Analysis of bouncing cosmology in non-Riemannian geometry

The main objective of this manuscript is to investigate the bouncing cosmology in the background of $f\left(Q\right)$ gravity, where $Q$ defines the non-metricity. For this purpose, we use the reconstruction approach and consider a flat Friedmann–Robertson–Walker spacetime with perfect matter configuration. We examine how the first contracting phase gives the expansion by using a temporal derivative of the scale factor, i.e., $\dot{a}<0$, $\dot{a}=0$ and $\dot{a}>0$ give contraction, bounce point and expansion phases, respectively. Further, we use the order reduction method to solve the modified field equations as these are very difficult due to the presence of additional non-linear expressions. It is analyzed that the original singularity of the universe diminishes for the required bounce conditions. We conclude that the acceleration occurs near the bouncing point and the considered $f\left(Q\right)$ models are consistent with the current cosmic accelerated expansion.