Cosmological volume acceleration in dust epoch: using scaling solutions and variable cosmological term Λ (t) within an anisotropic cosmological model

Under the premise that the current observations of the cosmic microwave background radiation set a very stringent limit to the anisotropy of the universe, we consider an anisotropic model in the presence of a barotropic perfect fluid and a homogeneous scalar field, which transits to a flat FRW cosmology for late times in a dust epoch, presenting an accelerated volume expansion. Furthermore, the scalar field is identified with a varying cosmological term via V(ϕ(t)) = 2 Λ (t). Exact solutions to the EKG system are obtained by proposing an anisotropic extension of the scaling solutions scenario: ρ∼ η^{− n}, ρ_ϕ∼ η^{− m}, with η³= a₁a₂a₃ the volume function of the anisotropic model (a₁, a₂, a₃ being the scale factors).