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We demonstrate in a general and analytic way how high-density informationabout the equation of state (EoS) of strongly interacting matter obtained usingperturbative Quantum Chromodynamics (pQCD) constrains the same EoS at densitiesreachable in physical neutron stars. Our approach is based on utilizing thefull information of the thermodynamic potentials at the high-density limittogether with thermodynamic stability and causality. This requires consideringthe pressure as a function of chemical potential $p(\mu)$ instead of thecommonly used pressure as a function of energy density $p(\epsilon)$. Theresults can be used to propagate the pQCD calculations reliable around 40$n_s$to lower densities in the most conservative way possible. We constrain the EoSstarting from only few times the nuclear saturation density $n \gtrsim 2.2 n_s$and at $n = 5 n_s$ we exclude at least 65% of otherwise allowed area in the$(\epsilon - p)$-plane. This provides information complementary toastrophysical observations that should be taken into account in any completestatistical inference study of the EoS. These purely theoretical results areindependent of astrophysical neutron-star input, and hence, they can also beused to test theories of modified gravity and BSM physics in neutron stars.

How perturbative QCD constrains the Equation of State at Neutron-Star densities