Acceleration and stability of universe models in non-linear Weyl-type <i>f</i> ( <i>Q</i> , <i>T</i> ) gravity

In the present study, we investigate the cosmic acceleration and stability of the generalized Weyl-type [Formula: see text] gravity model in a flat Friedmann-Lemaître–Robertson–Walker (FLRW) spacetime manifold. We consider both linear [Formula: see text] and nonlinear [Formula: see text] functions with dimensionless constants [Formula: see text], [Formula: see text], and [Formula: see text] to investigate the model in both cases of the Lagrange multiplier [Formula: see text] as constant and dynamical. We solve the field equations for the Weyl vector field component [Formula: see text], the Hubble function [Formula: see text], and [Formula: see text] for the dust and dark fluid sources. We constrain the model parameters using the Monte Carlo Markov Chain (MCMC) technique in the joint analysis of the Cosmic Chronometer (CC) dataset of the Hubble function [Formula: see text] and the Pantheon+SH0ES sample of the SNe Ia dataset. We discuss the characteristics of the model with the cosmic evolution of the effective equation of state (EoS) parameter [Formula: see text], deceleration parameter [Formula: see text], Lagrange multiplier [Formula: see text], effective dynamical mass [Formula: see text] of the Weyl vector particle, and transition redshift [Formula: see text]. We also investigate the models’ stability and physical acceptability. We find a transit phase accelerating a stable universe model with [Formula: see text] km/s/Mpc, [Formula: see text], [Formula: see text], transition redshift [Formula: see text], and [Formula: see text] in which particle creation or annihilation may occur during the interaction of matter-geometry.