Reconstruction of the singularity-free $$f({\mathcal {R}})$$ f ( R ) gravity via Raychaudhuri equations

Abstract

Abstract We study the bounce cosmology to construct a singularity-free $$f({\mathcal {R}})$$ f ( R ) model using the reconstruction technique. The formulation of the $$f({\mathcal {R}})$$ 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 $$f_{{\mathcal {R}}}>0$$ f R > 0 and $$f_{{\mathcal {R}}{\mathcal {R}}}>0$$ 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 $$\omega =-\,1/3$$ ω = - 1 / 3 and $$\omega =-\,2/3$$ ω = - 2 / 3 . While the model proves suitable for studying a singular-free accelerating universe in the $$\omega =-\,1/3$$ ω = - 1 / 3 case, it fails to demonstrate such behavior under energy conditions for the $$\omega =-\,2/3$$ ω = - 2 / 3 scenario. The reconstructed models accommodate early-time bouncing behavior and late-time cosmic acceleration within a unified framework.