and (\[rho\_punto\]) are $$\begin{aligned}
\dot{H}&=-3H^{2} \label{Hpunto2}, \\ 
\dot{\rho}&=-3\gamma\rho H+18\eta_{0}F_{0}\frac{\rho^{\alpha_{1}}}{R^{3}}H^{2} \label{rhopunto2}.\end{aligned}$$ It is easy to see that $\dot{\varphi}\rightarrow0$ as it contains a positive power-law of the energy density and hence we can fix, without loss of generality, $\varphi\equiv 0$. The constraint equation (\[integrale2\]) reduces to the following relation $$\label{integrale3}
H=\sqrt{3}qR^{-3}.$$ Then, one can easily check that the leading order asymptotic solutions for $t\rightarrow0$ of the simplified Einstein equations (\[Hpunto2\]), (\[rhopunto2\]), (\[integrale3\]) read as $$\begin{aligned}
H&=\frac{1}{3t}, && \rho=Kt^{\frac{2}{\alpha_{1}-1}}, && R^{3}&=\sqrt{3}qt,\\
R_{i}&=\left(\sqrt{3}qt\right)^{p_{i}}, && p_{i}=\frac{1}{3}+\frac{s_{i}}{3q}\end{aligned}$$ where $K$ is a constant depending on the parameters of the model. In order the solutions to be asymptotically self-consistent, the relations above are applicable only when $\alpha_{1}>3$, slightly different with respect to the results given by the Eckart approach in [@BK_Bianchi] where $\alpha_{1}>1$. It is worth noting that we found that the energy density in this causal model decays more rapidly to zero with respect to the non-regularized case studied in [@BK_Bianchi] by Belinskii and Khalatnikov (BK) where $$\rho^{BK}\sim t^{\frac{1}{\alpha_{1}-1}},\qquad\alpha_{1}>1.$$ In other words, we see how the Lichnerowicz approach leads to a cosmological model in which the universe emerges from the singularity with a greater matter-rate creation with respect to the Eckart case.

Viscous dynamics in the isotropic 