Constraint on Symmetric Teleparallel Gravity with Different Dark energy Parametrizations from DESI DR2 BAO Data

We investigate the cosmological viability of symmetric teleparallel gravity, specifically the $f(Q)$ gravity model with a power-law form $f(Q) = \alpha Q^n$, in combination with two widely used dark energy parameterizations: Chevallier Polarski Linder (CPL) and Barboza Alcaniz (BA). Employing the most recent DESI DR2 Baryon Acoustic Oscillation (BAO) dataset along with previous BAO measurements, we constrain the model parameters through a robust Markov Chain Monte Carlo (MCMC) analysis. We examine the background evolution via key cosmological indicators including the Hubble parameter $H(z)$, deceleration parameter $q(z)$, the effective equation of state $\omega_{\rm eff}(z)$, and the Om diagnostic. Our results indicate that the inclusion of DESI DR2 data significantly tightens constraints on the model parameters and supports a consistent transition from decelerated to accelerated expansion. The present-day values of $q(0)$ and $\omega_{\rm eff}(0)$ lie within the quintessence regime for all datasets. However, for lower redshift values the behaviour varies between phantom-like and quintessence-like phases. Statistical comparison via $\chi^2$, AIC, BIC, and $R^2$ further demonstrate that both CPL + $f(Q)$ and BA + $f(Q)$ provide better or competitive fits to data compared to $\Lambda$CDM, hence offering a compelling geometric alternative for explaining late-time cosmic acceleration.