Early viscous universe with variable gravitational and cosmological ‘constants’

Abstract

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 = (γ − 1)ρ, where the adiabatic parameter γ 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.

Totally Anisotropic Cosmological Models with Bulk Viscosity for Variable G and Λ

“…Again, from Equations (21), (23) and (26), we obtain the value of as given in Equation (27).  The Gravitational constant G is zero at t = 0 and gradually increases and tends to infinity at late times.…”

“…Arbab [24,25] and Singh et al [26] have considered cosmological models with viscous fluid considering variable cosmological and gravitational constants. Singh et al [27] presented a number of classes of solutions of Einstein's field equations with variable G,  and bulk viscosity coefficient in the framework of non causal theory. Several authors investigated anisotropic bulk viscous fluid cosmological models of various Bianchi types time-dependent G and  (see Pradhan and Kumhar [28], Verma and Shri Ram [29,30] and references cited therein).…”

Locally Rotationally Symmetric Bianchi Type I Massive String Cosmological Models with Bulk Viscosity and Decaying Vacuum Energy Density

“…The role of viscosity in cosmology has been studied by several authors viz. Pimentel [25], Berman [26], Beesham [27], Arbab [28], Pavon et al [29], Zimdahl [30], Gron [31], Saha [32,33], Singh et al [34], Bali et al [35,36], Mostafapoor and Gron [37].…”

A General Bianchi Type Viscous Fluid Cosmological Model with Both Deceleration and Acceleration

“…Production of entropy and viscous damping of anisotropy inhomogeneous cosmological models of Bianchi type I spaces have been studied by Caderni and Fabbri [7]. Pradhan and Pandey [8], Pradhan and Singh [9], Peebles [10], Bali and Pradhan [11], Singh et al [12], Dunn and Tupper [3], Coley and Tupper [14], Banerjee and Santos [15,16] discussed cosmological models under the influence of both bulk and shear viscosities. Goener and Kowalewsky [17] presented a method for constructing anisotropic viscous fluid cosmological models of Bianchi type-I satisfying the barotropic equation of state.…”