Late-Time Cosmic Acceleration from QCD Confinement Dynamics

We explore a phenomenological extension of the Polyakov-Nambu-Jona-Lasinio (PNJL) model by introducing a curvature-sensitive effective contribution to the Polyakov loop potential, motivated by the hypothesis that the non-perturbative QCD vacuum in the confined phase may retain a residual sensitivity to cosmic expansion. In a spatially flat FLRW background, this modification reduces to a term proportional to $\alpha(H/H_0)^d f(\Phi, \Phi^*)$, which naturally vanishes in the deconfined regime and behaves as an effective dynamical vacuum component at late times, without invoking a fundamental cosmological constant. The construction provides an effective thermodynamic description of the QCD sector within an adiabatic framework and introduces a minimal phenomenological extension characterized by the exponent $d$ and the amplitude parameter $\alpha$. We analyze the cosmological implications at the background level and confront the model with low-redshift observations, including cosmic chronometers, Type Ia supernovae, HII galaxies, and quasars. Using Bayesian Monte Carlo techniques, we constrain the model parameters and compare its performance with $\Lambda$CDM. Our results indicate that the modified PNJL cosmology provides a statistically competitive fit to current data while allowing small departures from $\Lambda$CDM within observational uncertainties. We also investigate the impact of the coupling on the QCD phase diagram and the critical end point. The framework offers a tractable effective approach to connect confinement physics with late-time cosmology and suggests directions for further theoretical development in QCD under curved backgrounds.