Abstract
In this study, we investigate the dynamics of the Universe during the observed late-time acceleration phase within the framework of the Weyl-type [Formula: see text] theory. Specifically, we consider a well-motivated model with the functional form [Formula: see text], where [Formula: see text] represents the scalar of non-metricity and [Formula: see text] denotes the trace of the energy–momentum tensor. In this context, the non-metricity [Formula: see text] of the space-time is established by the vector field [Formula: see text]. The parameters [Formula: see text] and [Formula: see text] 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 [Formula: see text] follows a power-law behavior with respect to redshift [Formula: see text]. To constrain the model parameters, we analyze various datasets including the Hubble, Pantheon datasets, and their combination. Our results indicate that the Weyl-type [Formula: see text] theory offers a viable alternative to explain the observed late-time acceleration of the Universe avoiding the use of dark energy.