Title:

Selfsimilar cosmological models

The Universe today is observed to be extremely homogeneous and isotropic on large scales. The dipole anisotropy of the microwave background, due to the relative motion of the Earth, is measured to be less than one part in 10 4. The quadropole component, due to intrinsic anisotropies, is even smaller. Thus, any viable mathematical or physical description of the large scale properties of the Universe must encompass the observational evidence and reflect this large degree of uniformity. The most popular, and certainly the most successful, description of the Universe at the present epoch is provided by the FriedmannRobertsonWalker (FRW) cosmological models. These spherically symmetric models consider the Universe as an isotropic, spatially homogeneous, perfect fluid matter distribution, which is in a state of dynamic evolution. All of the FRW cosmologies exhibit an expansion, i. e. the volume of the spatial sections varies with time, during some stage of their evolution, in agreement with the observed expansion of the Universe. An important consequence of this behaviour is that it leads to a singularity at a finite time in the past when the volume of the spatial sections becomes zero and matter becomes infinitely dense and infinitely hot (the hot Big Bang scenario). The isotropy and homogeneity of the Universe at the present epoch, cannot necessarily be extrapolated back to these earlier times. Certainly, there must exist inhomogeneities on small scales at all epochs in order to produce the observed structure, such as galaxies, clusters and superclusters. This raises the question of the effect of anisotropy on the initial stages of the evolution of the Universe. In this thesis we consider cosmological models which differ significantly from the FRW descriptions. We consider the effect of a large cosmological constant (vacuum energy term) on the behaviour of a spherically symmetric anisotropic universe, characterised by different expansion rates in the radial and transverse directions. The analysis is simplified considerably by imposing the condition that the model admits a selfsimilar symmetry. The techniques of similarity and dimensional analysis are employed to obtain a class of spatially inhomogeneous solutions to the Einstein field equations with a nonzero cosmological term. These solutions are found to contain some which tend asymptotically to a deSitter FRW solution and thereby extend the cosmological "nohair" theorems, which state that under certain restrictions any model containing a large positive cosmological term will evolve to a deSitter cosmology at late times. Such models are attractive since they tend to isotropic spacetimes. Similarity methods are also applied to the study of an anisotropic spacetime with an imperfect fluid as source. The fluid description of the cosmology is chosen to include the dissipative processes of shear and bulk viscosity but to neglect the effects due to the existence of magnetic fields, heat conduction or acceleration along the flow lines. In order to obtain a selfsimilar description of such a fluid we must impose certain conditions on the form of the viscous coefficients of bulk and shear. This allows a degree of tractability but restricts the physical significance of the models. Solutions are found for which the matter distribution acts as (i) a 'presureless fluid' with an equation of state given by T11=0 and (ii) a 'stiff' fluid with equation of state, T1 1=T0 0. The conditions under which the Universe may attain either of these extreme properties are discussed in relation to the physical processes occurring in the matter distribution at different epochs. It is found that the presence of viscosity has a marked effect on the dynamics of the Universe, particularly at early times. The selfsimilar viscous models with a stiff equation of state are then considered with respect to the formation of black holes in the early Universe. The difficulties of obtaining a smooth continuation of the viscous solutions from the Universe particle horizon to a black hole event horizon are discussed in view of the limitations encountered in the nonviscous black hole solutions. Finally, the possibility of future investigations inspired by the considerations of this thesis are discussed. In particular, the determination of a geometric symmetry corresponding to selfsymmetry of the second kind and the formation of a selfconsistent similarity treatment of imperfect fluid cosmologies are deemed important. Possible lines of research to these ends are considered.
