5 - Cosmology: nondiagonal metrics and perturbed FLRW

Summary

In this chapter we continue describing soliton solutions in cosmological models but now we concentrate on nondiagonal metrics and on backgrounds other than Kasner.

In section 5.1 soliton solutions with two polarizations are discussed. Although in this case explicit expressions for the metric coefficients cannot be displayed in general, a fairly complete understanding of these metrics and their relevance as cosmological models is possible. As in chapter 4, the metrics are also classified in terms of real and complex poles. In section 5.2 soliton solutions obtained from anisotropic Bianchi type II metrics are considered. In section 5.3 a solution describing the nonlinear interaction between a gravitational pulse wave and soliton-like waves is described. A polarization angle and wave amplitude are defined and used to characterize the interaction. As a consequence of the nonlinear interaction of the waves a time shift in the pulse-wave trajectory is observed. Finally, in section 5.4 we discuss soliton solutions which describe finite cylindrical perturbations on FLRW isotropic cosmological models. Models representing perturbations on the late time behaviour of low density open FLRW are derived and studied. Soliton solutions when a massless scalar field is coupled to the gravitational field, and their interpretation either as perfect fluids of stiff matter or as anisotropic fluids are described, together with some solutions representing perturbations on an FLRW model with stiff matter. Perturbations on more realistic radiative FLRW are also discussed, as well as related solutions of the Brans–Dicke theory.