Glueballs Confinement and Cosmological Phase Transitions

We develop a unified framework in which the dynamics of a scalar glueball field, originating from phenomenological nonperturbative QCD confinement, simultaneously governs the deconfinement transition of strongly interacting matter and drives cosmological inflation. Starting from a temperature-dependent effective potential $V_{eff}(\phi, T)$, we show that the glueball mass vanishes at a critical temperature $T_{c\phi}$, signaling a first-order phase transition characterized by supercooling and a transient metastable vacuum. In the high-temperature regime $T > T_{c\phi}$, the deconfined phase naturally produces an exponential expansion of the scale factor, providing the correct conditions for inflation. By computing the slow-roll parameters and the resulting spectral index $n_s$, tensor-to-scalar ratio $r_s$, and running $\alpha_s$, we confront the model with the Planck observations. The predicted values of $n_s$ and $r_s$ fall within the Planck confidence contours for a broad and physically motivated range of the parameter $\gamma$ and for $N \approx 50\text{--}60$ e-folds. A distinctive linear relation, $r_s = 4(1-n_s)-72\gamma$, emerges as a testable signature of the model. Normalization to the observed scalar amplitude further constrains the thermal correction parameter $\sigma^2$ and the coupling $\gamma$, linking cosmological data directly to QCD-scale dynamics. These results demonstrate that a confinement-inspired potential can naturally reproduce the observed inflationary phenomenology and offer a novel bridge between early-universe cosmology and the nonperturbative sector of QCD.