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

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 = (? ? 1)?, where the adiabatic parameter ? 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 ? 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.

https://iopscience.iop.org/article/10.1088/0264-9381/24/2/011/pdf

Early viscous universe with variable gravitational and cosmological ‘constants’

The behaviour of magnetic field in anisotropic Bianchi type I cosmological model for bulk viscous distribution is investigated. The distribution consists of an electrically neutral viscous fluid with an infinite electrical conductivity. It is assumed that the component $\sigma^1_1$ of shear tensor $\sigma^j_i$ is proportional to expansion (θ) and the coefficient of bulk viscosity is assumed to be a power function of mass density. Some physical and geometrical aspects of the models are also discussed in presence and also in absence of the magnetic field.

Bianchi type i magnetofluid cosmological models with variable cosmological constant revisited

We have studied an isotropic homogeneous FRW universe in the presence of a bulk viscous fluid within the framework of Lyra's geometry. We have obtained exact solutions of the Sen equations assuming the deceleration parameter to be constant. The coefficient of bulk viscosity has been assumed to be a power function of the mass density. With this assumption, we have considered the behavior of the displacement field and the energy density for both power-law and exponential expansions of the universe. We show that our models are generalised and we obtain the results of previous works by considering k=0 and k=-1.

Bulk Viscous FRW Cosmology in Lyra Geometry

Some Bianchi type I viscous fluid cosmological models with a variable cosmological constant are investigated in which the expansion is considered only in two direction i.e. one of the Hubble parameter $(H_{1} = \frac{A_{4}}{A})$ is zero. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density whereas the coefficient of shear viscosity is considered as constant in first case whereas in other case it is taken as proportional to scale of expansion in the model. The cosmological constant Λ is found to be positive and is a decreasing function of time which is supported by results from recent supernovae Ia observations. Some physical and geometric properties of the models are also discussed.

http://repository.iucaa.in:8080/jspui/bitstream/11007/976/1/3104.pdf

Some bianchi type i viscous fluid cosmological models with a variable cosmological constant

Exact solutions are obtained for the isotropic homogeneous cosmological model with viscous fluid. The fluid has only bulk viscosity and the viscosity coefficient is taken to be a power function of the mass density. The equation of state assumed obeys a linear relation between mass density and pressure. The models satisfying Hawking’s energy conditions are discussed. Murphy’s model is only a special case of this general set of solutions and it is shown that Murphy’s conclusion that the introduciton of bulk viscosity can avoid the occurrence of space‐time singularity at finite past is not, in general, valid.

N. O. Santos

Papers

Isotropic homogeneous universe with viscous fluid