Scalar field cosmologies with barotropic matter: models of Bianchi class B

We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter conten t is composed of two noninteracting components; the first component is desc ribed by a barotropic fluid having a gamma-law equation of state, whilst th e second is a non-interacting scalar field phi with an exponential potentia l V(phi) = Lambda e(k phi). In particular, we study the asymptotic properti es of the models both at early and late times, paying particular attention to whether the models isotropize (and inflate) to the future, and we discus s the genericity of the cosmological scaling solutions.