Observational cosmology of Weyl-type f ( Q, T ) modified gravity

We investigate the cosmological dynamics of Weyl-type f(Q,T) gravity, a modified theory formulated in Weyl geometry and depending on the non-metricity scalar Q and the trace of the energy-momentum tensor T. By starting from the full geometric framework with a Proca-like Weyl vector field and a Lagrange multiplier imposing the flat-Weyl condition, we derive the field equations and their cosmological reduction in a flat FLRW background. For a linear model f(Q,T) = αQ + βT/(6κ 2 )$ and the approximation λ ≃ κ 2 , the generalized Proca equation selects the branch ψ = H, fixing α and leaving β as the parameter controlling deviations from standard cosmology. We reconstruct the cosmic expansion using both constant and dynamical effective equations of state (EoS). While a constant EoS leads to simple power-law solutions for H(z), a redshift-dependent EoS allows a realistic transition from deceleration to acceleration and yields an analytic expression for the Hubble function. We constrain the model using cosmic chronometer H(z) data, the Pantheon+SH0ES supernova sample, and DESI BAO measurements. The results support late-time acceleration and show that the model reproduces the standard cosmological history while allowing controlled deviations from λCDM through β.