Dissipative or Conservative cosmology with dark energy ?

All evolutional paths for all admissible initial conditions of FRW cosmological models with dissipative dust fluid (described by dark matter, baryonic matter and dark energy) are analyzed using dynamical system approach. With that approach, one is able to see how generic the class of solutions leading to the desired property -- acceleration -- is. The theory of dynamical systems also offers a possibility of investigating all possible solutions and their stability with tools of Newtonian mechanics of a particle moving in a 1-dimensional potential which is parameterized by the cosmological scale factor. We demonstrate that flat cosmology with bulk viscosity can be treated as a conservative system with a potential function of the Chaplygin gas type. We also confront viscous models with SNIa observations. The best fitted models are obtained by minimizing the $\chi^{2}$ function which is illustrated by residuals and $\chi^{2}$ levels in the space of model independent parameters. The general conclusion is that SNIa data supports the viscous model without the cosmological constant. The obtained values of $\chi^{2}$ statistic are comparable for both the viscous model and LCDM model. The Bayesian information criteria are used to compare the models with different power law parameterization of viscous effects. Our result of this analysis shows that SNIa data supports viscous cosmology more than the LCDM model if the coefficient in viscosity parameterization is fixed. The Bayes factor is also used to obtain the posterior probability of the model.