Constraining $f(Q,\mathcal{L}_{m})$ gravity with redshift-dependent pressure: Insights from observational probes

We explore the late time cosmological dynamics of the Universe within the framework of $f(Q,\mathcal{L}_{m})$ gravity by considering the specific form $f(Q, \mathcal{L}_m)=-Q+2\mathcal{L}_m+\gamma$. To describe the cosmic pressure evolution, a redshift dependent parametrization of $p(z)=\alpha+\frac{\beta z}{1+z}$ is introduced. MCMC analysis is performed using a combined datasets from Hubble ($46$ points), BAO ($15$ points including DESI DR2) and Pantheon$+$ ($1701$ SNe Ia), the model parameters are constrained as $H_{0}=67.9476^{+0.7534}_{-0.7523}$ (km/s/Mpc), $\alpha=-0.0002^{+0.0211}_{-0.0208}$, $\beta=-0.0001^{+0.0410}_{-0.0404}$ and $\gamma=0.0002^{+0.0599}_{-0.0602}$. The model predicts a transition from deceleration to acceleration at $z_{tr} \approx 0.493$ with present values $q_{0}=-0.255$ and $\omega_{0}=-0.9001$. The evolution of energy density and pressure aligns with observational expectations. An analysis of energy conditions shows that NEC and DEC are satisfied, while SEC is violated, consistent with late time acceleration. Moreover, the slow roll parameters $\epsilon_{1}$ and $\epsilon_{2}$ confirm a smooth inflationary regime. These results demonstrate the capability of the model to unify early Universe inflation with the current phase of cosmic acceleration.