corresponding Eckart formulation (i.e. asymptotically to the singularity $F$ becomes a power-law in the energy density of the viscous fluid). We conclude this section by observing that the power-law solution (\[Htimepower\]), (\[rho4\]), (\[gammaeff\]) can be extended to the negative and positive curved Robertson-Walker geometry [^2], as far as the effective polytropic index $\gamma_{eff}$ remains greater than $2/3$. Under such a restriction, the spatial curvature term (behaving like $R^{-2}$), is asymptotically negligible near the singularity with respect to both the energy density $\rho$ and the viscous contribution. The situation is different in the case of the power-law inflation, when $\gamma_{eff} < 2/3$, since the curvature term can play a relevant role. However, this is a typical feature of the inflationary-like solutions, whose existence requires the spatial gradients to be sufficiently smooth [@KT90]. From a physical point of view, if we cut our asymptotic regime at the Planck time (assuming that before the quantum dynamics is concerned), we could require that the spatial curvature is, at that time, sufficiently small and then it will become negligible forward in time.

Conclusions {#conclusions .unnumbered}
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We have studied the influence of a viscous cosmological fluid on the Bianchi I Universe dynamics in the neighborhood 