Abstract
In this paper, we investigate alternative models within the framework of [Formula: see text] gravity theory to understand the acceleration of the universe, a longstanding mystery in cosmology. [Formula: see text] gravity extends [Formula: see text] gravity by including a geometry–matter coupling term [Formula: see text], where [Formula: see text] represents the non-metricity scalar and [Formula: see text] is the trace of the energy–momentum tensor. We focus on two specific cases of the model: [Formula: see text] for [Formula: see text], and [Formula: see text] for [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] are free parameters. By using a combination of observational datasets, including the Hubble, SNe Ia, and BAO datasets, we determine the best-fit values for the model parameters. We analyze various cosmological parameters, including the deceleration parameter and the equation of state (EoS) parameter. The deceleration parameter reveals a transition from deceleration to acceleration phases in the universe’s evolution. The EoS parameter analysis suggests that our [Formula: see text] cosmological models exhibit characteristics similar to a quintessence model, describing dark energy. Lastly, we validate the results by analyzing the energy conditions for both models, contributing to the understanding of the acceleration of the universe and the viability of [Formula: see text] gravity as an alternative theory.