scale-factor $$\begin{aligned}
 \rho=\frac{x^{2}}{3\chi}t^{-2}, \label{rho4}\\
 R={R_0} t^{\frac{2}{3\gamma_{eff}}}, && \gamma_{eff}\equiv\frac{2}{2\beta_{2}+1}. \label{gammaeff}
 \end{aligned}$$ where we introduced an effective equation of state $\gamma_{eff}$. One can check that $\gamma$ is related to $\beta_{2}$ via the following expression $$\label{gamma1}
\gamma=\frac{2}{2\beta_{2}+1}\left[\frac{1}{1-4\beta_{2}(2\beta_{2}+1)^{\beta_{2}}\frac{\zeta_{2}R_{0}^{3}}{(3\chi)^{\beta_{2}}\mu_{0}}}\right].$$ Furthermore, one can see that the regulator evolves with time as $$\label{F_t}
 F\sim t^{2\beta_{2}-1}$$ which is asymptotically growing when $0\leq\beta_{2}<1/2$ and reduces to a positive constant when $\beta_{2}=1/2$, leading to well-behaving regularized solutions. An interesting additional feature stands out from the behavior of the scale factor $R$. When the Robertson-Walker geometry is coupled to an ideal fluid the volume typically evolves as $R_{RW}\sim t^{\frac{2}{3\gamma}}$. Here we observe that we still have an isotropic limit, as it is found in [@BK_Bianchi], but instead of being negligible, the viscosity acquires a fundamental role in the dynamics of the Universe, driving the evolution trough an effective equation of state. Indeed, the range of the possible values of $R$ in (\[gammaeff\]) perfectly coincides with the standard non-viscous homogeneous and isotropic universe. In particular,

-   for $\beta_{2}=1/2$ we have $R\sim t^{\nicefrac{2}{3}}$: the universe maps a dust-dominated Friedmann Universe with an effective equation of state $\gamma_{eff}=1$;

-   for $\beta_{2}=0$ we get $R\sim t^{\nicefrac{1}{3}}$: the solution evolves toward a stiff-matter dominated Universe with 