Power Asymptotes of Homogeneous Cosmological Models in Einstein's Theory of Gravitation

For the Bianchi-types I, V, VII, VIII, and IX, the asymptotes of the metric, which show a power-like dependence on the synchronized time t near the cosmological singularity, are investigated. Comparing the influence of the terms which in Einstein's equations describe time-derivatives, spatial curvature, and matter, on the behaviour of the asymptotes, different assumptions and conjectures usually used in literature are discussed for the equations of state p = β? (0 ? β ? 1). For Bianchi-type-IX models both the outgoing power-asymptotes and the oscillatory phase for t → 0 are considered.