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.

\begin{abstract} The accelerated expansion of the universe can be interpreted as a tendency to satisfy the holographic equipartition. It can be expressed by a simple law, $\Delta V = \Delta t\left(N_{surf}-\epsilon N_{bulk}\right),$ where $V$ is the Hubble volume in Plank units, $t$ is the cosmic time plank units and $N_{surf/bulk}$ is the degrees of freedom on the horizon/bulk of the universe. We show that this holographic equipartition law effectively implies the maximization of entropy. In the cosmological context, a system that obeys the holographic equipartition law behaves as an ordinary macroscopic system that proceeds to an equilibrium state of maximum entropy. We consider the standard $\Lambda$CDM model of the universe and have shown that it is consistent with the holographic equipartition law. Analyzing the entropy evolution we find that it also proceeds to an equilibrium state of maximum entropy.Comment: 16 pages, 4 figure

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 accelerated expansion of the universe can be interpreted as a quest for satisfying holographic equipartition. It can be expressed by a simple law, ∆V = ∆t (N surf − N bulk ) which leads to the standard Friedmann equation. This novel idea suggested by Padmanabhan in the context of general relativity has been generalized by Cai and Yang et al. to Gauss-Bonnet and Lovelock gravities for a spatially flat universe in different methods. We investigate the consistency of these generalizations with the constraints imposed by the maximum entropy principle. Interestingly, both these generalizations imply entropy maximization even if their basic assumptions are different.Further, we analyze the consistency of Verlinde's emergent gravity with the maximum entropy principle in the cosmological context. In particular, we consider the generalization suggested by Shu and Gong, in which an energy flux through the horizon is assumed, in addition. Even though the conceptual formulations are different, these two emergent perspectives of gravity describes a universe which behaves as an ordinary macroscopic system. Our results provide further support to the emergent gravity paradigm.