Preface

Summary

This work is a review of inhomogeneous cosmological exact solutions of the Einstein equations and their properties. A solution is, by definition, cosmological if it can reproduce any metric of the Friedmann (1922, 1924)–Lemaître (1927, 1931)– Robertson (1929, 1933)–Walker (1935) class (abbreviated FLRW) by taking limiting values of arbitrary constants or functions. The book is intended to attain two objectives: (i) to list all independently derived cosmological solutions and reveal all interconnections between them; (ii) to collect in one text all discussions of the physical properties of our Universe based on inhomogeneous models. Objective (i) is attained by showing that the more than 300 independently published solutions can be derived by limiting transitions from about 60 parent solutions. The solutions are arranged in relatively few disjoint families, and a few of them have been rediscovered up to 20 times. In attaining objective (ii) it is shown that exact inhomogeneous solutions can describe several features of the Universe in agreement with observations. Examples are the presence of voids and high-density membranes in the distribution of mass or the fluctuations of temperature of the microwave background radiation. Among the effects predicted are: (i) cosmological expansion of planetary orbits (unmeasureably small, but nonzero); (ii) prevention of the Big Bang singularity by an arbitrarily small charge anywhere in the Universe. In addition, papers that have discussed averaging the small-scale Einstein equations to obtain large-scale cosmological field equations have been reviewed.