We investigate late-time cosmology in the context of modified $f(Q,L_m)$ gravity, considering a non-linear model$ f(Q,L_m) = \alpha Q + \beta L_m^n + \lambda$ where, $\alpha$, $\beta$, $\lambda$, and $n$ are some free parameters. The modified Friedmann equations are derived for a barotropic cosmic fluid, and an analytical solution for the Hubble parameter $H(z)$ is obtained. Using the latest DESI DR2 BAO data, previous BAO compilations (P-BAO), and cosmic chronometer (CC) datasets, we constrain the model parameters through a Markov Chain Monte Carlo analysis. Our results show that the model successfully describes the observed late-time cosmic acceleration with slightly tighter constraints from the inclusion of DESI dataset. The present-day Hubble constant is determined as $H_0 \simeq 69.5\ \mathrm{ km\ s^{ -1}\ Mpc^{ -1}}$, while the deceleration parameter confirms accelerated expansion with $q_0 \simeq -0.57$. The transition redshift, where the universe switches from deceleration to acceleration, occurs in the range $z_{ \rm tr} \sim 0.56 - 0.77$. Similarly, a smooth and physically consistent transition from a matter-dominated decelerated period at high redshifts to an accelerated phase at late times is revealed by the evolution of $\omega_{ eff}(z)$. While statefinder diagnostic shows the model favours a Chaplygin gas like nature for DESI and DESI+CC, whereas the model favours as quintessence dominated evolution for P-BAO+CC in the late time regime. Conclusively, all these results along with the study of the energy conditions and stability analysis showcases the given $f(Q,L_m)$ model offers a viable alternative to GR-based cosmology
Categories: gr-qc