General Relativistic Cosmology Research Articles

INFLATON POTENTIAL RECONSTRUCTION IN EINSTEIN–CARTAN COSMOLOGY

An extension of the reconstruction of inflaton potential in general relativistic cosmology to space–times with spin–torsion density is undertaken. Torsion effects are shown to decrease when the number of e-folds increases and are important only at the early stages of the inflation. The potential is computed in terms of a generalized equation of state and when the spin–torsion density is high and a chaotic inflation potential is found. A particle creation model in Einstein–Cartan cosmology is also shown to lead to chaotic inflation potential in de Sitter space–time.

From rapidity to vibracy (logarithmic frequency)

Logarithmic parameters have been been found useful for describing the translational and gravitational states of some systems. These parameters are additive, and may serve to push unwanted singularities off to infinity. The best known of these is rapidity, a speedlike parameter used in special relativity. Another is the so-called “linear time” of Misner and Lévy-Leblond, which applies to general relativistic cosmology. We point out that these two parameters are both logarithmic measures of frequency shift and represent a quantity we call “vibracy.” Majernik’s trigonometric variant of rapidity is found to be an aberration angle.

General Relativistic Cosmology with No Beginning of Time

We find that general relativity can be naturally free of cosmological singularities. Several nonsingular models are currently available that either assume ad hoc matter contents or are nonsingular only over a sector of solution space of zero measure or depart drastically from general relativity at high energies. After much uncertainty over whether cosmological inflation could help solve the initial-singularity problem, the prevailing belief today is that general relativistic cosmology, with inflation or without, is endemically singular. Here a homogeneous and isotropic inflationary cosmology is worked out that is naturally free of singularities, despite the fact that it uses only classical general relativity and assumes only the most generic inflationary matter contents.

Cosmological Redshift‐Space Distortion on Clustering of High‐Redshift Objects: Correction for Nonlinear Effects in the Power Spectrum and Tests withN‐Body Simulations

We examine the cosmological redshift-space distortion effect on the power spectrum of objects at high redshifts,which is an unavoidable observational contamination in general relativistic cosmology. In particular, we consider the nonlinear effects of density and velocity evolution using high-resolution N-body simulations in cold dark matter models. We find that theoretical modeling on the basis of the fitting formulae of nonlinear density and velocity fields accurately describes the numerical results, especially in quasi-nonlinear regimes. These corrections for nonlinear effects are essential in order to use the cosmological redshift-space distortion as a cosmological test. We perform a feasibility test to derive constraints from the future catalogs of high-redshift quasars using our theoretical modeling and results of N-body simulations. Applying the present methodology to the future data from ongoing surveys of high-redshift galaxies and quasars will provide a useful tool to constrain a geometry of the universe.

Cosmic microwave background temperature and polarization anisotropy in Brans-Dicke cosmology

We develop a formalism for calculating cosmic microwave background (CMB) temperature and polarization anisotropies in cosmological models with Brans-Dicke gravity. We then modify publicly available Boltzmann codes to calculate numerically the temperature and polarization power spectra. Results are illustrated with a few representative models. Comparing with the general-relativistic model of the same cosmological parameters, both the amplitude and the width of the acoustic peaks are different in the Brans-Dicke models. We use a covariance-matrix calculation to investigate whether the effects of Brans-Dicke gravity are degenerate with those of variation in other cosmological parameters and to simultaneously determine whether forthcoming CMB maps might be able to distinguish Brans-Dicke and general-relativistic cosmology. Although the predicted power spectra for plausible Brans-Dicke models differ from those in general relativity only slightly, we find that MAP and/or the Planck Surveyor may in principle provide a test of Brans-Dicke theory that is competitive to solar-system tests. For example, if all other parameters except for the CMB normalization are fixed, a value of the Brans-Dicke parameter ω as large as 500 could be identified (at the 2σ level) with MAP, and for Planck, values as large as ω≃3000 could be identified; these sensitivities are decreased roughly by a factor of 3 if we marginalize over the baryon density, Hubble constant, spectral index, and re-ionization optical depth. In more general scalar-tensor theories, ω may evolve with time, and in this case, the CMB probe would be complementary to that from solar-system tests.

An introduction to modern cosmology

Preface. Constants conversion factors and symbols. 1. A (Very) Brief History of Cosmological Ideas. 2. Observational Overview. 3. Newtonian Gravity. 4. The Geometry of the Universe. 5. Simple Cosmological Models. 6.Observational Parameters. 7. The Cosmological Constant. 8. The Age of the Universe. 9. The Density of the Universe and Dark Matter. 10. The Cosmic Microwave Background. 11. The Early Universe. 12. Nucleosynthesis: The Origin of the Light Elements. 13. The Inflationary Universe. 14. The Initial Singularity. 15. Overview: The Standard Cosmological Model. Advanced Topic 1: General Relativistic Cosmology Advanced Topic 2: Classic Cosmology: Distances and Luminosities. Advanced Topic 3: Neutrino Cosmology. Advanced Topic 4: Baryogenesis. Advanced Topic 5: Structures in the Universe. Bibliography. Numerical answers and hints to problems. Index.

Lagrangian description of fluid flow with vorticity in relativistic cosmology

We develop Lagrangian perturbation theory in general relativistic cosmology, which enables us to take into account the vortical effect of dust matter. Under the Lagrangian representation of fluid flow, the propagation equation for the vorticity as well as the density is exactly solved. Based on this, the coupling between the density and vorticity is clarified in a nonperturbative way. The relativistic correspondence to the Lagrangian perturbation theory in Newtonian cosmology is also emphasized.

A gauge-invariant analysis of magnetic fields in general-relativistic cosmology

We provide a fully general-relativistic treatment of cosmological perturbations in a universe permeated by a large-scale primordial magnetic field using the Ellis - Bruni gauge-invariant formalism. The exact nonlinear equations for general-relativistic magnetohydrodynamic evolution are derived. A number of applications are made: the behaviour of small perturbations to Friedmann universes is studied; a comparison is made with earlier Newtonian treatments of cosmological perturbations and some effects of inflationary expansion are examined.

As time goes by

The concept of temporal flow has been attacked both on the grounds that it is logically incoherent, and on the grounds that it conflicts with the theory of relativity. I argue that the charge of incoherence cannot be made to stick: McTaggart's argument commits the fallacy of equivocation, and arguments deployed by Smart and others turn out to be question‐begging. But objections arising from relativity, so I claim, have considerably more force than Lucas acknowledges. Moreover, the idea of equating the cosmic time which arises in general relativistic cosmology with a metaphysically preferred space‐time foliation, founders on the fact that the Friedmann models are idealisations. Finally, Lucas may be right in claiming that dynamical wave‐function collapse, provided it does not propagate superluminally, will define a preferred foliation. But it is arguable that this consideration, so far from supporting Lucas's position, is grounds for rejecting collapse interpretations of quantum mechanics.

Cosmological PPN formalism and non-Machian gravitational theories

By turning to a differential formulation, the post-Newtonian description of metric gravitational theories (PPN formalism) has been extended to include cosmological boundary conditions. The dimensionless expansion parameter is the ratio distance $L$ (measured from the center of a selected space region) to Hubble distance $c/H_0$. The aim was to explore the significance and applicability of a Newtonian cosmology and to clarify to some extent its relation to general-relativistic cosmology. It turns out that up to post-Newtonian order two classes of gravitational theories can be distinguished, here called Machian and non-Machian. In a non-Machian theory like General Relativity the dynamics of cosmic objects within a space region $L \ll c/H_0 $ is described by the usual PPN metric set up for the objects, without introducing time-dependent Newtonian potentials at the origin of the PPN coordinate system. Such potentials of obviously cosmological origin seem to be required for the majority of (by our definition) Machian gravitational theories (including, e.g., Brans-Dicke). Conditions for a theory to be Machian or non-Machian are given in terms of algebraic relations for the PPN parameters.

Of Cosmic Background Anisotropies

Observations of the Cosmic Microwave Background (CMB) Radiation have put the standard model of cosmology, the Big Bang, on firm footing and provide tests of various ideas of large scale structure formation. CMB observations now let us test the role of gravity and General Relativity in cosmology including the geometry, topology, and dynamics of the Universe. Foreground galactic emissions, dust thermal emission and emission from energetic electrons, provide a serious limit to observations. Nevertheless, observations may determine if the evolution of the Universe can be understood from fundamental physical principles.

General-relativistic cosmology with expansion and rotation

A model of an expanding and rotating universe is constructed in the framework of general relativity. The parameters of the model are compared with the fundamental observables and shown to be in good agreement.

Cosmologies based on Lyra's geometry

It is pointed out that the cosmologies based on Lyra's manifold, with constant gauge-vector which have been studied in the literature, will either include a creation field and be equal to Hoyle's creation field cosmology, or contain a special vacuum fluid which together with the gauge-vector term may be considered as a cosmological term. In the latter case the solutions are equal to the general relativistic cosmologies with a cosmological term.

Generalized Robertson-Walker metrics and some of their properties

The generalized Robertson-Walker (GRW) metrics in canonical coordinates ( t, χ 1, χ 2,..., χ n ) are defined. The following statements are proved to be equivalent: The GRW metrics are (a) expressible in t-independent form, (b) of constant curvature, (c) Einstein spaces. There are six, and only six, such metrics as in general relativistic cosmology.

Comments on the static spherically symmetric cosmologies of Ellis, Maartens, and Nel

Ellis, Maartens, and Nel have discussed the viability of static spherically symmetric (SSS) cosmologies in general relativity, and in doing so they have studied some of the mathematical aspects of the field equations in that situation. We investigate further these mathematical aspects. Since the field equations correspond to those studied for stellar models, this question is related to previous investigations in that context. In particular, it is shown that conditions at the center of symmetry do not always uniquely determine the space-time geometry; this has relevance to the numerical investigation of stellar systems. Finally, in view of the need to generalize SSS models, some remarks are made on the possibility of relaxing the staticity condition in the case of models that are shear-free.

Time variation of the cosmological redshift in Dicke-Brans-Jordan cosmologies

In this paper the time variation z of the cosmological redshift z is discussed for Dicke-Brans-Jordan (DBJ) cosmologies. We determine the general z-z relation in the functional form zH/sup -1//sub 0/ = F(z; q/sub 0/, sigma/sub 0/,xi/sub 0/, ..omega..) for small values of z, where all the symbols have their conventional meanings. For certain combinations of cosmological parameters, which are within the present observational limitations, the DBJ terms in the function F can dominate the general relativistic terms. Furthermore, zH/sup -1//sub 0/ can be positive in DBJ cosmologies in contrast to general relativistic cosmologies with q/sub 0/>0.

Zur kosmologischen Testung des Machschen Prinzips

AbstractThe Machian models of isotropic expanding universes according to the “inertia‐free” gravo‐dynamics imply the equations between the instantan values H0 and q0 of the HUBBLE parameter H, the acceleration q, and the matter density o. Therefore, in Machian universes with linear expansion q0 = 0 the energy integral E = ‐1/2ϵc2 is zero and the matter density becomes (with H02R02 = c2/3) (f0 the Newtonian gravitational constant). This is the critical density in general relativistic cosmology.

Plane-symmetric cosmologies

view Abstract Citations (45) References (17) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Plane-symmetric cosmologies. Centrella, J. ; Matzner, R. A. Abstract Plane-symmetric (general relativistic) cosmologies are studied from the viewpoint of the initial-value problem. A class of cosmologies exists which has the same extrinsic curvature at every point on the initial surface, T = Tzero, as an anisotropic or isotropic homogeneous cosmology, but with an anisotropy parameter or equation of state that varies as a function of one coordinate (Z) in this surface. As an example, initial data representing abutted vacuum Kasner half-spaces have been evolved. (This case is within the class of Gowdy cosmologies, and the evolution can be determined by analytic Green-function techniques.) This model may be viewed as describing the early evolution of a universe with matter, but before the matter became dynamically important. Depending on the specific parameters of the anisotropic model through which the shock travels, typically strong gravitational shock waves emanating from the join surface may be sufficient to disrupt matter condensations that occur while the model is valid; i.e., during the anisotropy-dominated epoch. In all cases they have an inhibiting effect on the formation of matter condensation. Publication: The Astrophysical Journal Pub Date: June 1979 DOI: 10.1086/157087 Bibcode: 1979ApJ...230..311C Keywords: Astronomical Models; Cosmology; Field Theory (Physics); Relativistic Theory; Anisotropy; Gravitational Waves; Green'S Functions; Symmetry; Universe; Astrophysics; Cosmological Models full text sources ADS |

A systematic investigation of the Petrov G4 types

In order to investigate exact solutions in general relativistic cosmology, one usually assumes the spacetime possesses symmetry. Here, we study exact solutions for the Petrov four-parameter Lie groups G4, acting on nonnull hypersurfaces where the energy-momentum tensor is that of a pressureless perfect fluid (a so-called ’’dust’’). We find that the preponderance of solutions are for a spacelike dust and, in several cases, are able to give their explicit forms. Among these are spacelike versions of previously known timelike matter cosmological models.

Linear density perturbation in relativistic and Brans-Dicke cosmologies

Linear density perturbation equation for general relativistic cosmologies using the homogeneous isotropic Robertson-Walker metric and the anisotropic Bianchi-I metric for the unperturbed model has been derived in a simple and rather general manner. The method has then been applied to consideration of the fate of density perturbation in the Brans-Dicke model of the universe. Two coupled differential equations connecting variations in the density rho and the scalar field phi of the model have been obtained. An approximate solution has been sought and a power law growth of the fluctuation density, delta rho , with time has been obtained.