Nonscalar singularities in spatially homogeneous cosmologies

Singularities in vacuum spatially homogeneous cosmological models are investigated. It is shown that in general the curvature scalarR _* ^abcd R^*abcddiverge and that the only solutions which have curvature singularities at which this scalar does not diverge describe certain plane-wave space-times. It is argued that with matter present these nonscalar singularities are even less likely to occur. The exceptional case of Bianchi type VI_–1/9 is not considered.     

Two Bianchi type VIII spatially homogeneous cosmologies

We study two Bianchi type VIII analogues of Taub space and maximal analytic extensions of them. The first one has SL(2,R) as an isometry group, which acts transitively on spacelike hypersurfaces. The maximal extension has all of the pathological features of Taub-NUT space. The second one has the universal covering group of SL(2,R) as an isometry group. The maximal extension of the latter does not have these pathological properties and is geodesically complete.Work supported in part by NSF Grant MPS 74-16311 AO1     

Exact solutions in Barker's homogeneous isotropic cosmologies

We derive a complete set of new exactk = 0, ±1 radiation solutions of Barker's homogeneous isotropic cosmologies. In the very early universe they reduce to the asymptotic solutions of Yepes and Dominguez-Tenreiro. Consistency with the standard cosmological model constrains the solution's free parameters.     

Power law singularities in orthogonal spatially homogeneous cosmologies

We investigate the structure of the so-called power asymptote singularities in orthogonal spatially homogeneous solutions of the Einstein field equations with perfect fluid source. We first give a systematic survey of the different possible power asymptotes, some of which are well known, and some new, and characterize them in a coordinate-independent manner. The known orthogonal spatially homogeneous exact solutions with perfect fluid source are then classified on the basis of which power asymptote they admit. In many cases this leads to simpler forms of the known solutions, and suggests methods for deriving new solutions.     

Using EXCALC to study nondiagonal multidimensional spatially homogeneous cosmologies

The exterior calculus package EXCALC2, developed by Schrüfer, is used to implement Siklos' method on a computer. By an appropriate choice of the 1-form basis of spatially homogeneous cosmological models, making use of the time-dependent automorphisms of the Lie algebra, it is possible to obtain a compact form of Einstein's field equations for general models of this type. The explicit expression of the equations, obtained with the help of EXCALC2, is given here for two nondiagonal five-dimensional spatially homogeneous models, namely G₁ and G₈. These equations constitute an ideal tool for the study of the dynamics of these models: an oscillatory behavior has been found for model G₁, while model G₈ exhibits a monotonous kasnerian mode of approach to the initial singularity.     

Anisotropic stresses in homogeneous cosmologies

Recently a certain class of homogeneous world models filled with perfect fluid have been discussed, [1, 2]. The corresponding results when anisotropic stresses are included are now examined.     

Exact scalar field cosmologies in a higher derivative theory

We obtain exact cosmological solutions of a higher derivative theory described by the Lagrangian L=R+2αR ² in the presence of interacting scalar field. The interacting scalar field potential required for a known evolution of the FRW universe in the framework of the theory is obtained using a technique different from the usual approach to solve the Einstein field equations. We follow here a technique to determine potential similar to that used by Ellis and Madsen in Einstein gravity. Some new and interesting potentials are noted in the presence of R ² term in the Einstein action for the known behaviours of the universe. These potentials in general do not obey the slow rollover approximation.     

Field equations for spatially homogeneous space-times

It is shown that there is a natural tetrad for each Bianchi type cosmological model in which the metric and field equations take a simple and convenient form.     

Some spatially homogeneous string cosmological models

The Einstein field equations of massive strings are solved completely with and without a source free magnetic field for the Bianchi type I metric in a different basic form. Some physical properties of the models are studied.     

Perfect fluid sources for spatially homogeneous spacetimes

Spatially homogeneous perfect fluid spacetimes are studied from a point of view which emphasizes the spatial geometry and the action of that subgroup of the spatial gauge group of the three-plus-one formulation of general relativity which is compatible with the spatial homogeneity. The specializations of the dynamics which correspond to the existence of additional spacetime symmetries are classified. An unconstrained set of gravitational and fluid variables is obtained by elimination of the gravitational constraints using an approach which obtains the gravitational evolution equations from a suitably modified Lagrangian/Hamiltonian formalism. A slightly different choice of variables is then described which allows one to take full advantage of the spatial gauge group and of the 1-parameter group of scale transformations of the unit of length.     

Stability of certain spatially homogeneous cosmological models

We investigate the general behavior of spatially homogeneous cosmological models at large times. Using existing techniques from stability theory we discover that some known exact solutions are asymptotically stable despite possessing special properties. Some consequences of these results are then discussed.This essay received an honorable mention from the Gravity Research Foundation for the year 1984-Ed.     

Some global properties of closed spatially homogeneous space-times

We consider some properties of the space-times which contain a spatially homogeneous domain of dependenceD(V), whereF is acompact achronal spatial hypersurface of homogeneity. For example, it is shown that ifV has a nonempty future Cauchy horizon then the timelike geodesies orthogonal toV are future incomplete and there is strong causality failure onH ⁺(V). Also, conditions for the global hyperbolicity of such space-times are obtained.     

Exact viscous fluid FRW cosmologies: The case of general k

Exact solutions of the Einstein field equations for a viscous fluid in which the geometrical part is identical to that of the FRW dust models with k = 0, ±1 is presented. The solutions have a radially flowing fluid, all necessary energy and thermodynamic conditions are satisfied, and all physical quantities are well behaved everywhere in space-time if the model is expanding.     

The behavior of null geodesics in a class of rotating space-time homogeneous cosmologies

The null geodesics are investigated in a class of open space-time homogeneous cosmological models with rotating sheared matter (Ozsváth classIII). Gödel's model is a special case. A stationary polar coordinate system is employed in which matter rotates rigidly. The geodesic equations are solved. Caustics and global rotation are discussed.     

The dynamical degrees of freedom in spatially homogeneous cosmology

The true analogues of superspace and conformal superspace for spatially homogeneous cosmology are introduced and discussed in relation to the kinematics of the evolution of Cauchy data from a spatially homogeneous initial value surface using a spatially homogeneous lapse function. Having fixed the slicing of spatially homogeneous spacetimes to be the natural one, an obvious restriction on the freedom of choice of the shift vector field occurs, and its relation to the three-dimensional diffeomorphism gauge group of the problem is explained. In this context the minimal distortion shift equation of Smarr and York naturally arises. Finally these ideas are used to simplify the dynamics.Work supported by NSF grant MCS-7621525