Modified cosmology in $f(Q,L_m)$ gravity

In this letter, we investigate cosmology within the framework of modified $f(Q,L_m)$ gravity using the non-linear model $f(Q,L_m)=-Q+\alpha L_m^n+\beta$, where $\alpha$, $\beta$, and $n$ are free parameters. The modified Friedmann equations are derived for a matter-dominated universe, and an analytical solution is obtained. Using Hubble, Pantheon+, and joint datasets, we constrain the model parameters and examine their implications. The results indicate that the model accommodates varying $H_0$ values, contributing to the Hubble tension, while $n\mathrm{\ne }1$ suggests deviations from general relativity (GR). The deceleration parameter confirms a transition to acceleration at $z_t\approx 0.6-0.8$, with present values supporting cosmic acceleration. This model offers a viable alternative to GR-based cosmology.