A multidimensional radiation-filled universe

We consider a radiation-filled universe which possesses the product symmetry: (N-dimensional space of constant curvature) × (n sphere). The solutions of all the types, within this class, to the classical field equations are given. In the case of theN-dimensional space of zero or negative curvature constant, the solutions exhibit a tendency to approach asymptotically the Kasner-like state in which theN-dimensional subspace expands while then sphere shrinks to the final singularity. Our conclusions based on the phase-diagram method are in agreement with the results concerning the ^N × S ⁿ universe calculated by Sahdev with the help of numerical methods.     

Brans-Dicke cosmological exact solution in a radiation-filled Robertson-Walker universe

Considering a Robertson-Walker line element, exact solutions are obtained for radiation-filled cosmological differential equations of Brans-Dicke theory with the assumption that the radius of curvatureQ of the universe varies directly as thenth power of time. The solution is found to be valid for closed space only and the coupling constantw of the scalar tensor theory is necessarily negative. The radius of curvature of increases linearly with respect to the age of the universe, while the gravitational constantk varies directly as the square of the radius of the universe. The solution obtained is in contradiction to Dirac's hypothesis, in which the gravitational constant should decrease with time in an expanding universe.     

Fermions and expanding universe

The coupledDirac-Einstein equations for a homogeneous isotropic space-time forbid aclosed universe but lead to the standard cosmological model for aflat universe. Therefore only theopen universe is left as a nontrivial situation. There some of the desired cosmological effects emerge in a natural way:inflation, creation ex nihilo, etc.     

Brans-Dicke cosmological exact solution in a radiation-filled Robertson-Walker universe

In a recent paper Singh and Deo obtained the field equations in Brans-Dicke theory for a radiation-filled universe with Robertson-Walker metric and solved the equations for a particular case. Here we obtain the complete set of solutions of these equations.     

Is the universe expanding?

It is shown that spherically symmetric static general relativistic cosmological space-times can reproduce the same cosmological observations as the currently favored Friedmann-Robertson-Walker universes, if the usual assumptions are made about the local physical laws determining the behavior of matter, provided that the universe is inhomogeneous and our galaxy is situated close to one of its centers. Only (i) unverifiable a priori assumptions, (ii) detailed physical and astrophysical arguments, or (iii) observation of the time variation of cosmological quantities can lead us to conclude that the universe we live in is not such a static space-time.This essay was awarded the second prize for 1977 by the Gravity Research Foundation.     

Eigenvibrations of the expanding universe

A theoretical interpretation of the observed periodicity of large-scale (128 Mpc) correlations of galaxies is proposed as due to eigenvibrations of the closed expanding universe. Eigensolutions of the equations of motion for a scalar field in an inflationary model allow one to compute the energy density, interpreted as matter density. Isotropic eigensolution give rise to a matter density distribution having a periodic structure centered at the north pole of the closed Robertson-Walker universe represented by S³/Z₂. It is able to reproduce well the striking periodicity of the observational data, in the galactic north-south directions. The dipole and quadrupole eigensolutions and the location of the co-moving observer in a point of S³/Z₂ different from the center of the vibrational structure would imply, in a theoretically well predictable way, a decrease of the observed periodicity in some other directions.Partially supported by the State Committee for Scientific Research, Grant No. 2-0206-91-01.     

Tachyons in an expanding universe

It has been suggested that causality problems associated with tachyons can be eliminated by the existence of a perferred frame of rest in which backward time travel is impossible. Furthermore, cosmology provides a de facto preferred rest frame. However, it is demonstrated here that the observed expansion of the universe raises further problems for the existence of tachyons.     

Electrodynamics in an expanding universe

An algebraic form of the energy momentum tensor of the electromagnetic field is derived in terms of two scalars and two mutually orthogonal vector fields. Upon inserting this tensor into the field equations, solutions of the co-determined Einstein-Maxwell equations are obtained. The line element used is that corresponding to a conformal flat universe, whose form is then uniquely determined by the field equations. The case of a charged fluid is also considered and it is found that the particular form of the velocity field chosen limits the choice of the possible equation of state connecting the pressure and density distributions.     

Vector bosons in the expanding universe

We exactly solve the relativistic wave equation for vector bosons in the expanding universe and show that the current of the vector bosons in this background is rapidly oscillating in early time. Additionally, we derive the solutions of the Proca equation from the solutions of the Duffin-Kemmer-Petiau (DKP) equations in the same background and obtain the massless-particle, photon, solutions by taking the limit of these solutions. PACS. 03.65.Pm, 04.60.-m, 98.80.Cq Received: 20 May 2005, Published online: 30 August 2005     

Bubble dynamics in the expanding universe

Using the Gauss-Codazzi equations, the behavior of a singular hypersurface, which divides the universe into two Friedmann-Robertson-Walker space-time regionsV ⁺ andV ^–, is investigated. The equation of motion for a spherical bubble in the expanding universe is presented and the physical meaning of the equation is clarified. The equations of state for fluids inV ^± and on the boundary shell, which should be determined by microscopic physics, are arbitrary in the present geometrical approach. The derived equations are quite similar to those for a shell in a vacuum and can be applied to the case that one ofV ^± or both are Schwarzschild-de Sitter space-time too.     

Nonstandard model of the expanding universe

A reformulation of general relativity is proposed with the relativity principle being invalid. Consequently the space-time manifold carries a natural (1+3)-foliation, where the foliation variables supersede the metric as the fundamental object. The Einstein equations become modified by some kind of foliation energy, but otherwise remain part of the dynamics. The theory is applied to a homogeneous and isotropic universe; the generation of mass can be explained by conversion of foliation energy and inflation is driven by the negative foliation pressure.     

Gravitational energy in the expanding universe

The role of gravitational energy in the evolution of the universe is examined. In co-moving coordinates, calculation of the Landau-Lifshitz pseudotensor for FRW models reveals that: (i) the total energy of a spatially closed universe irrespective of the equation of state of the cosmic fluid is zero at all times, (ii) the total energy enclosed within any finite volume of the spatially flat universe is zero at all times, (iii) during inflation the vacuum energy driving the accelerated expansion and ultimately responsible for the creation of matter (radiation) in the universe, is drawn from the energy of the gravitational field. In a similar fashion, certain cosmological models which abandon adiabaticity by allowing for particle creation, use the gravitational energy directly as an energy source.     

Analogue model for an expanding universe

Over the last few years numerous papers concerning analogue models of (and for) gravity have been published. It has been shown that the dynamical equations for several condensed matter systems, (e.g., simple fluids, superfluids, Bose–Einstein condensates with a sink or a vortex) permit perturbations that are governed by the same type of wave equation as light in a curved spacetime—the curved-space d'Alembertian equation. More recently, several papers have been released which use analogue models to simulate the expanding universe. In this article the de Sitter universe will be simulated using a freely expanding three-dimensional Bose–Einstein condensate with spherical symmetry. Initially the condensate is in a harmonic trap, which is then suddenly switched off. At the same time a small perturbation is injected in the center of the condensate cloud. The motion of this perturbation in the expanding condensate will be discussed, and (after some transformations) the similarity of this system to an expanding universe will be exhibited. Finally, we briefly discuss questions of experimental observability of these effects. Presented at the 4th Australasian conference on General Relativity and Cosmology, Monash University, Melbourne, 7–9 January 2004     

Scalar field fluctuations in the expanding universe and the new inflationary universe scenario

The behaviour of the scalar fied fluctuations in the exponentially expanding universe and their role in the new inflationary universe scenario are investigated.