In this study, we investigate the late-time accelerated expansion of the universe within the framework of non-minimally coupled f (Q, Lₘ) gravity, where Q is the non-metricity scalar and Lₘ is the matter Lagrangian. We derive modified Friedmann equations in a flat FLRW background and employ the Gong-Zhang parameterization for the DE equation of state (EoS), allowing an analytical form of the Hubble parameter H (z). The model parameters are constrained using recent Cosmic Chronometers (CC) and Pantheon+SH0ES Type Ia supernova datasets through MCMC-based chi-squared minimization. We analyze various cosmological quantities including the deceleration parameter, EoS, jerk, snap, lerk, and diagnostic tools such as Om (z) and the statefinder pair (r, s). Our findings indicate a viable transition from deceleration to acceleration and reveal a quintessence-to-phantom-like evolution of dark energy. Furthermore, energy conditions are examined, showing a violation of the strong energy condition, consistent with current cosmic acceleration. The results establish that the f (Q, Lₘ) framework with non-minimal coupling and parameterized EoS provides a compelling alternative to ΛCDM in describing cosmic acceleration.
Ingole et al. (Thu,) studied this question.