Viscous dissipative Chaplygin gas dominated homogenous and isotropic cosmological models

Abstract

The generalized Chaplygin gas, which interpolates between a high density relativistic era and a nonrelativistic matter phase, is a popular dark energy candidate. We consider a generalization of the Chaplygin gas model, by assuming the presence of a bulk viscous type dissipative term in the effective thermodynamic pressure of the gas. The dissipative effects are described by using the truncated Israel-Stewart model, with the bulk viscosity coefficient and the relaxation time functions of the energy density only. The corresponding cosmological dynamics of the bulk viscous Chaplygin gas dominated universe is considered in detail for a flat homogeneous isotropic Friedmann-Robertson-Walker geometry. For different values of the model parameters we consider the evolution of the cosmological parameters (scale factor, energy density, Hubble function, deceleration parameter, and luminosity distance, respectively), by using both analytical and numerical methods. In the large time limit the model describes an accelerating universe, with the effective negative pressure induced by the Chaplygin gas and the bulk viscous pressure driving the acceleration. The theoretical predictions of the luminosity distance of our model are compared with the observations of the type Ia supernovae. The model fits well the recent supernova data. From the fitting we determine both the equation of state of the Chaplygin gas, and the parameters characterizing the bulk viscosity. The evolution of the scalar field associated to the viscous Chaplygin fluid is also considered, and the corresponding potential is obtained. Hence the viscous Chaplygin gas model offers an effective dynamical possibility for replacing the cosmological constant, and for explaining the recent acceleration of the universe. © 2008 The American Physical Society.