The scope of this review

Ever since the 1930s, it has been conventional wisdom in cosmology that the Friedmann (1922, 1924)–Lemaître (1927, 1931)–Robertson (1929, 1933)–Walker (1935) (FLRW) models describe the large-scale properties of our observed Universe faithfully. At the same time, it has been conventional wisdom in relativity theory that finding exact solutions of the Einstein equations is extremely difficult and possible only for exceptionally simple cases. Both these views were challenged repeatedly by lone rebels, but a few generations of physicists and astronomers have been educated with these conventional wisdoms solidly incorporated into their minds. As a result of this situation, a large body of literature has come into existence in which exact solutions generalizing FLRW have been derived and applied to the description of our observed Universe, but most of it remains unknown to the physics community and is not being introduced into textbooks. This book is intended to achieve the following two objectives:

1. To list all the independently derived cosmological solutions of the Einstein equations and to reveal all the interconnections between them.

2. To compile an encyclopaedia of physics in an inhomogeneous Universe by gathering together all physical conclusions drawn from such solutions.

An exact solution of the Einstein equations is termed “cosmological” if it can reproduce a FLRW metric when its arbitrary constants or functions assume certain values or limits. This requirement will be discussed in Section 1.2. The solutions are organized into a few families.