Growth of covariant perturbations in the contracting phase of a bouncing universe

In this paper we examine the validity of the linear perturbation theory near a bounce in the covariant analysis. Some linearity parameters are defined to set up conditions for a linear theory. Linear evolution of density perturbation and gravitational waves have been computed previously. We have calculated the vector and scalar induced parts of the shear tensor. For radiationlike and dustlike single fluid dominated collapsing Friedmann-Lemaitre-Robertson-Walker background it is shown that the linearity conditions are not satisfied near a bounce.Comment: 9 pages, final versio

Exact non-equilibrium solutions of the Einstein-Boltzmann equations. II

We find exact solutions of the Einstein-Boltzmann equations with relaxational collision term in FRW and Bianchi I spacetimes. The kinematic and thermodynamic properties of the solutions are investigated. We give an exact expression for the bulk viscous pressure of an FRW distribution that relaxes towards collision-dominated equilibrium. If the relaxation is toward collision-free equilibrium, the bulk viscosity vanishes - but there is still entropy production. The Bianchi I solutions have zero heat flux and bulk viscosity, but nonzero shear viscosity. The solutions are used to construct a realisation of the Weyl Curvature Hypothesis.Comment: 16 pages LaTex, CQG documentstyle (ioplppt

Integrability of irrotational silent cosmological models

We revisit the issue of integrability conditions for the irrotational silent cosmological models. We formulate the problem both in 1+3 covariant and 1+3 orthonormal frame notation, and show there exists a series of constraint equations that need to be satisfied. These conditions hold identically for FLRW-linearised silent models, but not in the general exact non-linear case. Thus there is a linearisation instability, and it is highly unlikely that there is a large class of silent models. We conjecture that there are no spatially inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate further issues that await clarification.Comment: Minor corrections and improvements; 1 new reference; to appear Class. Quantum Grav.; 16 pages Ioplpp

Linearisation instability of gravity waves?

Gravity waves in irrotational dust spacetimes are characterised by nonzero magnetic Weyl tensor $H_{ab}$. In the linearised theory, the divergence of $H_{ab}$ is set to zero. Recently Lesame et al. [Phys. Rev. D {\bf 53}, 738 (1996)] presented an argument to show that, in the exact nonlinear theory, $div H=0$ forces $H_{ab}=0$, thus implying a linearisation instability for gravity waves interacting with matter. However a sign error in the equations invalidates their conclusion. Bianchi type V spacetimes are shown to include examples with $div H=0\neq H_{ab}$. An improved covariant formalism is used to show that in a generic irrotational dust spacetime, the covariant constraint equations are preserved under evolution. It is shown elsewhere that \mbox{div} H=0 does not generate further conditions.Comment: 8 pages Revtex; to appear Phys. Rev.

Constraints on Inflationary Solutions in the Presence of Shear and Bulk Viscosity

Inflationary models and their claim to solve many of the outstanding problems in cosmology have been the subject of a great deal of debate over the last few years. A major sticking point has been the lack of both good observational and theoretical arguments to single out one particular model out of the many that solve these problems. Here we examine the degree of restrictiveness on the dynamical relationship between the cosmological scale factor and the inflation driving self-interaction potential of a minimally coupled scalar field, imposed by the condition that the scalar field is required to be real during a classical regime (the reality condition). We systema\-tically look at the effects of this constraint on many of the inflationary models found in the literature within the FLRW framework, and also look at what happens when physically motivated perturbations such as shear and bulk viscosity are introduced. We find that in many cases, either the models are totally excluded or the reality condition gives rise to constraints on the scale factor and on the various parameters of the model.Comment: 21 pages, LaTe

Dynamics of Inflationary Universes with Positive Spatial Curvature

If the spatial curvature of the universe is positive, then the curvature term will always dominate at early enough times in a slow-rolling inflationary epoch. This enhances inflationary effects and hence puts limits on the possible number of e-foldings that can have occurred, independently of what happened before inflation began and in particular without regard for what may have happened in the Planck era. We use a simple multi-stage model to examine this limit as a function of the present density parameter $\Omega_0$ and the epoch when inflation ends.Comment: 9 Pages RevTex4. Revised and update

Consistency of dust solutions with div H=0

One of the necessary covariant conditions for gravitational radiation is the vanishing of the divergence of the magnetic Weyl tensor H_{ab}, while H_{ab} itself is nonzero. We complete a recent analysis by showing that in irrotational dust spacetimes, the condition div H=0 evolves consistently in the exact nonlinear theory.Comment: 3 pages Revte

Large Scale Inhomogeneity Versus Source Evolution -- Can We Distinguish Them Observationally?

We reconsider the issue of proving large scale spatial homogeneity of the universe, given isotropic observations about us and the possibility of source evolution both in numbers and luminosities. Two theorems make precise the freedom available in constructing cosmological models that will fit the observations. They make quite clear that homogeneity cannot be proven without either a fully determinate theory of source evolution, or availability of distance measures that are independent of source evolution. We contrast this goal with the standard approach that assumes spatial homogeneity a priori, and determines source evolution functions on the basis of this assumption.Comment: mn style, mn.sty file included, mn.sty file remove

Classical Signature Change in the Black Hole Topology

Investigations of classical signature change have generally envisaged applications to cosmological models, usually a Friedmann-Lemaitre-Robertson-Walker model. The purpose has been to avoid the inevitable singularity of models with purely Lorentzian signature, replacing the neighbourhood of the big bang with an initial, singularity free region of Euclidean signture, and a signature change. We here show that signature change can also avoid the singularity of gravitational collapse. We investigate the process of re-birth of Schwarzschild type black holes, modelling it as a double signature change, joining two universes of Lorentzian signature through a Euclidean region which provides a `bounce'. We show that this process is viable both with and without matter present, but realistic models -- which have the signature change surfaces hidden inside the horizons -- require non-zero density. In fact the most realistic models are those that start as a finite cloud of collapsing matter, surrounded by vacuum. We consider how geodesics may be matched across a signature change surface, and conclude that the particle `masses' must jump in value. This scenario may be relevant to Smolin's recent proposal that a form of natural selection operates on the level of universes, which favours the type of universe we live in.Comment: LaTeX, 19 pages, 11 Figures. Replacement - only change is following comment: For a pdf version with the figures embedded, see http://www.mth.uct.ac.za/~cwh/mypub.htm