Bulk viscous Bianchi-V cosmological model within the formalism of $f(R,T)=f_{1}(R)+f_{2}(R)f_{3}(T) $ gravity

Abstract

In this paper, we have studied transitioning Bianchi-V cosmological universe with bulk viscous matter within formalism of $f(R,T) $ gravity. The negative pressure which is generated by bulk viscosity may act as dark energy component and can drive accelerated expansion of universe. This is the main reason for taking into account the bulk viscosity in the present model. To describe the simplest coupling between matter and geometry using specific model $f(R,T)=f_{1}(R)+f _{2}(R)f_{3}(T) $ in Bianchi-V space-time; where $f_{1}(R)=f_{2}(R)=R $ and $f_{3}(T)=\gamma T $ , $\gamma $ is a constant. The dynamic bulk viscosity coefficient $\xi $ expected to enhance the rate of expansion is taken as $\xi =\frac{p^{(\mathit{eff})}-\bar{p}^{(\mathit{eff})}}{3 H} $ , where $\bar{p}^{(\mathit{eff})} $ is effective bulk viscous pressure and $p^{(\mathit{eff})} $ is normal fluid pressure. The bulk viscosity increases, which in turn leads to rise in negative pressure, that shows accelerated expansion. The equation of state is taken as $p^{(\mathit{eff})}=\zeta \rho ^{(\mathit{eff})} $ , where $\zeta $ is a constant whose value lies between 0 and 1. We assume hybrid scale factor $a= \{t^{m}\exp (\lambda t) \} ^{\frac{1}{n}} $ (where $m, \lambda $ and $n $ are constants) to obtained deterministic solutions of Einstein’s field equations. It has been observed that in the presence of bulk viscosity, the solutions are more stable and explains well the physical behavior of the phase transition of universe and also confirms the stability of the model through validation of energy conditions.