Dark energy density and Israel–Stewart (IS) bulk viscosity model

Abstract

In this paper, we investigate the thermodynamics of a dark energy bulk viscosity model as a cosmic fluid. In this regard, the two theories of Eckart and Israel–Stewart (IS) are the bases of our work. Therefore, we first investigate the thermodynamics of cosmic fluids in the dark energy bulk viscosity model and the general relationships. Then, we express the thermodynamic relationships of Eckart’s theory. Due to the basic equations of Eckart’s theory and Friedmann’s equations, we consider two states, one is [Formula: see text] (standard) and the other is [Formula: see text] (non-standard). In the standard state, we define the pressure [Formula: see text], energy density [Formula: see text] and bulk viscosity coefficient [Formula: see text] of the cosmic fluid in terms of cosmic time and we obtain its relations. We also mention that in this standard state, because of [Formula: see text], the value of [Formula: see text] is zero, so [Formula: see text] is not defined in this state. But in the non-standard case [Formula: see text], the bulk viscosity coefficient [Formula: see text] is zero and only the scale factor, pressure and energy density of the cosmic fluid are defined. We also consider two states of constant and variable bulk viscosity coefficients and obtain three Hubble constant parameters and scale factor in terms of cosmic time, and energy density in terms of scale factor. In the state of variable bulk viscosity coefficient, we consider the viscosity coefficient as the power law from energy density [Formula: see text], which is [Formula: see text] and a constant. Following this, we discuss about the dissipative effects of cosmic fluids and examine the effects of energy density for dark energy in the IS theory. The results are comprehensively presented in Tables 1 and 2. Also, according to observational constraints, the results of the likelihood analysis for the IS viscous model are summarized in Table 3.