a clear physical meaning. In fact, as far as such a restriction holds, the negative effective pressure, due to bulk viscosity, behaves like $\rho^{\beta_{2}+\nicefrac{1}{2}}<\rho$, for large $\rho$ values. This means that the standard (positive) thermodynamical pressure $p = (\gamma - 1)\rho$ remains always the dominant contribution. This is coherent with the idea that the bulk viscosity representation of non-equilibrium effects is valid only on a perturbative level. Clearly, the presence of the regulator $F$ slightly changes this situation since it enhances the weight of viscosity in the dynamics and this is at the ground of the present results. Nonetheless, the regime $\beta_{2}>1$ can be qualitative interpreted as a fluid-like representation for strong non-equilibrium effects, not surprising in the limit of the singularity, when the geometrical velocity of Universe collapse diverges. Thus, the power-law inflation solution we find in such an extreme regime can be thought as the qualitative feature induced by a cosmological continuous source, whose thermodynamical evolution can not be approximated via equilibrium stages. If we accept a fluid representation for such a limiting scenario, we can argue that the superluminar geometrical velocity of the early phases of the Universe expansion is able to open the horizon size, making 