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In this work we test the capability of an exact solution found in theframework of a non linear extension of the Israel-Stewart theory to fit thesupernovae Ia data. This exact solution is a generalization of one previouslyfound in the context of the near equilibrium description of dissipativeprocesses, where a dissipative unified dark matter model is studied, suchgeneralized solution does not represent the full regime of the non linearpicture, we restrict ourselves to the case where a positive entropy productionis guaranteed. It is found that for some specific values of the parameter thatcharacterizes the non linear effects, namely $k$, the $\chi^{2}_{min}$ valueobtained from the statistical analysis is slightly lower than the correspondingone to the $\Lambda$CDM model. Given that we are dealing with a more realisticdescription of the fluid we must introduce more free parameters, this resultsas evidence against the model based on the BIC value. However, despite thisstatistical drawback we find that this model could be a good candidate to mimicthe $\Lambda$CDM model for redshift values at $z<1$. In this sense, we showthat the non linear regime of the Israel-Stewart theory describes consistentlythe recent accelerated expansion of the universe without the inclusion of somekind of dark energy component.

Testing a non linear solution of the Israel-Stewart theory with supernovae