Dark Energy Density and IS (Israel-Stewart) Bulk Viscosity Model

Abstract

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 basis 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 $p=-\rho$ (standard) and the other is $p\ne -\rho$ (non-standard). In the standard state, we define the pressure $(p)$, energy density $(\rho )$, and bulk viscosity coefficient $(\xi )$ of the cosmic fluid in terms of cosmic time and we obtain its relations. We also mention that in this standard state, because of $p=-\rho$, the value of $a(t)$ is zero, so $a(t)$ is not defined in this state. But in the non-standard case $(p\ne -\rho )$ the bulk viscosity coefficient $(\xi )$ is zero and only the scale factor and pressure and energy density of the cosmic fluid is defined. We also consider two states of constant and variable bulk viscosity coefficients and obtain three Hubble constant parameters and scale factors in terms of cosmic time, and energy density in terms of the scale factor. In the state of variable bulk viscosity coefficient, we consider the viscosity coefficient as the power-law from energy density $(\xi =\alpha {\rho }^s)$, which is $\alpha >0$ and a constant. Following, we discuss the dissipative effects of cosmic fluids and examine the effects of energy density for dark energy in the Israel-Stewart(IS) theory. The results are comprehensively presented in two tables (1) and (2).

arXiv comment28 pages, 11 figurs, 2 tables

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