Abstract
In this paper, we study three different Bianchi type line elements, like Bianchi type-I (BT-I), Bianchi type-III (BT-III) and Kantowski Sachs space-time in the framework of f(R, ϕ) theory of gravity, where R and ϕ represent the Ricci scalar and the scalar potential function respectively. We find the exact solution of vacuum field equations of f(R, ϕ) theory by taking valuable assumption that the expansion scalar θ is proportional to the shear scalar σ that is P=Qn. We also see some physical parameters like Hubble parameter H, volume scale factor V, average scale factor a, the expansion scalar θ and shear scalar σ for each metric. Finally, we analyze that the exact solution satisfied the present cosmic condition of universe and singularity (Big-Bang) is also justified through our evaluated solutions.
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