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arXiv · 2402.04813

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

Gaurav N. Gadbail·Simran Arora·P. K. Sahoo·Kazuharu Bamba
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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-

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Gaurav N. Gadbail, Simran Arora, P. K. Sahoo, Kazuharu Bamba. 2024-02-07. Reconstruction of the singularity-free $f(\mathcal{R})$ gravity via Raychaudhuri equations. https://doi.org/10.1140/epjc%2Fs10052-024-13107-8

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