Integrability and explicit solutions in some Bianchi cosmological dynamical systems
arXiv:gr-qc/0101127 · doi:10.2991/jnmp.2001.8.1.9
Abstract
The Einstein field equations for several cosmological models reduce to polynomial systems of ordinary differential equations. In this paper we shall concentrate our attention to the spatially homogeneous diagonal G_2 cosmologies. By using Darboux's theory in order to study ordinary differential equations in the complex projective plane CP^2 we solve the Bianchi V models totally. Moreover, we carry out a study of Bianchi VI models and first integrals are given in particular cases.