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

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2024-07, Vol.84 (7), p.752, Article 752
• Main Authors: Gadbail, Gaurav N., Arora, Simran, Sahoo, P. K., Bamba, Kazuharu
• Format: Article
• Language: English
• Subjects: Acceleration; Astronomical models; Astronomy; Astrophysics and Cosmology; Cosmology; Dark energy; Elementary Particles; Gravity; Hadrons; Heavy Ions; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Reconstruction; Regular Article - Theoretical Physics; Singularities; String Theory; Theory of relativity; Universe
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-024-13107-8

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.