LAUSR

Neutron star constraints and {\it ab initio} pQCD evaluations require the EoS representing cold quark matter to be stiff at intermediate baryonic densities and soft at high-$n_B$. Here, I suggest that the three flavor NJL model with a density dependent repulsive coupling, $G_V(\mu)$, can generate an EoS which interpolates between these two regimes. Such an interpolation requires repulsion to start decreasing with the chemical potential just after chiral transition takes place. The conjecture behind this mechanism is that repulsion should be necessary only as long as the quark condensates, which dress the effective masses, have non-vanishing values. This assumption guarantees that an initially hard EoS suffers a conspicuous change of slope at ${\cal E} \simeq 0.7 \,{\rm GeV fm^{-3}}$ converging to the pQCD results at higher energy densities. Then, the speed of sound naturally reaches a non-conformal maximum at $n_B = 3.23 \, n_0 = 0.52 \, {\rm fm}^{-3}$ while the trace anomaly remains positive for all densities, in agreement with recent investigations. These non-trivial results {\it cannot} be simultaneously obtained when $G_V$ vanishes or has a fixed value. Therefore, the simple model proposed here is able to link the (non-perturbative) region of intermediate densities to the region where pQCD becomes reliable.