Constraining $f(Q, L_m)$ gravity with bulk viscosity

We investigate the influence of bulk viscosity on late-time cosmic acceleration within an extended $f(Q, L_m)$ gravity framework, where the non-metricity $Q$ is non-minimally coupled with the matter Lagrangian $L_m$. Analyzing the function $f(Q, L_m) = \alpha Q + \beta L_m$, we derive exact solutions under non-relativistic matter domination. Using observational datasets ($H(z)$, Pantheon supernovae, and their combination), we constrain the model parameters $H_0$, $\alpha$, $\beta$, and $\zeta$. The deceleration parameter transitions from positive to negative values around redshifts $z_t \approx 0.80$ to $0.99 $, indicating current accelerated expansion. Moreover, the effective equation of state parameter, $\omega_{eff}$, resembles quintessence dark energy ($-1 < \omega_{eff} < -\frac{1}{3}$), with corresponding values from respective datasets. Finally, we use the $Om(z)$ diagnostic, which confirms that our model demonstrates quintessence-like behavior. Our findings underscore the significant role of bulk viscosity in understanding accelerated expansion in the universe within alternative gravity theories.