Investigating the compatibility of exact solutions in Weyl-type $f(Q,T)$ gravity with observational data

In this study, we investigate the dynamics of the Universe during the observed late-time acceleration phase within the framework of the Weyl-type $f(Q,T)$ theory. Specifically, we consider a well-motivated model with the functional form $f(Q,T)=\alpha Q+\frac{\beta }{6\kappa ^2}T$, where $Q$ represents the scalar of non-metricity and $T$ denotes the trace of the energy-momentum tensor. In this context, the non-metricity $Q_{\mu\alpha\beta}$ of the space-time is established by the vector field $w_\mu$. The parameters $\alpha$ and $\beta$ govern the gravitational field and its interaction with the matter content of the Universe. By considering the case of dust matter, we obtain exact solutions for the field equations and observe that the Hubble parameter $H(z)$ follows a power-law behavior with respect to redshift $z$. To constrain the model parameters, we analyze various datasets including the $Hubble$, $Pantheon$ datasets, and their combination. Our results indicate that the Weyl-type $f(Q,T)$ theory offers a viable alternative to explain the observed late-time acceleration of the Universe avoiding the use of dark energy.