Constraining Generalized Chaplygin Gas in Non-Minimally Coupled $f(Q)$ Cosmology using Quasars and $H(z)$ Data

In the current framework of Einstein's equations in general relativity (GR), gravity is described by the spacetime curvature. However, there are other descriptions where the origin of gravity can be understood through torsion and non-metricity $Q$. In this work, we discuss a modified theory of gravity namely $f(Q)$ gravity, which considers a non-linear extension of $Q$. In particular, we study the case where it is non-minimally coupled to matter. Motivated by the recent success of Chaplygin gas models in the explanation of dark energy, we assume a pressureless baryonic matter and a generalized Chaplygin gas as the background fluid. We constrain the proposed model using two different datasets: one for Hubble measurements and the other for quasars (which we calibrated) with Markov-Chain Monte Carlo (MCMC) methods. We employ kinematic tools such as deceleration and jerk parameters to determine deviations of the proposed model from $\Lambda$CDM. We establish that the transition redshift $z_T$ in the deceleration parameter $q$ is $0.607$ and $0.204$ with the two datasets respectively, therefore describing the universe's acceleration.