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 α(H/H0)df(Φ,Φ*), 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 α. We analyze the cosmological implications at the background level and compare 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 the ΛCDM. Our results indicate that the modified PNJL cosmology provides a statistically competitive fit to current data while allowing small departures from the ΛCDM 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.
Saucedo et al. (Tue,) studied this question.