Tilted homogeneous cosmological models

We examine spatially homogeneous cosmological models in which the matter content of space-time is a perfect fluid, and in which the fluid flow vector is not normal to the surfaces of homogeneity. In such universes, the matter may move with non-zero expansion, rotation and shear; we examine the relation between these kinematic quantities and the Bianchi classification of the symmetry group. Detailed characterizations of some of the simplest such universe models are given.     

Spatially homogeneous cosmological models

We study nonviscous and viscous fluids in Bianchi types II, VIII, and IX space-times under the restriction that the ratio of shear to expansion be constant.     

A class of homogeneous cosmological models

Einstein's field equations are studied under the assumptions that (1) the source of the gravitational field is a perfect fluid, and (2) there exists a group of motions simply transitive on three-surfaces orthogonal to the fluid flow vector. There are two classes of solutions; these are studied in detail. Three special families of solutions examined include all analytic solutions of the field equations obeying (1) and (2) of which the authors are aware. The relation of these solutions to various vacuum solutions is indicated.     

A class of homogeneous cosmological models

This paper discusses the application of geometric optics to the study of observational properties of cosmological models examined in a previous paper. A number of results concerning these properties are derived, the most interesting of which is the invariance of observational relations under certain discrete isotropy groups. Closed form expressions are obtained in certain cases.     

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.     

Gauge-invariant perfect-fluid Robertson-Walker perturbations

In the preceding paper, a complete set of basic gauge-invariant variables was defined that uniquely characterizes cosmological perturbations in homogeneous, isotropic, ideal-fluid universe models. The calculations were presented in some detail for the case of a general perfect fluid with two essential thermodynamic variables. Among other things, it was demonstrated that the aforementioned set consists of 17 linearly independent, not identically vanishing gauge-invariant variables. One can think of these basic variables as having two aspects. First, their definitions are such that they provide a unique representation of the physical perturbation. (By way of digression, inspection shows that such perturbations can be regarded as being the elements of a certain quotient space.) Second, any complicated gauge-invariant quantity is obtainable directly from the basic variables through purely algebraic and differential operations. The object here is the systematic derivation of the linear propagation equations governing the evolution of these basic variables. To make clear the relation of the present formalism to a series of standard results in the literature, this paper also points out how general propagation equations can be adapted to situations where the pressure vanishes in the background. Finally, the physical interpretation of basic variables and comparison with other gauge-invariant approaches are briefly presented.     

Dipole and quadrupole anisotropies in homogeneous cosmological models

We calculate the relative strengh of the dipole and quadrupole anisotropies of the cosmic background raidiation in homogeneous anisotropic cosmologies. We find that the quadrupole amplitude typically exceeds the dipole one, especially for the curvature-driven mode of anisotropy.     

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.     

Higher-dimensional homogeneous cosmological models as autonomous dynamical systems

The field equations for homogeneous models in an arbitrary number of dimensions form a Hamiltonian system with constraint forces. Due to the monotonic behavior of the determinant of the induced metric, the evolution of the system can be interpreted as the motion of a particle in an explicitly time-dependent potential. Considering vacuum models, we show that this explicit time-dependence can be eliminated. Using the scaling properties of the Ricci tensor we obtain an autonomous system, for which we can also find a Liapunov function in terms of the n-dimensional Ricci curvature.     

Inhomogeneous cosmological models with homogeneous inner hypersurface geometry

Space-times which allow a slicing into homogeneous spatial hypersurfaces generalize the usual Bianchi models. One knows already that in these models the Bianchi type may change with time. Here we show which of the changes really appear. To this end we characterize the topological space whose points are the 3-dimensional oriented homogeneous Riemannian manifolds; locally isometric manifolds are considered as identical.     

What initial perturbations may be generated in inflationary cosmological models

Isothermal (isoinflaton) perturbations generated in cosmological models at the inflationary stage are discussed. The spectrum of such perturbations has been calculated for the example of a cosmological model with axion-type matter. The possibility of the cut-off of the spectrum at long wavelengths has been shown. This leads to the suppression of large-scale fluctuations of the temperature of the background radiation.     

The singularity of homogeneous cosmological models with electromagnetic fields

The regime of approaching the singularity in the presence of electromagnetic fields has been found. The rotation angles of the Kasner axes are calculated.     

Gauge-invariant perturbations for a collapsing dust sphere

We study the first-order gauge-invariant perturbations of the metric (the scalar type), the energy density and the four-velocity of matter inside a collapsing homogeneous sphere of dust. Unless in a particular case, these perturbations grow towards the end of the collapse.