Anisotropic and inhomogeneous cosmologies

Inhomogeneous and anisotropic cosmologies

“…Bardeen, Brandenberger, Dunsby and Ellis) gave very full discussions of perturbation theory. Here I continue my previous practice (MacCallum 1979(MacCallum , 1984, by using the mathematical classification of the solutions as an overall scheme of organization; the earlier reviews give additional details and references. (A survey organized by the nature of the applications is to appear in the proceedings of Dennis Sciama's 65th birthday meeting.)…”

Selected Solutions of Einstein’s Field Equations: Their Role in General Relativity and Astrophysics

“…Some of these models had already appeared in the PhD thesis of Kip Thorne in 1965 (see also [303] for magnetic Kantowski-Sachs models). Here, however, we just refer the reader to [304,305] for their classical description, to [306] for a canonical and quantum treatment, and to [307] for the latest discussion of the Kantowski-Sachs quantum cosmologies.…”

“…It is less known that at approximately the same time, if not earlier, the first explicit spatially homogeneous expanding and rotating cosmological models with matter (of the Bianchi type IX) were constructed by Gödel, An exposition of Bianchi models has been given in a number of places: in the account on relativistic cosmology by Heckmann and Schücking [308] (complementing the chapter on exact solutions by Ehlers and Kundt [53]), in the monographs of Ryan and Shepley [304], and Zel'dovich and Novikov [309], in several comprehensive surveys by MacCallum (see e.g. [305] and [310] for his latest review containing a number of references), most recently, in the book on the dynamical system approach in cosmology (in the Bianchi models in particular) edited by Wainwright and Ellis [311]; and, first but not least, in the classics of Landau and Lifshitz [139]. The Hamiltonian approach initiated by Misner [312] in 1968, and used in, amongst other things, the construction of various minisuperspace models in quantum gravity, has been reviewed by Ryan [266]; for more recent accounts, see several contributions to Misner's Festschrift [313].…”

Tilted Bianchi Type IX Dust Fluid Cosmological Model in General Relativity

“…In these models, neutrino viscosity explains the large radiation entropy in the universe and the degree of isotropy of the cosmic background radiation. The standard cosmological models are too restrictive because of the insistence on the isotropy of the physical three spaces; several attempts have been made to study nonstandard cosmological models [1][2][3]. It is therefore interesting to carry out the detailed studies of gravitational fields, which are described by space-time of various Bianchi types.…”