Exact causal bulk viscous stiff cosmologies.

Abstract

An exact solution of the gravitational fleld equations is presented for a homogeneous ∞at Friedmann{Robertson{Walker universe fllled with a causal bulk viscous ∞uid obeying the Zeldovich stifi equation of state and having bulk viscosity coe‐cient proportional to the fourth root of the energy density. Dissipative thermodynamic processes of bulk viscous type are supposed to play a crucial role in the dynamics and evolution of the early universe. Over thirty years ago Misner (1966) suggested that the observed large-scale isotropy of the universe is due to the action of the neutrino viscosity which was efiective when the universe was about 1 second old. There are many processes capable of producing bulk viscous stresses in the early universe, such as interaction between matter and radiation, quark and gluon plasma viscosity, strings and superstrings, difierent components of dark matter or particle creation (Chimento and Jakubi 1996). Traditionally the theories of Eckart (1940) and Landau and Lifshitz (1987) were used for the description of these phenomena. However, the results of Israel (1976), Israel and Stewart (1976) and Hiscock and Lindblom (1989) showed that the Eckart-type theories sufier from serious drawbacks concerning causality and stability. Regardless of the choice of equation of state, all equilibrium states in these theories are unstable and in addition signals may be propagated through the ∞uid at velocities exceeding the speed of light (Israel 1976; Israel and Stewart 1976; Hiscock and Lindblom 1989; Hiscock and Salmonson 1991). These problems arise due to the flrst-order nature of the theory, i.e. it considers only flrst-order deviations from equilibrium. The neglected second-order terms are necessary to prevent non-causal and unstable behaviour. A relativistic second-order theory was found by Israel (1976) and developed by Israel and Stewart (1976) into what is called ‘transient’ or ‘extended’ irreversible thermodynamics. Due to the complicated nonlinear character of the evolution equations, very few exact cosmological solutions of the gravitational fleld equations in the framework of the full causal theory are known. For a homogeneous universe fllled with a full causal viscous ∞uid source obeying the relation »»‰ 1 2 , exact general solutions of