Cold quark matter: Renormalization group improvement of the perturbative series

We discuss recent improvements of the cold and dense QCD pressure owing to an all-order resummation of the soft modes, or to the so-called renormalization group optimized perturbation theory (RGOPT). Both approaches show a significant improvement of the residual renormalization scale dependence with respect to the state-of-the-art results for the perturbative pressure.