to that obtained by the previous work (Yamada et al. 2015) and is valid for the general perturbations, is obtained from the lying perturbations.     

Stable magnetic universes revisited

Recent discovery of magnetars (B～10¹⁵ G) motivates us to consider magnetic universes in general relativity a new. A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d>3 such spacetimes are stable at both near r≈0 and large radius r→∞. For d=3, however, simultaneous stability requirement at both, near and far radial distances can not be reconciled for time-dependent perturbations. We argue that this distinct property may be the cause for the absence of pure magnetic black holes in d=3. Restricted, numerical geodesics for neutral particles reveal a gravitational confinement around the center in the polar plane. Charged, time-like geodesics for d=4 are shown numerically to remain confined as well.     

Fourier analysis of the light curves of eclipsing variable stars

The aim of the present paper is to establish the explicit forms of the photometric perturbations, in the frequency-domain, of close binaries, whose components are distorted by axial rotation and mutual tidal action.Following a brief introduction, Section 2 describes the light changes and the photometric perturbations within eclipses in the frequency-domain. In Section 3 the explicit forms of the perturbations for occultation eclipses terminating in totality are given; while in Section 4 analogous results are established for transit eclipses terminating in annular phases. In this latter case the results can be expressed in terms of the photometric perturbations for total eclipses and in terms of some series. To facilitate applications to actual stars these series have been computed and their results are represented in Table I and by the Graphs. Finally, Section 5 gives a discussion of the results.An extension of the photometric perturbations to the case of partial eclipses will be given in a subsequent communication.     

Perturbations of a close-Earth satellite due to sunlight diffusely reflected from the Earth

A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-Earth satellite due to sunlight reflected from the Earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the Earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomalyv. The perturbations within a given revolution can be obtained analytically by integrating with respect tov while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution.     

Quantum Perturbative Approach to Discrete Redshift

On the largest scales there is evidence of discrete structure, examples of this are superclusters and voids and also by redshift taking discrete values. In this paper it is proposed that discrete redshift can be explained by using the spherical harmonic integer l; this occurs both in the metric or density perturbations and also in the solution of wave equations in Robertson-Walker spacetime. It is argued that the near conservation of energy implies that l varies regularly for wave equations in Robertson-Walker spacetime, whereas for density perturbations l cannot vary regularly. Once this is assumed then perhaps the observed value of discrete redshift provides the only observational or experimental data that directly requires an explanation using both gravitational and quantum theory. In principle a model using this data could predict the scale factor R (or equivalently the deceleration parameter q). Solutions of the Klein-Gordon equation in Robertson-Walker spacetimes are used to devise models which have redshift taking discrete values, but they predict a microscopic value for R. A model in which the stress of the Klein-Gordon equation induces a metrical perturbation of Robertson-Walker spacetime is devised. Calculations based upon this model predict that the Universe is closed with 2 _q0 - 1=10^-4. This revised version was published online in July 2006 with corrections to the Cover Date.     

Position and velocity perturbations in the orbital frame in terms of classical element perturbations

The transformation of classical orbit element perturbations to perturbations in position and velocity in the radial, transverse and normal directions of the orbital frame is developed. The formulation is given for the case of mean anomaly perturbations as well as for eccentric and true anomaly perturbations. Approximate formulas are also developed for the case of nearly circular orbits and compared with those found in the literature.     

Perturbation spectrum in the inflationary stage when a cosmic string is present

We examine the spectrum of perturbations for a scalar field with an arbitrary curvature coupling parameter in the de Sitter stage of cosmological expansion when a cosmic string is present. These perturbations are caused by vacuum fluctuations in the field and serve as seed perturbations for the formation of galaxies in the postinflationary stage. A cosmic string disrupts the homogeneity of a de Sitter space, so that the spectrum of the perturbations depends on the distance from the string. This dependence is oscillatory in character with a period on the order of the perturbation wavelength.     

The perturbations of the orbital elements of Trojan asteriods

An asymptotic solution for the cylindrical coordinates of Trojan asteroids is derived by using a three-variable expansion method in the elliptic restricted three-body problem. The perturbations of the orbital elements are obtained from this solution by applying the formulas of the two-body problem. The main perturbations of the mean motion are studied in detail.