We present and constrain a cosmological model where the only component is a pressureless fluid with bulk viscosity as an explanation for the present accelerated expansion of the universe. We study the particular model of a bulk viscosity coefficient proportional to the Hubble parameter. The model is constrained using the SNe Ia Gold 2006 sample, the Cosmic Microwave Background (CMB) shift parameter R, the Baryon Acoustic Oscillation (BAO) peak A and the Second Law of Thermodynamics (SLT). It was found that this model is in agreement with the SLT using only the SNe Ia test. However when the model is constrained using the three cosmological tests together (SNe+CMB+BAO) we found: 1.- The model violates the SLT, 2.- It predicts a value of H_0 approx 53 km sec^{-1} Mpc^{-1} for the Hubble constant, and 3.- We obtain a bad fit to data with a chi^2_{min} approx 532. These results indicate that this model is viable just if the bulk viscosity is triggered in recent times.
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