Abstract
In this paper, we considered a bulk viscosity described by non-linear inhomogeneous equation of state of the type \(p=\omega(\rho)+f(\rho)+\Lambda(H)\), where \(\omega(\rho)=b_{0}\rho^{\delta-1}-1\), \(f(\rho)=A \rho^{\alpha}\) and \(\Lambda(H)= \Lambda_{0}H\). We assume the bulk viscosity as a linear combination of two terms of the form \(\zeta=\zeta_{0}+\zeta_{1}H\) i.e. one is constant and the other is proportional to Hubble parameter \(H\). In the first part of the paper we find the solution of the field equations in terms of time-dependent dark energy density \(\rho\), Hubble parameter \(H\), scale factor \(a\) and also obtain the transition from non-phantom era to the phantom era by using exponential function method. In the second part of the paper, we again find the solutions of the field equations by using the simple integration method and again obtain \(\rho\), \(H\), and \(a\) for the particular case. Finally, we discuss the stability of the model.
Highlights
The discovery of accelerating universe has led to the appearance of a new theoretical model [8]
We have studied the cosmological model of the universe in which there is a non-linear inhomogeneous equation of state with equation of state parameter ω is of the form ω = b0ρδ−1−1
We find the complete description of evolutionary transition according to the value of scale factor a(t) and its first, second derivative which characterized different types accelerating and decelerating expansion of the universe
Summary
The discovery of accelerating universe has led to the appearance of a new theoretical model [8]. Brevik et al [1] investigated the specific model for a dark fluid with a non-linear inhomogeneous equation of state of the type p = ω(ρ) + f (ρ) + Λ(t) and find the solutions of the field equation in terms of Hubble parameter H(t), Scale factor a(t) and investigated the transition from non-phantom to the phantom era In particular they studied the transition towards super acceleration, i.e., the case in which the third derivative of the scale factor a(t) is positive. We use the exponential function method to solve the non-linear inhomogeneous equation of state and obtained the time dependent dark energy density ρ, Hubble parameter H(t) and scale factor a(t) and investigate the effect of viscosity to the evolution of the universe.
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