Observational constraints on viscous cosmology in $f(T,L_m)$ gravity

We investigate the late-time cosmic acceleration within the framework of viscous $f(T,L_m)$ gravity, where the gravitational action depends on both the torsion scalar $T$ and the matter Lagrangian $L_m$. In this context, the Universe is modeled as a bulk viscous fluid, allowing for dissipative effects that generate an effective negative pressure capable of driving acceleration without invoking a cosmological constant. We adopt a simple linear model $f(T,L_m) = \alpha T + \beta L_m$ and assume a constant bulk viscosity coefficient $\zeta = \zeta_0 > 0$. The model parameters are constrained using a joint analysis of recent observational datasets, including 31 Hubble parameter measurements, the Pantheon+ sample of 1701 Type Ia Supernovae, and the latest baryon acoustic oscillation data from DESI, employing a Markov Chain Monte Carlo (MCMC) approach. The best-fit results, $H_0 = 68.16 \pm 0.65$, $\alpha = 1.53^{+0.49}_{-0.61}$, $\beta = 0.40 \pm 0.96$, and $\zeta_0 = 2.15^{+0.69}_{-0.81}$, are consistent with current cosmological observations and indicate that bulk viscosity plays a significant role in the late-time dynamics. The deceleration parameter $q_0 = -0.33 \pm 0.41$ confirms the current accelerated expansion, while the effective equation of state (EoS) evolves from a matter-like regime at high redshift toward a quintessence phase at late times. The $Om(z)$ diagnostic further supports this behavior, suggesting a mild deviation from $\Lambda$CDM toward a dynamical dark energy component. Although information criteria ($\Delta \mathrm{AIC} = 2.2$, $\Delta \mathrm{BIC} = 13.13$) slightly favor the simpler $\Lambda$CDM model, the viscous $f(T,L_m)$ framework remains a viable and physically motivated alternative capable of explaining cosmic acceleration through the combined effects of torsion-matter coupling and viscosity.