The present study explores the dynamics of late-time cosmic acceleration through the lens of non-minimally coupled f(Q, L m ) modified gravity. In this framework, an explicit coupling is introduced between the non-metricity scalar Q and the matter Lagrangian density L m . We consider a specific non-linear functional form of the theory to derive the modified Friedmann equations governing cosmic evolution. To obtain an exact analytical solution for the Hubble parameter H(z), we employ a parameterization technique where the effective Equation of State (EoS) of the model is equated to a logarithmic parametrization form, given by 𝜔 eff (z) = 𝜔 0 + 𝜔 1 log(1 + z). We constrain the model free parameters by performing a Bayesian statistical analysis using Markov Chain Monte Carlo (MCMC) methods, utilizing a combination of observational datasets, specifically Cosmic Chronometers (CC) and Dark Energy Spectroscopic Instrument (DESI)-Baryon Acoustic Oscillations (BAO). Further, we reconstruct the evolution of kinematic quantities such as the energy density, pressure, and the deceleration parameter q(z), which exhibits a smooth transition from a decelerated epoch to the present accelerated phase. Additionally, we analyse the behaviour of the effective EoS to distinguish between quintessence-like and phantom-like regions. The geometrical diagnosis of the model is performed using the Om(z) diagnostic and higher-order cosmographic parameters, including the Jerk, Snap, and Lerk, as well as the State-finder hierarchy. Further, the violation of the Strong Energy Condition (SEC), validates the accelerating behaviour of the universe, while the model remains consistent with other stability criteria. Our findings suggest that our gravity model serves as a viable alternative to the ΛCDM model.
Bayaskar et al. (Wed,) studied this question.
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