Bianchi type-$\mathit{II}$, $\mathit{VIII}$ and $\mathit{IX}$ cosmological models in a modified theory of gravity with variable $\varLambda$

Abstract

Spatially homogeneous Bianchi type-$\mathit{II}$, $\mathit{VIII}$ and $\mathit{IX}$ perfect fluid cosmological models in $f(R,T)$ modified theory of gravity have been investigated for a special choice of $f(R,T)=f_{1}(R)+f_{2}(T)$ with $f_{1}(R)=\lambda_{1}R$ and $f_{2}(T)=\lambda_{2}T$. This special choice leads to a cosmological constant $\varLambda$, which depends on stress energy tensor of matter source. To get the deterministic model of Universe, we assume that the expansion scalar ($\theta$) in the model is proportional to shear scalar ($\sigma$). This condition leads to relation between metric potentials, which yields a time dependent deceleration parameter. Various physical and geometrical features of the models are also discussed.