Constraint on symmetric teleparallel gravity with different dark energy parametrizations from DESI DR2 BAO data

Despite the increasing interest in non-Riemannian gravity formulations, the cosmological feasibility of power-law Formula: see text models is still not thoroughly explored in light of the most recent DESI DR2 BAO data. We investigate the cosmological viability of symmetric teleparallel gravity, specifically the Formula: see text gravity model with a power-law form Formula: see text, 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 Formula: see text, deceleration parameter Formula: see text, the effective equation of state (EoS) Formula: see text, 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, yielding parameter values such as Formula: see text for CPL + Formula: see text and Formula: see text for BA + Formula: see text. The present-day deceleration parameter and effective EoS are constrained to Formula: see text and Formula: see text in the CPL case, and Formula: see text and Formula: see text in the BA case, all lying within the quintessence regime. For lower redshifts, the behavior varies between phantom-like and quintessence-like phases depending on the parameterization. Statistical comparison via Formula: see text, AIC, BIC, and Formula: see text indicates that both CPL + Formula: see text and BA + Formula: see text yield fits to observational data that are competitive with the Formula: see textCDM model. While the improvements in AIC and BIC are positive but not statistically decisive, the Formula: see text framework remains a compelling geometric alternative for modeling late-time cosmic acceleration.