that the time derivative of $F$ yields $$\dot{F}=\left(3H+\frac{\dot{\rho}}{\rho}\right)F.$$ Then, in this limiting case, the Einstein equations take the form $$\begin{aligned}
\dot{H}&=\chi\left(1-\frac{1}{2}\gamma\right)\rho-3H^{2}+3\chi\zeta  FH+\frac{1}{2}\chi\zeta F\frac{\dot{\rho}}{\rho}, \label{Hpunto3}  \\ 
\dot{\rho}&=-3H\gamma\rho+18H^{2}\varsigma F+3H\varsigma  F\frac{\dot{\rho}}{\rho}. \label{rhopunto3}\end{aligned}$$ For the bulk viscosity coefficient in the limit of large density, we still have a power-law behavior of the type: $$\begin{aligned}
 \zeta=\zeta_{2}\rho^{\beta_{2}}, && \rho\rightarrow\infty, && 0\leq\beta_{2}\leq\frac{1}{2}\,. \label{visc2}
 \end{aligned}$$ Notice that we are using a different subscript with respect to equation (\[visc1\]), corresponding to a different asymptotic region of the energy density. The solutions of the full-set of the field equations given by (\[H\]), (\[integrale3\]), (\[Hpunto3\]) and (\[rhopunto3\]) are investigated assuming that the energy density and the volume are evolving like powers of time according to the relations $$\begin{aligned}
 \label{timepowers}
 \rho=\rho_{0}t^{y}, && R^{3}=R_{0}^{3}t^{x}, && y<0, && x>0,
 \end{aligned}$$ as the time $t\rightarrow 0$. As a consequence, the viscosity evolves trough the following expression $$\zeta=\zeta_2{\rho_0}^{\beta_{2}}{t}^{\beta_{2} y}.$$ From equation (\[timepowers\]) with the use of (\[H\]) we immediately get $$\label{Htimepower}
 H=\frac{x}{3t}.$$ Using equation (\[Hpunto3\]) and being $\dot{H}\sim t^{-2}$, it is necessary that $y=-2$ in order the system to be self-consistent. Similar arguments lead us to conclude that $$\label{x_beta}
  x=2\beta_{2}+1.$$ Then, one finds the following evolutions in terms of $t$ for the energy density and the 