Abstract
We consider a cosmological model dominated by bulk viscous matter with total bulk viscosity coefficient proportional to the velocity and acceleration of the expansion of the universe in such a way that $\zeta=\zeta_{0}+\zeta_{1}\frac{\dot{a}}{a}+\zeta_{2}\frac{\ddot{a}}{\dot{a}}.$ We show that there exist two limiting conditions in the bulk viscous coefficients, ($\zeta_{0}$, $\zeta_{1}$, $\zeta_{2}$) which corresponds 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 the limiting conditions. A recent acceleration would occur if $\tilde{\zeta}_{0}+\tilde{\zeta}_{1}>1$ for the first limiting conditions and if $\tilde{\zeta}_{0}+\tilde{\zeta}_{1}<1$ 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 $z\leq0.8$. 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 $\Lambda$CDM model at present, but shows a de Sitter type behavior in the far future of the evolution.
Highlights
It was noted by several authors that the bulk viscous fluid can produce an acceleration in the expansion of the universe
A shortcoming in considering the bulk viscous fluid is the problem of finding a viable mechanism for the origin of bulk viscosity in the expanding universe
Bulk viscosity arises as an effective pressure to restore the system back to its thermal equilibrium, which was broken when the cosmological fluid expands too fast
Summary
It was noted by several authors that the bulk viscous fluid can produce an acceleration in the expansion of the universe. This was first studied in the context of inflationary phase in the early universe [18,19]. It is effectively a two parameter model In this reference the authors have ruled out the possibility of bulk viscous matter to be a candidate for dark energy. We think that one should study the model by evaluating all the parameters simultaneously, which may lead to a more mature conclusion regarding the status of bulk viscous dark matter as dark energy.
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