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In the present paper, an attempt has been made to study the spatially homogeneous and isotropic FRW model and axially symmetric space–time in f(R) theory of gravity. We have obtained the solutions of the field equations in vacuum. To find the solutions of axially symmetric space–time, we have assumed the relation between scale factor and scalar field and also we considered that scalar expansion \((\theta )\) in the model is proportional to shear scalar \((\sigma )\). The physical behavior for both models has been discussed using physical parameters. The function of Ricci scalar is investigated for these models.

Vacuum Solutions of FRW and Axially Symmetric Space–Time in f(R) Theory of Gravity