Bulk viscous matter in extended symmetric teleparallel Weyl-type f(Q,T) gravity

In this work, we investigate a specific extension of symmetric teleparallel gravity (STG), commonly referred to as $f\left(Q\right)$ gravity, in which the non-metricity scalar $Q$ serves as the fundamental geometric quantity describing gravitation. We focus on the Weyl-type $f(Q,T)$ framework, where $Q$ is non-minimally coupled to the trace of the matter energy–momentum tensor $T$, with the non-metricity scalar $Q$ constructed from the outset within Weyl geometry. In this formulation, the covariant divergence of the metric tensor satisfies ${\nabla }_{\mu }{g}_{\alpha \beta }=-w_{\mu }{g}_{\alpha \beta }$, where $w^{\mu }$ is the Weyl vector. This geometric setting enables us to examine the late-time accelerated expansion of the universe by considering bulk viscous matter as the dominant cosmic component. By adopting the functional form $f(Q,T)=\alpha Q+\frac{\beta }{6{\kappa }^2}T$, we derive exact solutions to the corresponding field equations and confront the model with $H\left(z\right)$ and Type Ia supernovae observational data. Our analysis reveals that bulk viscosity in the cosmic fluid plays a significant role in driving the current acceleration, and the model exhibits behavior consistent with a quintessence-like dark energy scenario. These results suggest that standard $\Lambda$CDM cosmology may represent an effective limit of a more general gravitational theory based on Weyl-type $f(Q,T)$ gravity.