Power-Law Cosmology in Non-Minimally Coupled f ( Q , L M ) $ f(Q, \mathcal {L}_{\mathrm{M}})$ Gravity: Misner–Sharp Thermodynamic Analysis

Abstract

We investigate the cosmological implications of a non-minimally coupled $f(Q,L_M)$ gravity model within the symmetric teleparallel framework, in which the non-metricity scalar $Q$ is coupled to the matter Lagrangian $L_M$, where both curvature and torsion vanish identically. This framework is a specific form of the gravitational action that includes a coupling term $f_2\left(Q\right)L_M$, thereby extending $f\left(Q\right)$-gravity. We consider a power-law parameterization of the coupling functions and evaluate the Hubble parameter $H\left(z\right)$. We use observational hubble data (OHD), the Union3 supernova compilation, dark energy spectroscopic instrument data release 2 (DESI DR2) baryon acoustic oscillation (BAO) data, and their joint datasets to constrain the model parameters with the Markov Chain Monte Carlo (MCMC) technique. The obtained model transitions from a decelerating state to an accelerating state and exhibits the quintessence model in late times. Furthermore, we discuss the various physical features of the model to show the model's physical viability. Additionally, we examine the Misner–Sharp mass as a bridge between geometry and thermodynamics, providing a quasi-local measure of energy in spherically symmetric space-times and linking spacetime dynamics to thermodynamic laws in modified gravity.