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.     

A class of homogeneous cosmological models III: Asymptotic behaviour

The behaviour near to and far from an initial singularity in a broad subclass of the models studied in previous papers [1–3] is examined. The influence of the matter on the evolution at these times is discussed. The singularity types for the various models, which are mostly of cigar or oscillatory nature, are found. It is discovered that among these models, only those of the same Bianchi type as a Robertson-Walker model can become approximately Robertson-Walker in a sense defined in the paper. Qualitative conclusions concerning black-body isotropy, the Hubble relation, helium abundance and horizon structure are given.     

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 inhomogeneous cosmological models

All solutions of Einstein's field equations representing irrotational dust and possessing a metric of the formds ²=dt ²?e ^2α dr ²?e ^2β(dy ²+dz ²) are found. The new metrics generalize the earlier Bondi-Tolman, Eardley-Liang-Sachs, and Kantowski-Sachs cosmological models.     

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.     

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.     

Gauge-invariant perturbations in anisotropie homogeneous cosmological models

In a recent paper K. Tomita and M. Den found a set of coupled differential equations for spatially flat, anisotropic homogeneous,N- dimensional cosmological models. Some particular exact solutions of those differential equations for a few specific equations of state were obtained by D. Lorentz-Petzold. In the present work we solve those differential equations completely.     

A class of stationary rotating string cosmological models

We obtain a one parameter class of stationary rotating string cosmological models of which the well-known Gödel universe is a particular case. By suitably choosing the free parameter function, it is always possible to satisfy the energy conditions. The rotation of the model hinges on the cosmological constant which turns out to be negative. String-dust distribution in Gödel-type universes is also briefly discussed.     

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.     

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.     

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.     

A new class of cosmological models in Lyra geometry

FRW models have been studied in the cosmological theory based on Lyra’s geometry. A new class of exact solutions has been obtained by considering a time dependent displacement field for constant deceleration parameter models of the universe. Dedicated to Professor V B Johri on his sixtieth birthday.     

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.     

A new class of inhomogeneous cosmological models with Yang-Mills fields

Exact solutions corresponding to spherically symmetric inhomogeneous nonstationary Tolman metrics are obtained for the self-consistent system of Einstein-Yang-Mills equations for the gauge group SO ₃ . Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 65–70 (25 July 1996)     

An interesting property of the isotropic and homogeneous cosmological models

It is shown by using covariant expressions that in the framework of the isotropic and homogeneous cosmology the gravitational energy and matter energy, the gravitational and matter linear and angular momentum, cancel each other out locally, resulting in the corresponding global quantities being zero.     

Higher symmetries in a class of cosmological models

A particular class of solutions of Einstein's field equations, in which the source is a perfect fluid and the geometry admits a two-parameter Abelian isometry group with spacelike orbits, is examined for the possible admission of higher symmetries. It is shown that in certain cases the geometry is spatially homogeneous, being either of the orthogonal Bianchi type I or of the tilted Bianchi-Behr type VIU_h withh = –4, and that no other cases of higher symmetry (in the sense of isometry groups) are possible. The global behaviour of the Bianchi-Behr type VIU_h, models is studied, and conformal diagrams are given. This investigation is extended to the case when additional homothetic vectors are admitted, and a parallel study of the global behaviour, complete with conformal diagrams, is provided. A brief argument also shows that, within the class considered, whenever the fluid flow-lines possess identical thermal histories, the geometry is necessarily spatially homogeneous.