Stable f(Q) gravity model through non-trivial connection

Abstract

This study effectively reconstructs a cosmological model utilizing covariant $f\left(Q\right)$ gravity within Connection-III and FLRW spacetime. The dynamic behavior of the reconstructed model is thoroughly analyzed using the Hubble parameter $H\left(z\right)$ and various observational datasets. Our robust findings demonstrate that the model displays quintessence behavior at the present epoch and converges to the $\Lambda$CDM model at late time. It is confirmed through comprehensive evaluations against energy conditions that the Null Energy Condition remains positive throughout cosmic evolution, and the Dominant Energy Condition is consistently satisfied. The Strong Energy Condition is initially fulfilled in the early Universe but violated in the late epoch. Moreover, scalar perturbations extensively assess stability, affirming the strength of the model with respect to the Hubble parameter. This research offers compelling insights into cosmic acceleration, suggesting that $f\left(Q\right)$ gravity can effectively displace the $\Lambda$CDM model and provides a convincing alternative explanation for the current accelerating expansion of the Universe without relying on the cosmological constant.