Unveiling late-time acceleration in f(Q,Lm) gravity: Insights from logarithmic parametrization of deceleration parameter, cosmography, and energy bounds

In this study, we explore the late-time cosmic acceleration using the [Formula: see text] gravity framework, where the non-metricity Q is coupled to the matter Lagrangian [Formula: see text]. We investigate a nonlinear model defined by [Formula: see text]. To reconstruct the cosmological evolution, we employ a kinematic ansatz with a logarithmic parametrization of the deceleration parameter, [Formula: see text]. We constrain the model parameters using the latest observational data from Cosmic Chronometers (CC) and Baryon Acoustic Oscillations (BAO) via the Dark Energy Spectroscopic Instrument (DESI). The Markov Chain Monte Carlo (MCMC) analysis yields a current Hubble parameter of [Formula: see text] and indicates a transition from deceleration to acceleration at [Formula: see text]. Solving the modified Friedmann equations allows us to determine the evolution of the Hubble parameter and effective thermodynamic quantities. Further, we analyze the energy density ([Formula: see text]), pressure (p), and Equation of State (EoS) parameter ([Formula: see text]). Additionally, we distinguish the proposed [Formula: see text] model from the standard [Formula: see text]CDM paradigm using geometrical diagnostics, including the Statefinder hierarchy [Formula: see text] and [Formula: see text], as well as cosmographic parameters like Jerk, lerk and Snap. Finally, we test the model’s validity against standard Energy Conditions. The results demonstrate that while the model violates the Strong Energy Condition (SEC) to support cosmic acceleration, it satisfies the Null Energy Condition (NEC) within the observational range, ensuring the stability of the cosmic fluid.