Cosmological volume acceleration in dust epoch: using scaling solutions and variable cosmological term $\Lambda(t)$ 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 anistropic 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. Furtheremore, the scalar field is identified with a varying cosmological term via $V(\phi(t))=2\Lambda(t)$. Exact solutions to the EKG system are obtained by proposing an anisotropic extension of the scaling solutions scenario: $\rm\rho\sim \eta^{-n},\ \rho_\phi\sim \eta^{-m}$, with $\rm\eta^3=a_1a_2a_3$ the volume function of the anistropic model ($\rm a_1,\, a_2,\, a_3$ being the scale factors).