Reconstruction of the singularity-free f(R) gravity via Raychaudhuri equations.

We study the bounce cosmology to construct a singularity-free f (R) model using the reconstruction technique. The formulation of the f (R) model is based on the Raychaudhari equation, a key element employed in reconstructed models to eliminate singularities. We explore the feasibility of obtaining stable gravitational Lagrangians, adhering to the conditions f R > 0 and f R R > 0 . Consequently, both models demonstrate stability, effectively avoiding the Dolgov–Kawasaki instability. Our assessment extends to testing the reconstructed model using energy conditions and the effective equation-of-state (EoS). Our findings indicate that the reconstructed super-bounce model facilitates the examination of a singularity-free accelerating universe for both phantom and non-phantom phases. However, in the case of the reconstructed oscillatory bounce model, two scenarios are considered with ω = - 1 / 3 and ω = - 2 / 3 . While the model proves suitable for studying a singular-free accelerating universe in the ω = - 1 / 3 case, it fails to demonstrate such behavior under energy conditions for the ω = - 2 / 3 scenario. The reconstructed models accommodate early-time bouncing behavior and late-time cosmic acceleration within a unified framework. [ABSTRACT FROM AUTHOR]