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 text]CDM 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.