Stiffening of matter in quark-hadron continuity: a mini-review

Recent observations of neutron stars, combined with causality, thermodynamic stability, and nuclear constraints, indicate a rapid stiffening of QCD matter at densities slightly above nuclear saturation density ($n_0 \simeq 0.16\,{\rm fm}^{-3}$). The evolution of the stiffening is faster than expected from purely nucleonic models with many-body repulsion. Taking into account the quark substructure of baryons, we argue that the saturation of quark states occurs at $\sim$ 2-3$n_0$, driving quark matter formation even before baryonic cores of radius $\sim$0.5 fm spatially overlap. We describe the continuous transitions from hadronic to quark matter within a quarkyonic matter model in which gluons are assumed to remain confining at densities of interest. To obtain analytic insight into the transient regime, we construct an ideal model of quarkyonic matter, the {\it IdylliQ} model, in which one can freely switch from baryonic to quark descriptions and vice versa.