A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies

To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of spacetime anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.     

Two-Fluid Cosmological Models in Kaluza-Klein Space Time

In this paper we presented a class of solutions of Einstein’s field equations describing two-fluid models of the universe in a five dimensional spherical symmetric space time. In these models one fluid is the radiation distribution which represents the cosmic microwave background and the other fluid is the perfect fluid representing the matter content of the universe. The radiation and matter content of the universe are in interactive phase. Also we have discussed physical and kinematical behaviors of the model.     

LRS Bianchi type I universes exhibiting Noether symmetry in the scalar–tensor Brans-Dicke theory

Following up on hints of anisotropy in the cosmic microwave background radiation data, we investigate locally rotational symmetric Bianchi type I spacetimes with non-minimally coupled scalar fields. To single out potentially more interesting solutions, we search for Noether symmetry in this system. We then specialize to the Brans-Dicke field in such a way that the Lagrangian becomes degenerate (nontrivial) and solve the equations for Noether symmetry and the potential that allows it. Then we find the exact solutions of the equations of motion in terms of three parameters and an arbitrary function. We illustrate with families of examples designed to be generalizations of the well-known power-expansion, exponential expansion and Big Rip models in the Friedmann-Robertson-Walker framework. The solutions display surprising variation, a large subset of which features late-time acceleration as is usually ascribed to dark energy (phantom or quintessence), and is consistent with observational data.     

Inhomogeneous Cosmologies, the Copernican Principle and the Cosmic Microwave Background: More on the EGS Theorem

We discuss inhomogeneous cosmological models which satisfy the Copernican principle. We construct some inhomogeneous cosmological models starting from the ansatz that the all the observers in the models view an isotropic cosmic microwave background. We discuss multi-fluid models, and illustrate how more general inhomogeneous models may be derived, both in General Relativity and in scalar-tensor theories of gravity. Thus we illustrate that the cosmologicalprinciple, the assumption that the Universe we live in is spatially homogeneous, does not necessarily follow from the Copernican principle and the high isotropy of the cosmic microwave background. We also present some new conformally flat two-fluid solutions of Einstein's field equations.     

Temperature of the inflaton and duration of inflation from Wilkinson microwave anisotropy probe data

If the initial state of the inflaton field is taken to have a thermal distribution instead of the conventional zero particle vacuum state then the curvature power spectrum gets modified by a temperature dependent factor such that the fluctuation spectrum of the microwave background radiation is enhanced at larger angles. We compare this modified cosmic microwave background spectrum with Wilkinson microwave anisotropy probe data to obtain an upper bound on the temperature of the inflaton at the time our current horizon crossed the horizon during inflation. We further conclude that there must be additional -foldings of inflation beyond what is needed to solve the horizon problem.     

Affine symmetry,geodesics, and homogeneous spacetimes

We show that the conservation laws for the geodesic equation which are associated to affine symmetries can be obtained from symmetries of the Lagrangian for affinely parametrized geodesics according to Noether’s theorem, in contrast to claims found in the literature. In particular, using Aminova’s classification of affine motions of Lorentzian manifolds, we show in detail how affine motions define generalized symmetries of the geodesic Lagrangian. We compute all infinitesimal proper affine symmetries and the corresponding geodesic conservation laws for all homogeneous solutions to the Einstein field equations in four spacetime dimensions with each of the following energy–momentum contents: vacuum, cosmological constant, perfect fluid, pure radiation, and homogeneous electromagnetic fields.     

Modelling background radiation in isotropic cosmologies

Using explicit perturbations of isotropic cosmological models which describe simple gravitational waves, an isotropic tensor having the algebraic symmetries of the Bel–Robinson tensor is derived as a model of cosmic background gravitational radiation and this is used to provide an answer to the question: in what sense can an energy–momentum–stress tensor similar to that describing the cosmic microwave background radiation (neglecting anisotropies) be associated with an isotropic background of gravitational radiation?     

A dynamical dark energy model with a given luminosity distance

It is assumed that the current cosmic acceleration is driven by a scalar field, the Lagrangian of which is a function of the kinetic term only, and that the luminosity distance is a given function of the red-shift. Upon comparison with baryon acoustic oscillations and cosmic microwave background data the parameters of the models are determined, and then the time evolution of the scalar field is determined by the dynamics using the cosmological equations. We find that the solution is very different than the corresponding solution when the non-relativistic matter is ignored, and that the universe enters the acceleration era at larger red-shift compared to the standard ΛCDM model.     

Kasner Cosmological Models with Two-Fluid Source in General Relativity

In this paper we present Bianchi type-I metric of the Kasner form describing two-fluid source of the universe in general relativity. In Kasner cosmological models one fluid is a radiation field modeling the cosmic microwave background, while the other is a matter field, modeling material content of the universe. The radiation and matter content of the universe are in interactive phase. We have also presented anisotropic, homogeneous nature of Kasner cosmological models with two-fluid. The behavior of fluid parameters and kinematical parameters of the models are also discussed.     

Geodesics in open universes

We present the geodesics on homogeneous and isotropic negatively curved spaces in a simple form suitable for application to cosmological problems. The pattern of geodesics translates into a pattern on the microwave background radiation. Generalizing, we discuss how the patterns in the microwave sky of anisotropic homogeneous universes can be predicted qualitatively by looking at the invariances that generate their three-geometries and their geodesics.     

Evidence for dark energy from the cosmic microwave background alone using the Atacama Cosmology Telescope lensing measurements

For the first time, measurements of the cosmic microwave background radiation (CMB) alone favor cosmologies with w = -1 dark energy over models without dark energy at a 3.2-sigma level. We demonstrate this by combining the CMB lensing deflection power spectrum from the Atacama Cosmology Telescope with temperature and polarization power spectra from the Wilkinson Microwave Anisotropy Probe. The lensing data break the geometric degeneracy of different cosmological models with similar CMB temperature power spectra. Our CMB-only measurement of the dark energy density Ω(Λ) confirms other measurements from supernovae, galaxy clusters, and baryon acoustic oscillations, and demonstrates the power of CMB lensing as a new cosmological tool.     

Remarks on the Idea of Spontaneous Break-Down of Symmetry,Cosmic Variability of Eddington's Number,Mach's Idea Concering the Origin of Inertia,and Field Equations Describing Global and Local Gravitational Fields

Subject is considered on the level of classical field theory. We start from some aspects of the theory of ferromagnets. Their counterpart in classical field theory is pointed out using the over simplified model of a selfinteracting scalar field. The ground state (“vacuum expection value”) of the scalar field is interpreted as cosmic background field, which can be considered as constant for local physical phenomena. In practice, however, it is a function of the age of universe. Which kind of function it could be is suggested by a discussion of the cosmic variability of Eddington's number γ = 10⁴⁰, which refers to Dirac's consideration of this problem. But contrary to Dirac's assumption that atomic quantities are constant, we suppose that the inertial mass of elementary particles is a function of the age of universe. The cosmic gravitational field is described by other equations than the gravitational field created by local matter distributions. The field equations for the local gravitational field we start from reduce to Einstein's equations, if we neglect the possible influence of the universe on local phenomena. In case that the cosmic matter is homogeneously and isotropically distributed, the field equations for the cosmic gravitational field permit only such a time dependent solution the three-spaces of which are linearly expanding and spherically closed. The different field equations for cosmic and local gravitational fields are considered approximations of more fundamental field equations which approximately split into two sets of equations, if it is possible to contrast local physical systems with the universe. The described cosmological model taken as a basis, the inertial mass of elementary particles becomes a function of the matter density creating the cosmic gravitational field. This could be considered as, at least, partly realisation of Mach's idea concerning the origin of inertia. Starting from the interpretation of the ground state (vacuum expection value) as a function of a certain cosmic background field, more realistic gage field models could give the following picture of cosmic development: In the far past there was a state of the universe characterized by enormous contraction of matter. In this stage of development, it was impossible to contrast particles with the universe. Matter expands and it becomes possible to contrast certain physical systems with the universe. But the ground state is such a symmetric one that only fields with vanishing rest mass can be contrasted with the universe (ferromagnet above Curie temperature). With further expansion of the universe the ground state will lose certain symmetry properties. By this it becomes possible that you get the impression there are particles with nonvanishing rest mass (ferromagnet below Curie temperature). Finally, the influence of the universe on local physical systems goes to zero with further expansion. Especially, this means the inertial mass of elementary particles goes to zero, too (Curie temperature of ferromagnetic material goes to zero with cosmic expansion).     

Neutrino fields in Einstein-Cartan theory

The spin-coefficient formalism presented elsewhere is here applied to classical neutrino fields in Einstein-Cartan theory. It is shown that the neutrino current vector is tangent to an expansion-free null geodesic congruence with constant and equal twist and shear, which vanish if and only if the congruence is a repeated principal null congruence of the gravitational field. The geodesics are both extremals and autoparallels. All exact solutions for the case of pure radiation fields are obtained, and it is shown that the only possible ghost solutions have a plane wave metric.     

Ultra-high energy cosmic rays threshold in Randers-Finsler space

Kinematics in Finsler space is used to study the propagation of ultra high energy cosmic rays particles through the cosmic microwave background radiation. We find that the GZK threshold is lifted dramatically in Randers-Finsler space. A tiny deformation of spacetime from Minkowskian to Finslerian allows more ultra-high energy cosmic rays particles to arrive at the earth. It is suggested that the lower bound of particle mass is related with the negative second invariant speed in Randers-Finsler space.     

Ultra-high energy cosmic rays threshold in Randers-Finsler space

Kinematics in Finsler space is used to study the propagation of ultra high energy cosmic rays particles through the cosmic microwave background radiation. We find that the GZK threshold is lifted dramatically in Randers-Finsler space. A tiny deformation of spacetime from Minkowskian to Finslerian allows more ultra-high energy cosmic rays particles to arrive at the earth. It is suggested that the lower bound of particle mass is related with the negative second invariant speed in Randers-Finsler space.     

Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.     

Extended bodies with quadrupole moment interacting with gravitational monopoles: reciprocity relations

An exact solution of Einstein’s equations representing the static gravitational field of a quasi-spherical source endowed with both mass and mass quadrupole moment is considered. It belongs to the Weyl class of solutions and reduces to the Schwarzschild solution when the quadrupole moment vanishes. The geometric properties of timelike circular orbits (including geodesics) in this spacetime are investigated. Moreover, a comparison between geodesic motion in the spacetime of a quasi-spherical source and non-geodesic motion of an extended body also endowed with both mass and mass quadrupole moment as described by Dixon’s model in the gravitational field of a Schwarzschild black hole is discussed. Certain “reciprocity relations” between the source and the particle parameters are obtained, providing a further argument in favor of the acceptability of Dixon’s model for extended bodies in general relativity.     

Observational constraints on extended Chaplygin gas cosmologies

We investigate cosmological models with extended Chaplygin gas (ECG) as a candidate for dark energy and determine the equation of state parameters using observed data namely, observed Hubble data, baryon acoustic oscillation data and cosmic microwave background shift data. Cosmological models are investigated considering cosmic fluid which is an extension of Chaplygin gas, however, it reduces to modified Chaplygin gas (MCG) and also to generalized Chaplygin gas (GCG) in special cases. It is found that in the case of MCG and GCG, the best-fit values of all the parameters are positive. The distance modulus agrees quite well with the experimental Union2 data. The speed of sound obtained in the model is small, necessary for structure formation. We also determine the observational constraints on the constants of the ECG equation.     

Geodesics in rotating systems

The paper investigates the equations for geodesics, null geodesics, and spatial geodesics in rotating systems. Geodesics and null geodesics have, as usual, been interpreted as the paths of free particles and of light rays, respectively. Spatial geodesics are given a firm interpretation as the shortest paths between points within the rotating system, where the path length is measured by an observer in the rotating system who moves along the spatial geodesic. The paper shows that equations for geodesics in rotating systems may be derived by the traditional method, i.e., from the flat-space metric of general relativity, or by means of the instantaneous Lorentz frames approach. This supports the use of instantaneous Lorentz frames as a valid method for the analysis of events in rotating systems.