Matter Bounce Scenario in Extended Symmetric Teleparallel Gravity

Abstract: In this paper, we have shown the matter bounce scenario of the Universe in an extended symmetric teleparallel gravity, the f(Q) gravity. Motivated from the bouncing scenario and loop quantum cosmology (LQC), the form of the function $f(Q)$ has been obtained at the backdrop of Friedmann-Lemaitre-Robertson Walker (FLRW) space time. Considering the background cosmology dominated by dust fluid, the e-folding parameter has been expressed, which contains the nonmetricity term. Since the slow roll criterion in the bouncing context is not valid, we used a conformal equivalence between f(Q) and scalar-tensor model to apply the bottom-up reconstruction technique in the bouncing model. The dynamics of the model has been studied through the phase space analysis, where both the stable and unstable nodes are obtained. Also, the stability analysis has been performed with the first order scalar perturbation of the Hubble parameter and matter energy density to verify the stability of the model.