of the initial singularity. The characterizing aspect of the presented analysis consists of describing the viscous fluid via the Lichnerowicz formulation, introducing a causal regulator (the index of the fluid) in order to ensure a causal dynamics. We have also pointed out how this additional new degree of freedom must be properly linked to the geometrical and thermodynamical variables. We have investigated the role of the two viscosity coefficients in two different limits, when only one of them is dynamically relevant. The shear viscosity has been taken into account in the case of an incompressible fluid, evaluating the modification that the regulator introduces in the well-known solution with matter creation derived in [@BK_Bianchi]. We have shown that such a peculiar phenomenon, characterized by an asymptotically vanishing energy density, not only survives in the Lichnerowicz formulation but it is actually enhanced. The presence of a bulk viscosity term has been analyzed in the isotropic limit of the Bianchi I cosmology and again asymptotically to the initial singularity. We derived a power-law solution, which outlines some interesting features: i) the standard non-viscous Friedmannian behavior is encountered when bulk viscosity is a small deviation from equilibrium ($\beta_{2}<\nicefrac{1}{2}$), but this time the fluid presents 