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

We investigate the cosmological dynamics of Weyl-type [Formula: see text] gravity, a modified theory formulated in Weyl geometry and depending on the non-metricity scalar [Formula: see text] and the trace of the energy–momentum tensor [Formula: see text]. 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 [Formula: see text] and the approximation [Formula: see text], the generalized Proca equation selects the branch [Formula: see text], fixing [Formula: see text] and leaving [Formula: see text] 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 [Formula: see text], 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 [Formula: see text] 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 [Formula: see text]CDM through [Formula: see text].

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