Observing pulsars with f(R) gravity and using van der Waals equation of state in model

This research focuses on the evolution of the universe and observes pulsars using modified gravitational theory. We computed the Einstein field equations for an anisotropic spherical structure with f(R) gravity. Furthermore, our density–pressure relationship is defined using the well-known van der Waals equation of state (VdW EoS). Graphs are used to investigate the behavior of physical parameters, and energy conditions are used to demonstrate the physical continuity of dense stars. Plotting the adiabatic index shows the model’s stability. The resulting figures of physical parameters confirm the model’s practical and conceptual feasibility. Under the effect of f(R) gravity, our work demonstrates regularity, viability and stability, supporting the presence of heavy pulsars such as PSR \(J0348+0432\), PSR \(J0740+6620\) and PSR \(J0030+0451\).