Cosmological perturbations in the inflationary universe

In the framework of the gauge-invariant formalism the problem of the evolution of adiabatic perturbations in the metric for the theory of gravity with higher derivatives, which contains inflation, has been solved. The results are compared with the case when inflation arises due to a scalar field. The restrictions on the parameters of the models are given.     

Cosmological parameters

There is some consensus emerging on the values of the basic parameters of classical cosmology. The baryon number density estimated from the light element abundance or X-ray gas in galaxy clusters tends towards 5% of closure density; the dark matter content based on a number of independent methods appears to be somewhat less than half the closure density; Hubble constant obtained from local measurements, gravitational lens or Sunyaev Zeldovich method are all probably centred around 60 km/sec/Mpc and the age of the Universe is generally agree to be around 14 Gyr — all specified with bearable error bars. The supernova projects and CMBR anisotropy together favour a finite cosmological constant, and gravitational lens statistics support the same conclusion.     

A non-singular homogeneous universe with torsion

The Raychaudhuri equation and other relations for a spinning fluid in the framework of the Einstein-Cartan theory are obtained. It is shown that non-singular cosmological models of the Bianchi types I÷VIII are possible. As an example, a class of solutions for the I and the V type is presented.     

Ricci flow for homogeneous compact models of the universe

Using quaternions, we give a concise derivation of the Ricci tensor for homogeneous spaces with topology of the 3-dimensional sphere. We derive explicit and numerical solutions for the Ricci flow PDE and discuss their properties. In the collapse (or expansion) of these models, the interplay of the various components of the Ricci tensor are studied.     

Cosmological parameters are dressed

In the context of the averaging problem in relativistic cosmology, we provide a key to the interpretation of cosmological parameters by taking into account the actual inhomogeneous geometry of the Universe. We discuss the relation between "bare" cosmological parameters determining the cosmological model and the parameters interpreted by observers with a "Friedmannian bias," which are "dressed" by the smoothed-out geometrical inhomogeneities of the surveyed spatial region.     

Cosmological natural selection as the explanation for the complexity of the universe

A critical review is given of the theory of cosmological natural selection. The successes of the theory are described, and a number of published criticisms are answered. An observational test is described which could falsify the theory.     

Time travel in the homogeneous Som-Raychaudhuri universe

Properties of the rotating Som-Raychaudhuri homogeneous space-time are investigated: time-like and null geodesics, causality features, horizons and invariant characterization. An integral representation of its five isometries is also discussed.     

A rotating homogeneous universe with an electromagnetic field

The field equations of general relativity are solved to describe a gravitational field due to a rotating homogeneous fluid in the presence of a Maxwellian source-free electromagnetic field. It turns out that the metric to describe this field is the well-known Robertson-Walker metric with positive space-time curvature or its particular case, the metric of the closed Einstein universe.     

Cosmological black holes: A black hole in the Einstein-de Sitter universe

As an example of a dynamical cosmological black hole, a spacetime that describes an expanding black hole in the asymptotic background of the Einstein-de Sitter universe is constructed. The black hole is primordial in the sense that it forms ab initio with the big bang singularity and its expanding event horizon is represented by a conformal Killing horizon. The metric representing the black hole spacetime is obtained by applying a time dependent conformal transformation on the Schwarzschild metric, such that the result is an exact solution with a matter content described by a two-fluid source. Physical quantities such as the surface gravity and other effects like perihelion precession, light bending and circular orbits are studied in this spacetime and compared to their counterparts in the gravitational field of the isolated Schwarzschild black hole. No changes in the structure of null geodesics are recorded, but significant differences are obtained for timelike geodesics, particularly an increase in the perihelion precession and the non-existence of circular timelike orbits. The solution is expressed in the Newman-Penrose formalism.     

On the influence of extra dimensions on the homogeneous isotropic universe

The model of a homogeneous isotropic universe is studied in the presence of gauge fields, noninteracting dust, and two extra compact dimensions. It is found that the singular “big bang” type solution can be rejected because of the drastic growth of the radius of the universe. On the other hand, solutions without singularity can be found showing a very rapid oscillation (Planck frequency) with small amplitude around the data prescribing the present status of the universe.     

The time-symmetric initial value problem for a homogeneous,anisotropic, empty,closed universe,using Regge calculus

Models for a homogeneous, anisotropic, empty, closed universe at a particular moment of time are constructed from sets of empty tetrahedra. It is shown using Regge calculus that only two such models have a moment of time symmetry.On leave from Girton College, Cambridge CB3 OJG, and Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, England.     

Cosmological consequences of the particle-antiparticle gravitational repulsion hypothesis: the Newtonian model of the universe

The model of the gravitationally neutral Universe (GNU), i.e., a giant but finite 3D Ball expanding in the infinite static Euclidean space, is considered. The model is based on the antigravitation between particles and antiparticles. The GNU Ball is filled equally by matter and antimatter clusters and freely expands after epochs of partial annihilation and recombination. The abandonment of the cosmological principle and the problem of our Galaxy position in the GNU Ball are discussed.     

Transparent device with homogeneous material parameters

A transparent device is an electromagnetic structure that is explicitly designed to be transparent to incoming electromagnetic waves. Based on coordinate transformation theory, a novel diamond-shaped transparent device is proposed and designed. It can protect electronic equipments inside without affecting their performance. Compared with a traditional transparent device, the material parameters of the novel transparent device feature homogeneity and non-singularity, which can easily be realized in actual applications. Full-wave simulations are made to validate the performance of the transparent device.     

Stochastic evolution of cosmological parameters in the early universe

We develop a stochastic formulation of cosmology in the early universe, after considering the scatter in the redshift-apparent magnitude diagram in the early epochs as an observational evidence for the non-deterministic evolution of early universe. We consider the stochastic evolution of density parameter in the early universe after the inflationary phase qualitatively, under the assumption of fluctuating w factor in the equation of state, in the Fokker-Planck formalism. Since the scale factor for the universe depends on the energy density, from the coupled Friedmann equations we calculated the two variable probability distribution function assuming a flat space geometry.     

Diamond-shaped acoustic concentrator with homogeneous material parameters

Based on coordinate transformation method, the two-dimensional and three-dimensional acoustic concentrators with diamond shape composed of nonsingular homogeneous materials are designed in this paper. The mass density tensor and bulk modulus of the acoustic concentrators are derived. Performance of the concentrators is confirmed by full-wave simulation. The work represents an important progress towards the practical realization of the metamaterial-assisted acoustic concentrator and expands the application of the coordinate transformation method.