Bianchi cosmologies with anisotropic matter: Locally rotationally symmetric models

► A Bianchi spacetime is a spatially homogeneous cosmological model for the universe. ► Bianchi spacetimes are singular in the past (big bang) and sometimes in the future. ► The dynamics of Bianchi spacetimes are strongly influenced by the matter content. ► There exist Bianchi spacetimes of type IX which do not recollapse in the future. ► Bianchi spacetimes with Vlasov matter are oscillatory toward the big-bang singularity.