Probing Weyl-type $f(Q, T)$ gravity: Cosmological implications and constraints

In this paper, we investigate the cosmological implications and constraints of Weyl-type $f(Q, T)$ gravity. This theory introduces a coupling between the non-metricity $Q$ and the trace $T$ of the energy-momentum tensor, using the principles of proper Weyl geometry. In this geometry, the scalar non-metricity $Q$, which characterizes the deviations from Riemannian geometry, is expressed in its standard Weyl form $\nabla _{\mu }g_{\alpha \beta }=-w_{\mu }g_{\alpha \beta }$ and is determined by a vector field $w_{\mu }$. To study the implications of this theory, we propose a deceleration parameter with a single unknown parameter $\chi$, which we constrain by using the latest cosmological data. By solving the field equations derived from Weyl-type $f(Q, T)$ gravity, we aim to understand the behavior of the energy conditions within this framework. In the present work, we consider two well-motivated forms of the function $f(Q, T)$: (i) the linear model represented by $f(Q, T) = \alpha Q + \frac{\beta}{6\kappa^2} T$, and (ii) the coupling model represented by $f(Q, T) = \frac{\gamma}{6H_0^2 \kappa^2} QT$, where $\alpha$, $\beta$, and $\gamma$ are free parameters. Here, $\kappa^2 = \frac{1}{16\pi G}$ represents the gravitational coupling constant. In both of the models considered, the strong energy condition is violated, indicating consistency with the present accelerated expansion. However, the null, weak, and dominant energy conditions are satisfied in these models.