We test a cosmological model which the only component is a pressureless fluid with a constant bulk viscosity as an explanation for the present accelerated expansion of the universe. We classify all the possible scenarios for the universe predicted by the model according to their past, present and future evolution and we test its viability performing a Bayesian statistical analysis using the SCP ``Union data set (307 SNe Ia), imposing the second law of thermodynamics on the dimensionless constant bulk viscous coefficient zeta and comparing the predicted age of the universe by the model with the constraints coming from the oldest globular clusters. The best estimated values found for zeta and the Hubble constant Ho are: zeta=1.922 pm 0.089 and Ho=69.62 pm 0.59 km/s/Mpc with a chi^2=314. The age of the universe is found to be 14.95 pm 0.42 Gyr. We see that the estimated value of Ho as well as of chi^2 are very similar to those obtained from LCDM model using the same SNe Ia data set. The estimated age of the universe is in agreement with the constraints coming from the oldest globular clusters. Moreover, the estimated value of zeta is positive in agreement with the second law of thermodynamics (SLT). On the other hand, we perform different forms of marginalization over the parameter Ho in order to study the sensibility of the results to the way how Ho is marginalized. We found that it is almost negligible the dependence between the best estimated values of the free parameters of this model and the way how Ho is marginalized in the present work. Therefore, this simple model might be a viable candidate to explain the present acceleration in the expansion of the universe.
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