Eur. Phys. J. C (2024) 84: 752
https://doi.org/10.1140/epjc/s10052-024-13107-8

Regular Article - Theoretical Physics

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

¹ Department of Mathematics, Birla Institute of Technology and Science-Pilani, Hyderabad Campus, 500078, Hyderabad, India
² Department of Mathematics, CDOE, Chandigarh University, 140413, Punjab, India
³ Faculty of Symbiotic Systems Science, Fukushima University, 960-1296, Fukushima, Japan

^d bamba@sss.fukushima-u.ac.jp

Received: 18 April 2024
Accepted: 7 July 2024
Published online: 27 July 2024

Abstract

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