Inhomogeneous mixmaster universes: Some exact solutions

Algorithms for generating new exact solutions of the Einstein-Klein-Gordon field equations, which describe inhomogeneous universes with S³ topology of spatial sections, are developed. The known exact vacuum and stiff-fluid solutions with S³ topology are used as an input. The methods developed are further applied to derive inhomogenous generalizations of Bianchi type IX solutions and inhomogeneous S³ Gowdy models with gravitational and scalar waves. It is shown that the new solutions, which are generalizations of the Bianchi type IX models, permit identification of the scalar field with the velocity potential of the stiff irrotational fluid. The latter result is further used to study the growth rate of density perturbations of the isotropic and anisotropic Bianchi type IX universes in a fully nonlinear relativistic regime. The role of anisotropy of the rate of growth of density perturbations is studied in detail.