BIANCHI-V IMPERFECT FLUID COSMOLOGY

Bianchi V, spatially homogeneous imperfect fluid cosmological models which contain both viscosity and heat flow are investigated. The Einstein field equations are established in the case that the equations of state are given by p-(γ-1)ρ, ζ=ζo ρm, and η=ηoρn (where γ, ζo, ηo, m and n are constants). The physical constraints on the solutions of the Einstein field equations, and, in particular, the thermodynamical laws and energy conditions that govern such solutions, are discussed in some detail. Simple power law solutions and solutions in which there is no heat conduction are studied first. Exact solutions are then investigated in more generality, and it is shown that there exist two first integrals of the field equations for certain values of the physical parameters γ, m and n. Finally, it is shown that in a special case of interest (in which m =n = 1/2) the imperfect fluid Bianchi V field equations can be written as a plane-autonomous system, thus facilitating the qualitative analysis of these cosmological models. © 1990 Plenum Publishing Corporation.