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Early viscous universe with variable gravitational and cosmological ‘constants’. (English) Zbl 1133.83418
Summary: Einstein’s field equations with variable gravitational and cosmological ‘constants’ are considered in the presence of bulk viscosity for a spatially flat homogeneous and isotropic universe. Solutions are obtained by using a ‘gamma-law’ equation of state $p=\left(\gamma -1\right)\rho$ , where the adiabatic parameter $\gamma$ varies continuously as the universe expands. A unified description of the early evolution of universe is presented with a number of possible assumptions on the bulk viscous term and gravitational constant in which an inflationary phase is followed by radiation-dominated phase. We investigate the cosmological model with constant and time-dependent bulk viscosity (proportional to power function of energy density and to Hubble parameter) along with constant and variable gravitational constant. The effect of viscosity is shown to affect the past and future of the universe. In all cases, the cosmological constant ${\Lambda }$ is found to be positive and a decreasing function of time, which supports the results obtained from recent supernovae Ia observations. The possibility that the present acceleration of the universe is driven by a kind of viscous fluid is explained. At the background level this model is similar to the generalized Chaplygin gas model. The physical and geometrical significance of the early cosmological models has also been discussed.
##### MSC:
 83F05 Relativistic cosmology