an equation of state with an effective dependence on viscosity; ii) when bulk viscosity fully dominates the dynamics with allowance made for strong non-equilibrium effects ($\beta_{2}>1$), we see that the universe evolves trough a power-law inflation solution to the initial singularity, implying the divergence of the cosmological horizon and the subsequent disappearance of the Universe light-cone. Entropy production has been addressed in the isotropic Robertson-Walker limit and specifically for dominant viscosity, where entropy tremendously grows. Despite one may argue whether or not the above-mentioned fluid description is possible in this extreme regime of dominant bulk viscosity, the issues above strongly suggest that a comprehensive understanding of the Universe birth and of the so-called horizon and entropy paradox can not be achieved before a clear account of the non-equilibrium thermodynamical evolution near the singularity will be properly provided.

Acknowledgements {#acknowledgements .unnumbered}
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This paper has been developed within the CGW collaboration (www.cgwcollaboration.it) and supported by the *TornoSubito* project. We would like to thank Riccardo Moriconi for his valuable assistance in the numerical integration of the model. M. V. is thankful to Dr. Shabnam Beheshti who significantly motivated and assisted this work and to Queen Mary, University of London for providing all 