The research on viscous cosmological models is reviewed and carried further Inflationary cosmological models of Bianchi type-I with shear, bulk, and nonlinear viscosity are studied The inflation field energy is represented by a two-components cosmic fluid consisting of a vacuum fluid and a Zel'dovich fluid It is shown that there exist models in which the viscous Zel'dovich fluid removes the initial singularity of the corresponding viscosity free models The mean expansion of a Zel'dovich dominated unvierse is found to be independent of shear viscosity and anisotropy Bulk viscosity and shear viscosity cause exponential decay of anisotropy, while nonlinear viscosity causes power-law decay of anisotropy

Viscous Inflationary Universe Models

We investigate the behaviour of the solutions to the Einstein equations with a causal viscous fluid source in the case of the spatially flat Robertson-Walker metric. In our model, the bulk viscosity coefficient is related to the energy density as zeta = alpha rho m, and the relaxation time is given by zeta / rho . We find the exact solutions when m = 1/2 , and we study analytically the asymptotic stability of the distinct families of solutions for arbitrary m. We find that the qualitative asymptotic behaviour in the far future is not altered by relaxation processes, but they change the behaviour in the past, either excluding deflationary evolutions or making the Universe bounce due to the violation of the energy conditions.

http://iopscience.iop.org/article/10.1088/0264-9381/10/10/011/pdf

Cosmological solutions of the Einstein equations with a causal viscous fluid

The irrotational Bianchi V cosmological model under the influence of both shear and bulk viscosity, together with heat flux, has been studied. Exact solutions for the model are obtained with three assumptions of which the first two relate the matter density, shear scalar, and expansion scalar and the third is a barotropic equation of state, connecting the matter density and thermodynamic pressure. The properties of the solutions are studied and the temperature distribution is also given explicitly. It has been observed that along with the viscosity, heat flux further adds to the rate of entropy increase.

Irrotational Bianchi V viscous fluid cosmology with heat flux

Bianchi V, spatially homogeneous imperfect fluid cosmological models which contain both viscosity and heat flow are investigated. The Einstein field equations are established in the case that the equations of state are given byp-(γ-1)ρ,ζ=ζo ρ
m, andη=ηoρ

 n
 (whereγ, ζo, ηo,m andn are constants). The physical constraints on the solutions of the Einstein field equations, and, in particular, the thermodynamical laws and energy conditions that govern such solutions, are discussed in some detail. Simple power law solutions and solutions in which there is no heat conduction are studied first. Exact solutions are then investigated in more generality, and it is shown that there exist two first integrals of the field equations for certain values of the physical parametersγ, m andn. Finally, it is shown that in a special case of interest (in whichm =n = 1/2) the imperfect fluid Bianchi V field equations can be written as a plane-autonomous system, thus facilitating the qualitative analysis of these cosmological models.

Bianchi-V Imperfect Fluid Cosmology

Homogenization and isotropization of an inflationary cosmological model

We investigate world models in which strong initial anisotropies are damped out by viscous dissipation at temperatures lower than 1012K. The corresponding entropy production is calculated and is proved to be simply related to the initial anisotropy. The radiation entropy increases up to a factor 1010 in those models in which the big bang starts atT∼-1010 K. In all cases here investigated the volume expansion is dominated by viscosity in a «superviscous stage» preceding a Kasner epoch. In these models, despite of very different initial conditions, the anisotropy of the cosmic background radiation is approximately the same, namely ΔT/T∼-4·10−7 at the present epoch.

R. Fabbri

Papers

Production of entropy and viscous damping of anisotropy in homogeneous cosmological models: Bianchi type-I spaces