Exploring plane symmetric space-time in f(R) modified gravitational theory

This paper investigates a plane-symmetric cosmological model (PSCM) in the context of modified f(R) gravity theory, incorporating both vacuum and non-vacuum scenarios. A perfect fluid is assumed as the matter source. To obtain the solutions, we consider the premise of constant scalar curvature. By applying the conservation law for Einstein's field equation, Tij;j, and the power-law assumption, we retrieve some well-known solutions. We solved the field equations by making a specific assumption that involved a transformation A2B=U . This study explores the physical and kinematic characteristics of specific cosmological models, along with an examination of the statefinder diagnostic—a key tool for analysing the universe’s evolutionary trajectory. The work provides important insights into the behaviour of anisotropic models within the context of modified f(R) gravity. It highlights the interplay between matter distribution and spacetime geometry, particularly emphasizing how assuming a constant scalar curvature aids in simplifying and solving the corresponding field equations. The resulting solutions enhance our understanding of cosmic evolution governed by modified f(R) gravity.