We consider a cosmological model dominated by bulk viscous matter with a total bulk viscosity coefficient proportional to the velocity and acceleration of the expansion of the universe in such a way that ζ = ζ 0 + ζ 1ȧ a + ζ 2ä a . We show that there exist two limiting conditions in the bulk viscous coefficients (ζ 0 , ζ 1 , ζ 2 ) which correspond to a universe having a Big Bang at the origin, followed by an early decelerated epoch and then making a smooth transition into an accelerating epoch. We have constrained the model using the type Ia Supernovae data, evaluated the best estimated values of all the bulk viscous parameters and the Hubble parameter corresponding to the two limiting conditions. We found that even though the evolution of the cosmological parameters are in general different for the two limiting cases, they show identical behavior for the best estimated values of the parameters from both limiting conditions. A recent acceleration would occur ifζ 0 +ζ 1 > 1 for the first limiting conditions and if ζ 0 +ζ 1 < 1 for the second limiting conditions. The age of the universe predicted by this model is found to be less than that predicted from the oldest galactic globular clusters. The total bulk viscosity seems to be negative in the past and becomes positive when z ≤ 0.8. So the model violates the local second law of thermodynamics. However, the model satisfies the generalized second law of thermodynamics at the apparent horizon throughout the evolution of the universe. We also made a statefinder analysis of the model and found that it is distinguishably different from the standard ΛCDM model at present, but it shows a de Sitter type behavior in the far future of the evolution.

The evolution of the bulk viscous matter dominated universe has been analysed using the full causal theory for the evolution of the viscous pressure in the context of the recent acceleration of the universe. The form of the viscosity is taken as ξ = αρ 1/2 . We obtained analytical solutions for the Hubble parameter and scale factor of the universe. The model parameters have been computed using the observational data. The evolution of the prominent cosmological parameters was obtained. The age of the universe for the best estimated model parameters is found to be less than observational value. The viscous matter behaves like a stiff fluid in the early phase and evolves to a negative pressure fluid in the later phase. The equation of state is found to be stabilised with value ω > −1. The local as well as generalised second law of thermodynamics is satisfied. The statefinder diagnostic shows that this model is distinct from the standard ΛCDM. One of the marked deviations seen in this model to be compared with the corresponding model using the Eckart approach is that in this model the bulk viscosity decreases with the expansion of the universe, while in the Eckart formalism it increases from negative values in the early universe towards positive values.

Abstract:We consider a Friedmann model of the universe with bulk viscous matter and radiation as the cosmic components. We study the asymptotic properties in the equivalent phase space by considering the three cases for the bulk viscous coefficient as (i) ζ = ζ 0 , a constant (ii) ζ = ζ 0 + ζ 1ȧ a , depending on velocity of the expansion of the universe and (iii) ζ = ζ 0 + ζ 1ȧ a + ζ 2ä a , depending both on velocity and acceleration of the expansion of the universe. It is found that all the three cases predicts the late acceleration of the universe. However, a conventional realistic behaviour of the universe, i.e., a universe having an initial radiation dominated phase, followed by decelerated matter dominated phase and then finally evolving to accelerated epoch, is shown only when ζ = ζ 0 , a constant. For the other two cases, it does not show either a prior conventional radiation dominated phase or a matter dominated phase of the universe.

The dynamical system behaviour and thermal evolution of a homogeneous and isotropic dissipative universe are analyzed. The dissipation is driven by the bulk viscosity and the evolution of bulk viscous pressure is described using the full causal Israel–Stewart theory. We find that for s  =  1/2 the model possesses a prior decelerated epoch which is unstable and a stable future accelerated epoch. From the thermodynamic analysis, we have verified that the local as well as the generalised second law of thermodynamics are satisfied throughout the evolution of the universe. We also show that the convexity condition is satisfied at the end stage of the universe which implies an upper bound to the evolution of the entropy. For , the case s  <  1/2 is ruled out since it does not predict the conventional evolutionary stages of the universe. On the other hand, the case s  >  1/2 does imply a prior decelerated and a late de Sitter epochs, but both of them are unstable fixed points. The thermal evolution corresponding to the same case implies that GSL is satisfied at both the epochs but convexity condition is violated by both, so that entropy growth is unbounded. Hence for s  >  1/2 the model does not give a stable evolution of the universe.

In our previous works, we have analyzed the evolution of bulk viscous matter dominated universe with a more general form for bulk viscous coefficient, ζ = ζ 0 +ζ 1ȧ a +ζ 2ä a and also carried out the dynamical system analysis. We found that the model reasonably describes the evolution of the universe if the viscous coefficient is a constant. In the present work we are contrasting this model with the standard ΛCDM model of the universe using the Bayesian method. We have shown that, even though the viscous model gives a reasonable back ground evolution of the universe, the Bayes factor of the model indicates that, it is not so superior over the ΛCDM model, but have a slight advantage over it.